JP2024025989A - Dc magnetic field measuring method and dc magnetic field measuring device, and ac magnetic field measuring method and ac magnetic field measuring device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a magnetic field measuring method and device capable of quickly measuring a magnetic field value of a DC or AC magnetic field with a simple operation.

SOLUTION: A DC magnetic field measuring method, the method for measuring a DC magnetic field comprises the steps of: (a) exciting a cantilever including a superparamagnetic probe; (b) applying an AC magnetic field to the probe; (c) executing frequency demodulation of a detection signal of probe vibration; (d) measuring a frequency component of the AC magnetic field of the demodulated signal of the step (c); (e) scanning each of in-plane coordinates within a scanning area with the probe; (f) executing two-dimensional Fourier transform of information corresponding to the measurement result in the step (d) in the scanning area, in the in-plane direction; (g0) extracting from information of the Fourier transform obtained in the step (f), information of the DC magnetic field corresponding to the two-dimensional Fourier transform of the AC magnetic field direction component based on the information of the AC magnetic field and the wave number in the in-plane direction; and (i0) executing the two-dimensional Fourier transform based on the information extracted in the step (g0).

SELECTED DRAWING: Figure 4

COPYRIGHT: (C)2024,JPO&INPIT

Description

Application for application of Article 30, Paragraph 2 of the Patent Act (1) Magnetic Society of Japan, 45th Academic Conference Abstracts of the Magnetic Society of Japan (2021), page 140, published on the web on August 17, 2021, URL: https://www. magnetics. jp/kouenkai/2021/doc/program/26ALL. pdf (2) Magnetic Society of Japan, 45th Academic Conference Abstracts of the Magnetic Society of Japan (2021), page 143, published online on August 17, 2021, URL: https://www. magnetics. jp/kouenkai/2021/doc/program/26ALL. pdf (3) 45th Academic Conference of the Magnetic Society of Japan (held online), September 2, 2021, 02aA-1 "DC magnetic field imaging of permanent magnets using an alternating magnetic force microscope" (4) 45th Japan Magnetics Society Academic Conference (held online), September 2, 2021, 02aA-4 "Theory of DC magnetic field imaging using alternating magnetic force microscope"

The present invention relates to a magnetic force microscope, and more particularly to a DC magnetic field measuring method and a DC magnetic field measuring device, and an alternating current magnetic field measuring method and an alternating current magnetic field measuring device.

A magnetic force microscope (MFM) is known as a device that measures magnetization patterns and the like corresponding to magnetic information of a magnetic sample. A magnetic force microscope is equipped with a magnetic probe, and when the tip of the magnetic probe is brought close to the magnetic sample being observed, the magnetic interaction between the magnetic moment of the magnetic probe and the magnetic moment of the magnetic sample is detected. By detecting the effect, magnetization patterns and the like are measured.

As a magnetic probe for a magnetic force microscope, cobalt (Co)-chromium (Cr)-based alloy, nickel (Ni)-iron (Fe)-based alloy, cobalt (Co) is used on a probe material made of non-magnetic material Si. -Thin films of ferromagnetic materials such as platinum (Pt)-based alloys, iron (Fe)-platinum (Pt)-based ordered alloys, and iron (Fe)-based alloys are generally formed (Patent Documents 1- 3).

The present inventors developed an alternating magnetic force microscope (Patent Documents 4 and 5) in order to observe the magnetic field generated from a magnetic sample with high spatial resolution. These alternating magnetic force microscopes change the direction of magnetization of a ferromagnetic probe attached to the tip of an excited cantilever using an external alternating magnetic field, and the magnetization between the tip magnetization and the magnetic field of the magnetic sample is changed. The DC or AC magnetic field gradient near the sample surface is observed by detecting the frequency modulation that occurs in the tip vibration due to the alternating magnetic force caused by the interaction between the two.

Furthermore, the present inventors have discovered that it is possible to observe magnetic field gradients with high spatial resolution using a magnetic force microscope, even for magnetic samples that generate a strong DC magnetic field (e.g., 10 kOe or more), such as those typified by permanent magnets. In order to do so, we developed a magnetic force microscope probe using a new magnetic material and filed a patent application (Patent Document 7). Patent Document 7 discloses that the magnetic material is provided with at least one kind of magnetic material, and when a strong external magnetic field, specifically an external magnetic field of 20 kOe, is applied at room temperature, specifically over a temperature range of at least 10 to 30°C. magnetization is not saturated; (a) the magnetic material is a solid solution of one or more ferromagnetic elements and one or more non-magnetic elements; (b) the magnetic material is a solid solution of one or more ferromagnetic elements and one or more non-magnetic elements; or (c) the magnetic material contains one or more ferromagnetic particles and one or more non-magnetic materials, and the ferromagnetic particles A probe for a magnetic force microscope is disclosed, which is characterized in that it is made of a magnetic material having a structure in which it is dispersed and supported in a non-magnetic material. Such a magnetic material exhibits superparamagnetism when the crystal grain size of the ferromagnetic particles becomes less than the critical grain size for ferromagnetism (approximately 10 nm or less). A magnetic force microscope probe that includes a material exhibiting superparamagnetism (superparamagnetic material) as a magnetic material is called a "superparamagnetic probe."

Japanese Patent Application Publication No. 2008-209276 Japanese Patent Application Publication No. 2004-20213 Japanese Patent Application Publication No. 7-325139 Patent No. 4769918 International Publication No. 2013/047537 International Publication No. 2014/157661 International Publication No. 2016/024636

H. Saito, et al., Journal of Magnetism and Magnetic Materials, 191 (1999) 153-161.

The reason why magnetic force microscopes have high spatial resolution is because their principle is to detect magnetic field gradients. On the other hand, magnetic field gradients are not easy to analyze and interpret compared to the magnetic field itself. In this regard, the present inventors have developed a magnetic field measuring method and a magnetic field value measuring device that can measure the absolute value, including the positive and negative, of a DC magnetic field generated from a magnetic sample, and have filed a patent application (Patent Document 6). The method and apparatus for measuring a DC magnetic field described in Patent Document 6 excite a magnetic probe, which has a property that magnetization is zero when the external magnetic field is zero, in a state where a DC magnetic field generated from an observation sample is applied. By applying an AC external magnetic field having a non-zero (large) rate of change in the direction of vibration of the probe and a frequency different from the mechanical vibration frequency of the probe, the excitation vibration of the probe is frequency-modulated. Then, by canceling the DC magnetic field from the observation sample that is applied to the tip of the probe by adding a DC external magnetic field, the frequency modulation of the probe vibration is weakened, and when the frequency modulation becomes a minimum near zero, the DC magnetic field Measure external magnetic field. The DC magnetic field having the opposite polarity to the DC external magnetic field at this time is the DC magnetic field generated from the observation sample.

The DC magnetic field measurement method and apparatus described in Patent Document 6 was revolutionary in that it was possible to directly obtain the magnetic field itself as a measurement result, rather than the magnetic field gradient. However, when attempting to obtain a magnetic field image within a certain scanning region using the DC magnetic field method and apparatus described in Patent Document 6, each in-plane coordinate set within the scanning region is It is necessary to scan the values of the external DC magnetic field until finding an external DC magnetic field that cancels the DC magnetic field of . This problem worsens in proportion to the number of in-plane coordinates included in the scan area. Therefore, there is still room for improvement in that it takes time to obtain a magnetic field image of the entire scanning region. Furthermore, it has been difficult to apply the method and apparatus described in Patent Document 6 to measurement of alternating current magnetic fields.

Note that Patent Document 7 also discloses a magnetic field observation method and a magnetic field observation apparatus using a superparamagnetic probe. According to the magnetic field observation method and magnetic field observation device described in Patent Document 7, it is possible to observe the magnetic field with improved spatial resolution near the surface of a magnetic sample such as a permanent magnet that generates a strong DC magnetic field. . In addition, since tip magnetization caused by applying an alternating magnetic field to a superparamagnetic probe occurs only in the direction of application of the alternating magnetic field, the influence of the magnetic field component perpendicular to the applied alternating magnetic field is eliminated, and the applied alternating magnetic field It becomes easy to observe only parallel magnetic field components. However, the magnetic field observation method and magnetic field observation apparatus described in Patent Document 7 are techniques for observing magnetic field gradients, like the conventional magnetic field observation method and magnetic field observation apparatus. Therefore, it has the same problem as conventional magnetic field observation methods and magnetic field observation devices, in that it is not easy to analyze and interpret measurement results.

An object of the present invention is to provide a magnetic field measuring method that can quickly measure the magnetic field value of a DC magnetic field or an AC magnetic field with a simple operation. Furthermore, a magnetic field measuring device that can be preferably used in the magnetic field measuring method is provided.

The present invention includes the embodiments [1] to [4] below.
[1] A method for measuring a direct current magnetic field, comprising:
(a) exciting a cantilever having a superparamagnetic probe at one end that generates a magnetic moment in the direction of the applied magnetic field;
(b) While performing step (a), an alternating current magnetic field is applied to the probe from an alternating current magnetic field generator to periodically vary the magnetization of the probe, thereby modulating the frequency of the excitation vibration of the cantilever. process and
(c) while performing the step (b), detecting the vibration of the probe and demodulating the frequency of the detection signal of the vibration of the probe;
(d) measuring the frequency component of the alternating magnetic field of the signal demodulated in step (c);
(e) The probe is caused to scan a scanning area set in a plane intersecting the vibration direction of the probe, and the steps (a) to ( d);
(f) performing a two-dimensional Fourier transform on the information corresponding to the measurement result of the step (d) in the scanning region in the in-plane direction of the scanning region;
(g0) From the Fourier transform information obtained in step (f), extract information corresponding to the two-dimensional Fourier transform of the component of the DC magnetic field parallel to the AC magnetic field in the in-plane direction of the scanning area. The process of
(i0) Based on the information corresponding to the two-dimensional Fourier transform of the component of the direct current magnetic field parallel to the alternating current magnetic field in the in-plane direction of the scanning region, each of the components within the scanning region is For in-plane coordinates, obtaining a value corresponding to a component parallel to the alternating current magnetic field of the direct current magnetic field;
including;
The extraction in the step (g0) includes the amplitude of the alternating magnetic field at the position of the probe, the first-order differential of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe, and the a second derivative of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe, or a combination of two ratios therebetween and two wave numbers in the in-plane direction within the scanning region; carried out based on
A method for measuring a DC magnetic field, characterized in that the amplitude of the AC magnetic field at the position of the probe and the value of the second derivative of the amplitude with respect to the vibration direction of the probe are non-zero.

[2] A device for measuring a direct current magnetic field,
a cantilever having a superparamagnetic probe at one end that generates a magnetic moment in the direction of an applied magnetic field;
an exciter that excites the cantilever;
an alternating current magnetic field generator that frequency-modulates the excitation vibration of the cantilever by applying an alternating magnetic field to the probe and periodically varying the magnetization of the probe;
a vibration sensor that detects vibrations of the probe;
a scanning mechanism that causes the probe to scan a scanning area set within a plane intersecting the vibration direction of the probe;
a demodulator that frequency demodulates the detection signal of the vibration sensor;
a detector that measures a frequency component of the alternating magnetic field included in the demodulated signal from the demodulator;
a storage device that stores a measurement value corresponding to a measurement signal of the detector for each in-plane coordinate in the scanning area;
a Fourier transformer that performs a two-dimensional Fourier transform on the measured values for each in-plane coordinate of the scanning area stored in the storage device with respect to the in-plane coordinate;
From the Fourier transform information output from the Fourier transformer, it is possible to extract information corresponding to a two-dimensional Fourier transform of a component of the DC magnetic field parallel to the AC magnetic field in an in-plane direction of the scanning area. a first wave number filter computing unit configured to;
Each in-plane coordinate within the scanning area is determined by two-dimensional inverse Fourier transformation based on information corresponding to the two-dimensional Fourier transformation of the component of the DC magnetic field parallel to the alternating current magnetic field in the in-plane direction of the scanning area. an inverse Fourier transformer configured to be able to obtain a value corresponding to a component of the DC magnetic field parallel to the AC magnetic field;
including;
The extraction in the first wave number filter calculator includes the amplitude of the alternating magnetic field at the position of the probe, the first-order differential of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe; and the second derivative of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe, or two ratios therebetween, and two wave numbers in the in-plane direction within the scanning region. It is done based on a combination of
A DC magnetic field measuring device, wherein the amplitude of the AC magnetic field at the position of the probe and the value of the second derivative of the amplitude with respect to the vibration direction of the probe are non-zero.

[3] A method of measuring an alternating magnetic field, comprising:
(a) exciting a cantilever having a superparamagnetic probe at one end that generates a magnetic moment in the direction of the applied magnetic field;
(b) while performing the step (a), frequency-modulating the excitation vibration of the cantilever by applying a DC magnetic field to the probe from a DC magnetic field generator;
(c) while performing the step (b), detecting the vibration of the probe and demodulating the frequency of the detection signal of the vibration of the probe;
(d) measuring a frequency component of the signal demodulated in step (c) that corresponds to the frequency component to be measured of the alternating magnetic field;
(e) The probe is caused to scan a scanning area set within a plane intersecting the vibration direction of the probe, and the steps (a) to ( d);
(f) performing a two-dimensional Fourier transform on the information corresponding to the measurement result of the step (d) in the scanning region in the in-plane direction of the scanning region;
(g0) From the Fourier transform information obtained in step (f), two-dimensional Fourier transform of the amplitude of the frequency component of the alternating current magnetic field that is parallel to the direct current magnetic field is performed in the in-plane direction of the scanning area. a step of extracting information corresponding to the
(i0) By two-dimensional inverse Fourier transform based on information corresponding to two-dimensional Fourier transform of the amplitude of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field in the in-plane direction of the scanning area, For each in-plane coordinate within the scanning area, obtaining a value corresponding to the amplitude of a component of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field;
including;
The extraction in the step (g0) includes the DC magnetic field at the position of the probe, the first derivative of the DC magnetic field at the position of the probe with respect to the vibration direction of the probe, and the position of the probe. is performed based on the second derivative of the DC magnetic field with respect to the vibration direction of the probe, or two ratios therebetween, and a combination of two wave numbers in the in-plane direction within the scanning region,
AC magnetic field measurement, characterized in that the value of the DC magnetic field at the position of the probe and the second derivative of the DC magnetic field at the position of the probe with respect to the vibration direction of the probe are non-zero. Method.

[4] A device for measuring an alternating current magnetic field,
a cantilever having a superparamagnetic probe at one end that generates a magnetic moment in the direction of an applied magnetic field;
an exciter that excites the cantilever;
a DC magnetic field generator that frequency-modulates the excitation vibration of the cantilever by applying a DC magnetic field to the probe;
a vibration sensor that detects vibrations of the probe;
a scanning mechanism that causes the probe to scan a scanning area set within a plane intersecting the vibration direction of the probe;
a demodulator that frequency demodulates the detection signal of the vibration sensor;
a detector that measures a frequency component included in the demodulated signal from the demodulator that corresponds to a frequency component to be measured of the alternating current magnetic field;
a storage device that stores a measurement value corresponding to a measurement signal of the detector for each in-plane coordinate in the scanning area;
a Fourier transformer that performs a two-dimensional Fourier transform on the measured values for each in-plane coordinate of the scanning area stored in the storage device with respect to the in-plane coordinate;
Information corresponding to a two-dimensional Fourier transform of the amplitude of a component parallel to the DC magnetic field of the frequency component of the AC magnetic field in the in-plane direction of the scanning area, from the Fourier transform information output from the Fourier transformer. a first wave number filter calculator configured to be able to extract the
The scanning area is determined by two-dimensional inverse Fourier transformation based on information corresponding to two-dimensional Fourier transformation of the amplitude of the frequency component of the frequency component of the alternating current magnetic field parallel to the DC magnetic field in the in-plane direction of the scanning area. an inverse Fourier transformer configured to be able to obtain, for each in-plane coordinate within, a value corresponding to the amplitude of a component of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field;
including;
The extraction in the first wave number filter calculator includes the DC magnetic field at the position of the probe, the first derivative of the DC magnetic field at the position of the probe with respect to the vibration direction of the probe, and the probe. Based on the second derivative of the DC magnetic field at the needle position with respect to the vibration direction of the probe, or the two ratios therebetween, and the combination of two wave numbers in the in-plane direction within the scanning area. I,
AC magnetic field measurement, characterized in that the value of the DC magnetic field at the position of the probe and the second derivative of the DC magnetic field at the position of the probe with respect to the vibration direction of the probe are non-zero. Device.

In the DC magnetic field measurement method and the AC magnetic field measurement method of the present invention, the measurement results in step (d) corresponding to the magnetic force gradient are once subjected to two-dimensional Fourier transformation in the in-plane direction of the scanning region (step (f)). , in Fourier space, performs an extraction process based on the wave number and information on the alternating magnetic field applied to the probe (step (g0), and optionally, step (g2) and/or step (g1)). Through this extraction process, information corresponding to the Fourier transform of the magnetic field (and optionally information corresponding to the Fourier transform of the second derivative of the magnetic field and/or information corresponding to the first derivative of the magnetic field) is extracted from the information corresponding to the magnetic force gradient. (that is, information corresponding to the Fourier transform of the magnetic field gradient) can be directly extracted. Based on the information corresponding to the Fourier transform of the magnetic field, a magnetic field image in real space can be obtained by inverse Fourier transform (step (i0)). Such a magnetic field image could not be obtained by magnetic field gradient imaging using a conventional magnetic force microscope. Furthermore, when measuring a DC magnetic field, it is not necessary to change the strength of the AC magnetic field applied to the probe from the AC magnetic field generator each time measurement is made at each in-plane coordinate within the scanning area. In this case, it is not necessary to change the strength of the DC magnetic field applied to the probe from the DC magnetic field generator every time measurements are taken at each in-plane coordinate within the scanning region. Therefore, the measurement at each in-plane coordinate within the scanning area can be completed in a short time, so that the magnetic field itself of the DC magnetic field or the AC magnetic field can be quickly measured with simple operations.

The DC magnetic field measurement device or the AC magnetic field measurement device of the present invention can be preferably used for measuring a DC magnetic field or an AC magnetic field by the DC magnetic field measurement method or the AC magnetic field measurement method of the present invention, respectively.

FIG. 1 is a diagram schematically explaining the configuration of a superparamagnetic probe according to one embodiment. 2 is a view taken along the line AA in FIG. 1. FIG. FIG. 2 is a diagram schematically illustrating the configuration of a sputtering apparatus used for forming a magnetic coating. FIG. 1 is a diagram schematically explaining the configuration of a DC magnetic field measuring device 1000 according to an embodiment of the present invention. 6 is a diagram illustrating the configuration of a signal processing device 600 and the flow of data processing in the signal processing device 600 according to one embodiment. FIG. FIG. 2 is a diagram schematically illustrating the configuration of a DC magnetic field measuring device 2000 according to another embodiment of the present invention. FIG. 3 is a diagram schematically illustrating the configuration of an alternating current magnetic field measuring device 3000 according to an embodiment of the present invention. 3 is a diagram illustrating the configuration of a signal processing device 3600 and the flow of data processing in the signal processing device 3600 according to one embodiment. FIG. FIG. 4 is a diagram schematically illustrating the configuration of an alternating current magnetic field measuring device 4000 according to another embodiment of the present invention. FIG. 2 is a plan view (photograph) of an air-core coil used in Examples. (A) It is a _Hz ^{dc (sample)} (x, y, z) image when no external DC magnetic field is applied. (B) It is a figure showing the isopleth line of _Hzdc ^(sample) =0Oe. (C) H _z ^{dc (sample)} (x, y, z) image when an external DC magnetic field of H dc ^(ex) = -600 Oe is applied. (D) It is a figure showing the isopleth line of _Hz ^{dc (sample)} =600Oe. (E) H _z ^{dc (sample)} (x, y, z) image when an external DC magnetic field of H dc ^(ex) = -1 kOe is applied. (F) It is a figure showing the isopleth line of _Hz ^{dc (sample)} =1 kOe. (G) H _z ^dc(sample) (x, y, z) image after calibration. (A) is a ∂ ² _Hz ^dc(sample) /∂z ² (x, y, z) image obtained in step (i2-2). (B) _Hz ^dc(sample) (x, y, z) image obtained in step (i2-0).

Embodiments of the present invention will be described below with reference to the drawings. However, the present invention is not limited to these forms. Note that the drawings do not necessarily reflect exact dimensions. Also, some symbols may be omitted in the figures. In this specification, unless otherwise specified, the notation "A to B" for numerical values A and B means "above A and below B". In such a notation, if a unit is attached only to the numerical value B, the unit shall also be applied to the numerical value A. Furthermore, the words "or" and "or" shall mean a logical sum unless otherwise specified. Regarding elements E ₁ and E ₂ , the notation "E ₁ and/or E ₂ " means "E ₁ or E ₂ , or a combination thereof", and the elements E ₁ , ..., E _N (N is 3 (integers above), the notation "E ₁ , ..., E _N-1 , and/or E _N " means "E ₁ , ..., E _N-1 , or E _N , or a combination thereof". do.

<1. Superparamagnetic probe>
Before explaining the DC magnetic field measurement method and DC magnetic field measurement device, as well as the AC magnetic field measurement method and AC magnetic field measurement device of the present invention, we will explain the magnetic force microscope probe (superparamagnetic probe) used in these methods and devices. explain. FIG. 1 is a diagram schematically illustrating a magnetic force microscope probe 10 (hereinafter sometimes referred to as "probe 10") according to one embodiment, and FIG. It is a view from arrow A. As shown in FIGS. 1 and 2, the magnetic force microscope probe 10 includes a triangular pyramid-shaped core member 1 made of a non-magnetic material, and a coating made of a magnetic material that covers at least a part of the surface of the core member 1. 3 (hereinafter sometimes referred to as "magnetic coating 3"). The magnetic force microscope probe 10 is erected at one end of the cantilever 2 by fixing the bottom surface of a triangular pyramid-shaped core member to one end of the cantilever 2 . As shown in FIG. 1, the magnetic material coating 3 may cover not only the surface of the core member 1 but also the surface of the cantilever 2.

The probe 10 includes at least one kind of magnetic material by coating the surface of the core member 1 with a magnetic coating 3. The probe 10 is characterized in that its magnetization does not saturate when an external magnetic field with a strength of 20 kOe is applied at room temperature, more specifically over a temperature range of at least 10 to 30°C. Therefore, by using the probe 10 in a magnetic force microscope, saturation of the probe magnetization does not occur even when a strong magnetic field is applied, so even for observation samples that generate strong magnetic fields, the magnetic field can be applied with high sensitivity and spatial resolution. Observation becomes possible.

Preferably, the probe 10, whether after demagnetization or magnetization, has no magnetization under conditions in which no magnetic field is applied at room temperature, more specifically over a temperature range of at least 10 to 30°C. According to the probe 10 which has no residual magnetization (and therefore has no hysteresis) under conditions where no magnetic field is applied, highly accurate measurement is possible in magnetic field observation using a magnetic force microscope.

(Core member 1)
The core member 1 is made of a non-magnetic material, is a member that defines the general shape of the probe 10, and plays the role of holding the magnetic coating 3 on its surface. One end of the core member 1 is erected on one end of the cantilever 2, and the other end of the core member 1 is shaped to become sharper toward the tip. As the non-magnetic material constituting the core member 1, any non-magnetic material having the strength necessary to maintain the shape of the probe 10 can be used without any particular restriction, such as Si, Si-N, Si-O, etc. can be preferably used.
In the probe 10 shown in FIGS. 1 and 2, the core member 1 has a triangular pyramid shape, but the shape of the core member 1 is not limited to the triangular pyramid shape. The shape can be appropriately selected as long as the spatial resolution and strength required for magnetic field observation using a magnetic force microscope can be ensured. However, from the viewpoint of increasing the spatial resolution of magnetic field observation, it is preferable that the shape has a pointed tip, and the end on the side fixed to the cantilever 2 should be shaped to a certain extent in order to facilitate fixation with the cantilever 2. It is preferable to have a size of . Considering these circumstances, a pyramid shape such as a triangular pyramid shape, a quadrangular pyramid shape, or a conical shape can be preferably employed.

(Magnetic coating 3)
The magnetic material constituting the magnetic film 3 can be one or more magnetic materials selected from the group consisting of paramagnetic materials and superparamagnetic alloys. Since the magnetic moment of magnetic materials other than these ferromagnetic materials is smaller than that of ferromagnetic materials, by forming the magnetic film 3 with these magnetic materials, it is possible to use a magnetic force microscope to detect the magnetic field of a sample that generates a strong magnetic field such as a permanent magnet. Even when observing, the probe 10 is moved by the magnetic force acting on the probe 10 due to the magnetic interaction between the magnetic moment induced in the probe 10 by the magnetic field from the magnetic sample and the magnetic moment of the magnetic sample. It is possible to prevent a situation where the magnetic material is magnetically attracted to the magnetic sample. The thickness of the magnetic coating 3 is determined by the measurement sensitivity of the magnetic force microscope (the thicker the magnetic coating 3, the better the sensitivity) and the spatial resolution (the thicker the magnetic coating 3, the blunter the tip of the probe 10 becomes, and the spatial resolution decreases. The decision can be made as appropriate, taking into account the trade-off between Note that the initial magnetic susceptibility of the magnetic material constituting the magnetic coating 3 is preferably at least 3×10 ⁻⁸ H/m at room temperature, more specifically over a temperature range of at least 10 to 30° C.

Paramagnetic materials exhibit the highest magnetic susceptibility near the Curie temperature (Hopkinson effect). Therefore, as a paramagnetic material that can be preferably used as the magnetic material constituting the magnetic coating 3, it is possible to increase the magnetic susceptibility and increase the measurement sensitivity of the magnetic force microscope by adjusting the Curie temperature of the paramagnetic material. In this respect, a magnetic material containing one or more ferromagnetic elements and one or more non-magnetic elements can be preferably used. Specifically, (a) one or more ferromagnetic elements and one or more non-magnetic elements forming a solid solution (hereinafter sometimes referred to as "solid solution paramagnetic material"), and ( b) A material in which one or more ferromagnetic elements and one or more non-magnetic elements form an amorphous structure (hereinafter sometimes referred to as "amorphous paramagnetic material") can be preferably employed. In these multicomponent paramagnetic materials, the ferromagnetic element is one or more ferromagnetic elements selected from the group consisting of Ni, Fe, and Co, and the nonmagnetic elements are Ti, V, Cr, Preferably, it is one or more nonmagnetic elements selected from the group consisting of Mn, Cu, Zn, Zr, Nb, Mo, Ta, W, B, Al, C, O, N, and Si. Note that from the viewpoint of lowering the Curie temperature with a small amount of nonmagnetic element, it is more preferable to include one or more elements selected from Cr, Mn, and Mo as the nonmagnetic element.

The above solid solution paramagnetic material (a) has a composition in which the total content of ferromagnetic elements is 50 to 70 at% and the total content of nonmagnetic elements is 30 to 50 at% based on the total amount of the solid solution paramagnetic material. It is preferable to have.

The above (b) amorphous paramagnetic material has a total content of ferromagnetic elements of 70 to 90 at% and a total content of nonmagnetic elements of 10 to 30 at% based on the total amount of the amorphous paramagnetic material. %.

Specific examples of the solid solution type paramagnetic material (a) include Ni-Cr solid solution (for example, Ni ₉₃ Cr ₇ (initial magnetic susceptibility 4.7×10 ^-8 H/m at 25°C)), Fe-Cr solid solution ( For example, Fe ₅₉ Cr ₄₁ (initial magnetic susceptibility 6.0×10 ^-8 H/m at 25°C), Fe-Mn solid solution (eg Fe ₆₇ Mn ₃₃ (initial magnetic susceptibility 1.2×10 ^-7 H at 25°C) /m)) etc. can be preferably mentioned.

A specific example of the amorphous paramagnetic material (b) is an Fe-Mo-B amorphous material (for example, Fe ₈₆ Mo _7.5 B _6.5 (initial magnetic susceptibility 1.4×10 at 25°C) ^-7 H/m)) and the like can be preferably mentioned.

In producing the magnetic film 3 using these multi-component paramagnetic materials, for example, a method of depositing each component on the surface of the core member 1 by simultaneous sputtering can be preferably employed. At this time, the composition of the magnetic coating 3 deposited on the surface of the core member 1 can be adjusted by the amount of electric power applied to the sputtering target of each component and the amount of the thin film material sheet attached to the sputtering target.

In this specification, when a certain material "exhibits superparamagnetism", it refers to a ferromagnetic material that has spontaneous magnetization contained in the material (in the present invention, "ferromagnetic material" is a concept that includes ferrimagnetic material). A state in which the magnetic interaction between adjacent particles is weak and the particle size is small, so the direction of magnetization of each particle changes randomly due to the influence of thermal energy, and no magnetic field is applied. This means that the magnetization of the entire material is zero on average. Magnetic materials that can be used for the magnetic coating 3 and exhibit superparamagnetism include (c) containing one or more types of ferromagnetic particles and one or more types of non-magnetic material, where the ferromagnetic particles are non-magnetic; A preferred example is a magnetic material having a structure that is dispersed and supported within the material (hereinafter sometimes referred to as "granular superparamagnetic material"). In granular superparamagnetic materials, fine ferromagnetic particles are dispersed in a non-magnetic matrix and exist in a magnetically isolated state, and the magnetic energy of the ferromagnetic particles is below a certain threshold relative to thermal energy. As a result, the magnetic moment of the ferromagnetic particles randomly changes its direction due to the influence of heat, and thus superparamagnetism is developed.

When using a granular superparamagnetic material for the magnetic coating 3, the content of ferromagnetic particles is 10 to 45% by volume, and the content of nonmagnetic material is 55 to 90% by volume, based on the total amount of magnetic material. is preferred. By setting the content of the ferromagnetic particles within the above range, contact between the ferromagnetic particles can be suppressed, and therefore it becomes easy to realize a magnetically isolated state of the ferromagnetic particles. From the same viewpoint, it is more preferable that the content of the ferromagnetic particles is 15 to 40% by volume, and the content of the nonmagnetic material is 60 to 85% by volume.

From the viewpoint of reducing the magnetic energy of the ferromagnetic particles and making it easier to randomize the magnetic moment due to thermal energy, the particle size of the ferromagnetic material particles in the granular superparamagnetic material is determined based on the equivalent sphere diameter by image analysis method. The average value is preferably 30 nm or less, more preferably 5 to 10 nm. The particle size of ferromagnetic material has a material-specific critical particle size, and when the particle size of ferromagnetic material exceeds this critical particle size, the ferromagnetic material particles change from a superparamagnetic state to a ferromagnetic state and exhibit magnetic hysteresis. Therefore, it is preferable that the size of the ferromagnetic material particles be equal to or less than the critical grain size of the material. For example, when cobalt (Co) having a face-centered cubic structure (FCC) is used as the ferromagnetic material, the particle size of the cobalt particles is preferably 10 nm or less, more preferably 8 nm or less. Here, the equivalent spherical diameter of ferromagnetic particles determined by image analysis is defined as the diameter when the surface of a magnetic material is observed at a magnification of 100,000 to 200,000 times by secondary electron detection using a scanning electron microscope (SEM). , shall mean the diameter of a circle having an area equal to the area occupied by the ferromagnetic particles in the SEM image. The average value shall mean a value obtained by taking the arithmetic mean of the spherical equivalent diameters of 100 or more ferromagnetic particles of the same magnetic material sample.

(c) Examples of constituent materials of the granular superparamagnetic material include a combination of a non-solid solution metal consisting of a ferromagnetic metal and a nonmagnetic metal, and a combination of a ferromagnetic metal and a nonmagnetic nonmetallic material.

In the granular superparamagnetic material, as the ferromagnetic particles, particles of one or more ferromagnetic elements selected from the group consisting of Ni, Fe, and Co can be preferably employed, and as the nonmagnetic materials, Au, Ag, From Cu, silicon dioxide, titanium oxide, tungsten oxide, chromium oxide, cobalt oxide, tantalum oxide, boron oxide, magnesium oxide, cerium oxide, yttrium oxide, nickel oxide, aluminum oxide, ruthenium oxide, oxides of rare earth elements, and carbon One or more nonmagnetic materials selected from the group consisting of: As the rare earth element oxide, for example, gadolinium oxide, terbium oxide, etc. can be preferably employed.

As a granular superparamagnetic material made of a combination of non-solid solution metals, for example, particles of Co, which is a ferromagnetic metal, are dispersed in a matrix of one or more nonmagnetic metals selected from the group consisting of Cu, Ag, and Au. The following materials can be mentioned.

Examples of superparamagnetic materials made by combining ferromagnetic metals and nonmagnetic nonmetallic materials include silicon dioxide, titanium oxide, tungsten oxide, chromium oxide, cobalt oxide, tantalum oxide, boron oxide, magnesium oxide, cerium oxide, and yttrium oxide. , nickel oxide, aluminum oxide, ruthenium oxide, rare earth element oxide, and carbon, in a matrix of one or more nonmagnetic nonmetallic materials selected from the group consisting of Fe, Co, and Ni. Mention may be made of materials in which particles of one or more ferromagnetic metals are dispersed. As the rare earth element oxide, for example, gadolinium oxide, terbium oxide, etc. can be preferably employed.

As will be described later, a film of a granular superparamagnetic material is formed by, for example, depositing a non-magnetic material and a ferromagnetic material at a deposition rate higher than usual (for example, 0.2 to 1.0 nm/sec in the case of Ag-Co). ) can be produced by co-sputtering. Since the material is rapidly cooled by increasing the deposition rate, the size of the dispersed ferromagnetic material particles can be reduced.

Granular superparamagnetic materials can achieve high magnetic susceptibility that cannot be obtained with paramagnetic materials. For example, the initial magnetic susceptibility of the granular superparamagnetic material at room temperature is preferably 2×10 ⁻⁷ H/m or more, and can also be 1×10 ⁻⁶ H/m or more. Therefore, according to the probe 10 in which the magnetic coating 3 is made of a granular superparamagnetic material, it is possible to increase the measurement sensitivity of the magnetic force microscope even with the same film thickness. In addition, since the same level of measurement sensitivity can be obtained with a thinner film thickness, the tip of the probe 10 can be sharpened, and the spatial resolution of magnetic field measurement using a magnetic force microscope can therefore be further increased. Become.

Further, by using a granular superparamagnetic material for the magnetic coating 3, it is possible to obtain a probe 10 with improved temperature stability of magnetic properties. For example, the probe 10 may have a magnetic susceptibility that has substantially no temperature dependence in the range from room temperature 25° C. to 200° C. Here, in this specification, the fact that the magnetic susceptibility "has substantially no temperature dependence in the temperature range of 25 to 200°C" means 25°C, 50°C, 100°C, 150°C, and 200°C. This means that when the initial magnetic susceptibility of the magnetic material is measured under each of the following temperature conditions, the variation among the five measured values is within ±10% of the arithmetic mean of the five measured values. It shall be. The probe 10, which uses a granular superparamagnetic material for the magnetic coating 3, has improved temperature stability of magnetic properties such as initial magnetic susceptibility. Even when evaluating dependence, it is possible to obtain highly accurate evaluation results.

(Manufacture of magnetic force microscope probe 10)
A method of manufacturing the magnetic force microscope probe 10 will be explained. In the following, a mode in which the probe 10 is manufactured using a granular superparamagnetic material for the magnetic coating 3 will be mainly illustrated, but the present invention is not intended to be limited to this mode. The probe 10 is manufactured through a step S1 of preparing a core member 1 fixed to one end of the cantilever 2 and a step S2 of forming a magnetic coating 3 on the exposed surface of the core member 1. I can do it.

(Step S1)
In step S1, a core member 1 made of Si, which is a non-magnetic material, is prepared. The core member 1 is processed to have a shape desired for the probe 10. Specifically, the core member 1 can be manufactured, for example, by performing anisotropic etching on a Si single crystal wafer. The core member 1 is fixed to one end of the cantilever 2. The core member 1 can be fixed to the cantilever 2 by a known method. After this, the core member 1 and the cantilever 2 are treated as one body in subsequent steps.
Note that as the Si constituting the core member 1, impurity-doped Si may be used to ensure conductivity.

(Step S2)
Step S2 is a step of forming the magnetic coating 3 on the exposed surface of the core member 1 by simultaneous sputtering. FIG. 3 is a diagram schematically explaining a sputtering apparatus 900 used in step S2. The sputtering apparatus 900 has a sealed chamber 901 (a chamber for a magnetron sputtering apparatus. Hereinafter, it may be abbreviated as "chamber 901"). Inside the chamber 901, there is a rotary holding table 902 which is rotatably disposed via a rotary drive shaft 903 and rotatably holds the core member 1, and a ferromagnetic element target 904 (for example, a Co target; hereinafter referred to as "target"). 904) and a non-magnetic element target 905 (for example, an Ag target. Hereinafter, it may be abbreviated as "target 905"). Argon gas is supplied into the chamber 901 in a vacuumed state so that sputtering can be performed on the core member 1 . The distance between each target 904, 905 and the core member 1 can be varied from 70 mm to 120 mm.

The ferromagnetic element target 904 is connected to a DC power source for sputtering. The nonmagnetic element 905 is connected to a high frequency (eg, RF) power source for sputtering.

The frequency of the high frequency power source for the non-magnetic element target 905 can be, for example, 13.56 MHz. A large power is applied to each target 904, 905 so that high-speed argon ions for sputtering are directed toward each target 904, 905. The composition of the magnetic coating 3 formed by sputtering can be adjusted by changing the power applied to each target 904, 905 (the diameter can be, for example, 75 mm) (for example, from 50 W to 250 W). It looks like this.

The core member 1 integrated with the cantilever 2 is held on a rotary holding table 902. The rotating holding table 902 is rotated at a speed of 10 rpm, for example, during film formation. Further, the rotating holding table 902 can be moved up and down, and the distance between the rotating holding table 902 and the non-magnetic element target 905 can be changed from 70 mm to 120 mm.

Next, the magnetic coating 3 is formed by simultaneous sputtering at room temperature. That is, using both the ferromagnetic element target 904 and the nonmagnetic element target 905 as sputtering targets, both elements are sputtered to form a film at the same time. In the magnetic film 3 to be formed, the non-magnetic element (for example, Ag) does not form a solid solution in the ferromagnetic element (for example, Co), and the magnetic crystal particles of the ferromagnetic element (for example, Co) are mixed with the non-magnetic element (for example, Ag). ) exists in an isolated state dispersed in the non-magnetic grain boundary region (granular structure). The thickness of the magnetic film 3 containing a non-magnetic substance can be, for example, 10 to 100 nm. For example, when a Co target is used as the ferromagnetic element target 904 and an Ag target is used as the nonmagnetic element target 905, and the film formation thickness is 100 nm, the time required for film formation is about 3 to 5 minutes. The magnetic force microscope probe 10 is manufactured through Step S1 and Step S2.

In the above description regarding the manufacturing method of the magnetic force microscope probe 10, a manufacturing process in which the magnetic coating 3 is formed by simultaneous sputtering of a ferromagnetic element and a nonmagnetic element was exemplified. The manufacturing method is not limited to this form. For example, by alternately performing sputtering deposition of a nonmagnetic element (for example, Ag) and sputtering deposition of a ferromagnetic element (for example, Co), it is also possible to finally form the magnetic coating 3 containing a nonmagnetic substance. It is. However, it is easy to realize a state in which magnetic crystal grains of a ferromagnetic element (e.g. Co) are dispersed and isolated in a non-magnetic grain boundary region of a non-magnetic element (e.g. Ag). , a configuration in which the magnetic film is formed by simultaneous sputtering as described above can be preferably adopted.

<2. DC magnetic field measurement device and DC magnetic field measurement method>
The DC magnetic field measurement method of the present invention includes the embodiments [1] to [28] below.
[1] A method for measuring a direct current magnetic field, comprising:
(a) exciting a cantilever having a superparamagnetic probe at one end that generates a magnetic moment in the direction of the applied magnetic field;
(b) While performing step (a), an alternating current magnetic field is applied to the probe from an alternating current magnetic field generator to periodically vary the magnetization of the probe, thereby modulating the frequency of the excitation vibration of the cantilever. process and
(c) while performing the step (b), detecting the vibration of the probe and demodulating the frequency of the detection signal of the vibration of the probe;
(d) measuring the frequency component of the alternating magnetic field of the signal demodulated in step (c);
(e) The probe is caused to scan a scanning area set within a plane intersecting the vibration direction of the probe, and the steps (a) to ( d);
(f) performing a two-dimensional Fourier transform on the information corresponding to the measurement result of the step (d) in the scanning region in the in-plane direction of the scanning region;
(g0) From the Fourier transform information obtained in the step (f), extract information corresponding to the two-dimensional Fourier transform of the component of the DC magnetic field parallel to the AC magnetic field in the in-plane direction of the scanning area. The process of
(i0) Based on the information corresponding to the two-dimensional Fourier transform of the component of the direct current magnetic field parallel to the alternating current magnetic field in the in-plane direction of the scanning region, each of the components within the scanning region is For in-plane coordinates, obtaining a value corresponding to a component parallel to the alternating current magnetic field of the direct current magnetic field;
including;
The extraction in the step (g0) includes the amplitude of the alternating magnetic field at the position of the probe, the first-order differential of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe, and the a second derivative of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe, or a combination of two ratios therebetween and two wave numbers in the in-plane direction within the scanning region; carried out based on
A method for measuring a DC magnetic field, characterized in that the amplitude of the AC magnetic field at the position of the probe and the value of the second derivative of the amplitude with respect to the vibration direction of the probe are non-zero.

[2] The method for measuring a DC magnetic field according to [1], further comprising the step of (j) calibrating at least the measurement sensitivity.

[3] The direct current according to [2], wherein the step (j) further includes calibrating a constant value component of a component of the direct current magnetic field parallel to the alternating current magnetic field that does not depend on the position within the scanning area. Magnetic field measurement method.

[4] The step (j) is
(j1) The steps (a) to (f ⁾ and (g0) to (i0 ), and specifying a first in-plane coordinate within the scanning region where a value corresponding to a component parallel to the alternating current magnetic field of the direct current magnetic field obtained in the step (i0) is zero;
(j2) A component of the direct current magnetic field parallel to the alternating current magnetic field such that the value of the component parallel to the alternating current magnetic field of the direct current magnetic field becomes −H ^dc(ex) in the first in-plane coordinates. The method for measuring a direct current magnetic field according to [2] or [3], including the step of calibrating the intensity at each in-plane coordinate within the scanning region.

[5] The step (j) is
(j1) Performing the steps (a) to (f) and (g0) to (i0) while applying to the probe an external DC magnetic field whose intensity of the component parallel to the AC magnetic field is H ^{dc (ex).} , a step of specifying a first in-plane coordinate within the scanning region where a value corresponding to a component parallel to the alternating current magnetic field of the direct current magnetic field obtained in the step (i0) is zero;
(j3) When the external DC magnetic field is not applied to the probe, the DC magnetic field is parallel to the AC magnetic field obtained by performing the steps (a) to (f) and (g0) to (i0). specifying a second in-plane coordinate within the scanning area where the value corresponding to the component is zero;
(j4) The value of the component of the direct current magnetic field parallel to the alternating current magnetic field is −H ^dc(ex) at the first in-plane coordinate and zero at the second in-plane coordinate, The DC magnetic field measuring method according to [2] or [3], comprising the step of calibrating the intensity and constant value component at each in-plane coordinate in the scanning region of a component of the DC magnetic field parallel to the AC magnetic field.

[6] The step (j) is
(j1) Performing the steps (a) to (f) and (g0) to (i0) while applying to the probe an external DC magnetic field whose intensity of the component parallel to the AC magnetic field is H ^{dc (ex).} , a step of specifying a first in-plane coordinate within the scanning region where a value corresponding to a component parallel to the alternating current magnetic field of the direct current magnetic field obtained in the step (i0) is zero;
(j5) The steps (a ⁾ to (f ⁾ and ( g0) to (i0), and determine second in-plane coordinates within the scanning area where the value corresponding to the component parallel to the alternating current magnetic field of the direct current magnetic field obtained in the step (i0) is zero. The process of identifying;
(j6) The value of the component of the direct current magnetic field parallel to the alternating current magnetic field is -H ^dc(ex) in the first in-plane coordinates, and -H ^dc(ex2) in the second in-plane coordinates. The method according to [2] or [3], comprising the step of calibrating the intensity and constant value component at each in-plane coordinate in the scanning area of a component of the DC magnetic field parallel to the AC magnetic field so that Direct current magnetic field measurement method.

[7] The step (j) is
(j7) The above steps (a) to (f ⁾ and (g0) to (i0 ), and determine a first in-plane coordinate in the scanning area where the value corresponding to the component of the DC magnetic field parallel to the AC magnetic field obtained in the step (i0) is a first value α. The process of identifying;
(j8) The steps ⁽ a ⁾ to ( f) and (g0) to (i0), and the value corresponding to the component of the DC magnetic field parallel to the AC magnetic field obtained in the step (i0) is the first value α. identifying second in-plane coordinates within the region;
(j9) A value H ₁ ^{dc (sample)} at the first in-plane coordinate and a value H ₂ ^{dc (sample)} at the second in-plane coordinate of the component of the DC magnetic field parallel to the alternating current magnetic field. The scanning area of the component of the DC magnetic field parallel to the AC magnetic field such that the difference H ₁ ^dc(sample) - H ₂ ^dc(sample) is equal to the difference H ^dc(ex2) - H ^dc(ex). The method for measuring a direct current magnetic field according to [2] or [3], comprising the step of calibrating the intensity or measurement sensitivity at each in-plane coordinate within the range.

[8] The step (j) is
(j10) Performing the steps (a) to (e) while applying to the probe a first external DC magnetic field whose intensity of the component parallel to the AC magnetic field is H ^dc(ex) , extracting a first value corresponding to a constant value component of a component parallel to the alternating magnetic field that is independent of in-plane coordinates within the scanning region;
(j11) Performing the steps (a) to (e) while applying a second external DC magnetic field having the same strength and opposite polarity as the first external DC magnetic field to the probe, and extracting a second value corresponding to a constant value component of a component parallel to the alternating magnetic field that is independent of in-plane coordinates within the scanning area;
(j12) Based on the difference between the first value and the second value and the H ^dc(ex) , determine the measurement sensitivity of the value corresponding to the component parallel to the alternating current magnetic field of the direct current magnetic field. process and
(j13) Based on the sum of the first value and the second value and the measurement sensitivity obtained in the step (j12), the scanning area of the component parallel to the alternating current magnetic field of the direct current magnetic field The method for measuring a direct current magnetic field according to [2] or [3], comprising the step of determining a constant value component that does not depend on in-plane coordinates within.

[9] The step (j) is
(j10) Performing the steps (a) to (e) while applying to the probe a first external DC magnetic field whose intensity of the component parallel to the AC magnetic field is H ^dc(ex) , extracting a first value corresponding to a constant value component of a component parallel to the alternating magnetic field that is independent of in-plane coordinates within the scanning region;
(j14) Perform the steps (a) to (e) without applying an external DC magnetic field to the probe, and calculate the in-plane coordinates of the component of the DC magnetic field parallel to the AC magnetic field within the scanning area. extracting a third value corresponding to a constant value component that is not present;
(j15) Based on the difference between the first value and the third value and the H ^dc(ex) , determine the measurement sensitivity of the value corresponding to the component parallel to the alternating current magnetic field of the direct current magnetic field. process and
(j16) Based on the first value and the measurement sensitivity obtained in the step (j15), a constant value of the component of the DC magnetic field parallel to the AC magnetic field is determined to be constant regardless of the in-plane coordinates within the scanning area. The method for measuring a direct current magnetic field according to [2] or [3], comprising the step of determining a value component.

[10] The direction of the alternating magnetic field is parallel to the vibration direction of the probe,
The method includes:
(k0) Information corresponding to the two-dimensional Fourier transform of the component of the DC magnetic field parallel to the AC magnetic field in the in-plane direction of the scanning area is transmitted to the scanning area of the component of the DC magnetic field in the in-plane direction. a step of converting into information corresponding to a two-dimensional Fourier transform in the in-plane direction;
(l0) obtaining a value corresponding to the in-plane direction component of the DC magnetic field by two-dimensional inverse Fourier transform based on the information obtained in the step (k0);
further including;
The DC magnetic field measuring method according to any one of [1] to [9], wherein the conversion in the step (k0) is performed based on a combination of two wave numbers in an in-plane direction within the scanning region.

[11] (m0) The second component of the direct current magnetic field parallel to the alternating current magnetic field in the in-plane direction of the scanning region obtained by measurement at the first probe position in the vibration direction of the probe. The information corresponding to the dimensional Fourier transform is converted into a component of the DC magnetic field parallel to the AC magnetic field at a virtual second probe position shifted from the first probe position in the vibration direction of the probe. converting into information corresponding to two-dimensional Fourier transform in the in-plane direction of the scanning area;
(n0) Based on the information obtained in the step (m0), obtain a value corresponding to the component of the DC magnetic field parallel to the AC magnetic field at the second probe position by two-dimensional inverse Fourier transformation. further comprising a process;
The conversion in the step (m0) is based on the distance of the second probe position from the first probe position in the vibration direction of the probe, and two wave numbers in the in-plane direction within the scanning area. The DC magnetic field measurement method according to any one of [1] to [10], which is performed based on a combination of.

[12] (g2) From the Fourier transform information obtained in the step (f), calculate the second differential of the component of the DC magnetic field parallel to the AC magnetic field with respect to the vibration direction of the probe in the scanning area. further comprising the step of extracting information corresponding to a two-dimensional Fourier transform in an in-plane direction,
The extraction in the step (g2) includes: the amplitude of the alternating magnetic field at the position of the probe; the first-order differential of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe; Based on the combination of two ratios between the amplitude of the alternating magnetic field at the position of the probe and the second derivative with respect to the vibration direction of the probe, and two wave numbers in the in-plane direction within the scanning region. The DC magnetic field measurement method according to any one of [1] to [11], which is carried out.

[13] (h2-0) Convert the information extracted in step (g2) into information corresponding to two-dimensional Fourier transform of a component of the DC magnetic field parallel to the AC magnetic field in the in-plane direction of the scanning area. a process of converting into
(i2-0) Based on the information obtained in the step (h2-0), a component parallel to the alternating current magnetic field of the direct current magnetic field is determined for each in-plane coordinate within the scanning area by two-dimensional inverse Fourier transformation. and obtaining a value corresponding to
The DC magnetic field measurement method according to [12], wherein the conversion in the step (h2-0) is performed based on a combination of two wave numbers in an in-plane direction within the scanning region.

[14] (i2-2) Based on the information obtained in step (g2), two-dimensional inverse Fourier transform is used to calculate the direct current magnetic field parallel to the alternating current magnetic field for each in-plane coordinate within the scanning area. The DC magnetic field measuring method according to [12] or [13], further comprising the step of obtaining a value corresponding to a second-order differential of the component with respect to the vibration direction of the probe.

[15] The direction of the alternating magnetic field is parallel to the vibration direction of the probe,
The method includes:
(k2) Information corresponding to the two-dimensional Fourier transform in the in-plane direction of the scanning area of the second-order differential of the component of the DC magnetic field parallel to the AC magnetic field with respect to the vibration direction of the probe. converting a second-order differential of the in-plane direction component of the magnetic field with respect to the vibration direction of the probe into information corresponding to a two-dimensional Fourier transform in the in-plane direction of the scanning area;
(l2) Based on the information obtained in the step (k2), a two-dimensional inverse Fourier transform is performed to correspond to the second derivative of the in-plane direction component of the DC magnetic field with respect to the vibration direction of the probe. further comprising the step of obtaining a value,
The DC magnetic field measurement method according to [14], wherein the conversion in the step (k2) is performed based on a combination of two wave numbers in an in-plane direction within the scanning region.

[16] (m2) The second order of the component parallel to the AC magnetic field of the DC magnetic field in the vibration direction of the probe, obtained by measurement at the third probe position in the vibration direction of the probe. The information corresponding to the two-dimensional Fourier transform of the differential in the in-plane direction of the scanning area is converted into the DC magnetic field at a fourth probe position shifted from the third probe position in the vibration direction of the probe. converting a second-order differential of a component parallel to the alternating magnetic field with respect to the vibration direction of the probe into information corresponding to a two-dimensional Fourier transform in the in-plane direction of the scanning area;
(n2) Based on the information obtained in the step (m2), a two-dimensional inverse Fourier transform is performed to transform the component of the DC magnetic field parallel to the alternating current magnetic field at the fourth probe position of the probe. and obtaining a value corresponding to a second derivative with respect to the vibration direction,
The conversion in the step (m2) includes the distance of the fourth probe position from the third probe position in the vibration direction of the probe, and two wave numbers in the in-plane direction within the scanning area. The DC magnetic field measurement method according to any one of [12] to [15], which is performed based on a combination of.

[17] (h2-1) The information extracted in the step (g2) is calculated by calculating the first derivative of the component of the DC magnetic field parallel to the AC magnetic field with respect to the vibration direction of the probe in the scanning area. further comprising the step of converting into information corresponding to two-dimensional Fourier transform in the in-plane direction,
The DC magnetic field measuring method according to any one of [12] to [16], wherein the conversion in the step (h2-1) is performed based on a combination of two wave numbers in an in-plane direction within the scanning region.

[18] (g1) Based on the Fourier transform information obtained in step (f), calculate the first-order differential of the component of the DC magnetic field parallel to the AC magnetic field with respect to the vibration direction of the probe. further comprising the step of extracting information corresponding to a two-dimensional Fourier transform about the in-plane direction of the scanning area,
The extraction in the step (g1) includes: the amplitude of the alternating magnetic field at the position of the probe, the first-order differential of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe; Based on the combination of two ratios between the amplitude of the alternating magnetic field at the position of the probe and the second derivative with respect to the vibration direction of the probe, and two wave numbers in the in-plane direction within the scanning region. carried out,
The DC magnetic field measurement method according to any one of [1] to [16], wherein the value of the first-order differential of the amplitude of the AC magnetic field at the position of the probe with respect to the vibration direction of the probe is non-zero.

[19] (h1-0) Convert the information extracted in step (g1) into information corresponding to two-dimensional Fourier transform of a component of the DC magnetic field parallel to the AC magnetic field in the in-plane direction of the scanning area. a process of converting into
(i1-0) Based on the information obtained in the step (h1-0), a component parallel to the alternating current magnetic field of the direct current magnetic field is determined for each in-plane coordinate within the scanning area by two-dimensional inverse Fourier transformation. and obtaining a value corresponding to
The DC magnetic field measurement method according to [18], wherein the conversion in the step (h1-0) is performed based on a combination of two wave numbers in an in-plane direction within the scanning region.

[20] (i1) Information corresponding to a two-dimensional Fourier transform of a first-order differential of a component of the DC magnetic field parallel to the AC magnetic field with respect to the vibration direction of the probe in the in-plane direction of the scanning area. Based on this, a value corresponding to the first-order differential of the component of the DC magnetic field parallel to the AC magnetic field with respect to the vibration direction of the probe is calculated for each in-plane coordinate in the scanning area by two-dimensional inverse Fourier transformation. The DC magnetic field measurement method according to any one of [17] to [19], further comprising the step of obtaining.

[21] The direction of the alternating magnetic field is parallel to the vibration direction of the probe,
The method includes:
(k3) Information corresponding to the two-dimensional Fourier transform in the in-plane direction of the scanning area of the first-order differential of the component of the DC magnetic field parallel to the AC magnetic field with respect to the vibration direction of the probe. converting a first-order differential of a component of the magnetic field in the in-plane direction with respect to the vibration direction of the probe into information corresponding to a two-dimensional Fourier transform in the in-plane direction of the scanning area;
(l3) Based on the information obtained in the step (k3), a two-dimensional inverse Fourier transform is performed to correspond to the first-order differential of the in-plane direction component of the DC magnetic field with respect to the vibration direction of the probe. further comprising the step of obtaining a value,
The DC magnetic field measurement method according to any one of [17] to [20], wherein the conversion in the step (k3) is performed based on a combination of two wave numbers in an in-plane direction within the scanning region.

[22] (m1) The first order of the component parallel to the AC magnetic field of the DC magnetic field in the vibration direction of the probe, obtained by measurement at the first probe position in the vibration direction of the probe. information corresponding to the two-dimensional Fourier transform of the differential in the in-plane direction of the scanning area at a virtual second probe position shifted from the first probe position in the vibration direction of the probe; converting a first-order differential of a component of the DC magnetic field parallel to the AC magnetic field with respect to the vibration direction of the probe into information corresponding to a two-dimensional Fourier transform in the in-plane direction of the scanning area;
(n1) Based on the information obtained in the step (m1), a two-dimensional inverse Fourier transform is performed to convert the component of the direct current magnetic field parallel to the alternating current magnetic field at the second probe position to the tip of the probe. further comprising the step of obtaining a value corresponding to a first-order differential with respect to the vibration direction,
The conversion in the step (m1) includes the distance of the second probe position from the first probe position in the vibration direction of the probe, and two wave numbers in the in-plane direction within the scanning area. The DC magnetic field measurement method according to any one of [17] to [21], which is performed based on a combination of.

[23] The alternating current magnetic field generator,
air core coil,
an alternating current source that supplies alternating current to the air-core coil;
The DC magnetic field measurement method according to any one of [1] to [22], comprising:

[24] The DC magnetic field measuring method according to [23], wherein the probe is placed in a cavity of the air-core coil.

[25] The DC magnetic field measuring method according to [23] or [24], wherein the probe is placed on the central axis of the air-core coil.

[26] The alternating current magnetic field generator,
an electromagnet comprising an electromagnetic core and a coil wound around the electromagnetic core;
an alternating current source that supplies alternating current to the electromagnet;
The DC magnetic field measurement method according to any one of [1] to [22], comprising:

[27] (o) The amplitude of the alternating magnetic field at the position of the probe, the first derivative of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe, and the position of the probe further comprising the step of determining two ratios between the amplitude of the alternating magnetic field and the second derivative with respect to the vibration direction of the probe;
The step (o) includes:
A measurement result of a component of the DC magnetic field parallel to the AC magnetic field when the electromagnet is used as the AC magnetic field generator is made to match a measurement result when an air-core coil is used as the AC magnetic field generator. , the DC magnetic field measurement method according to [26], including the step of optimizing the two ratios.

[28] (o) The amplitude of the alternating magnetic field at the position of the probe, the first derivative of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe, and the position of the probe further comprising the step of determining two ratios between the amplitude of the alternating magnetic field and the second derivative with respect to the vibration direction of the probe;
The step (o) includes:
When the electromagnet is used as the alternating current magnetic field generator, the measurement result of the second order differential in the vibration direction of the probe of the component parallel to the alternating current magnetic field of the direct current magnetic field is measured using an air core as the alternating current magnetic field generator. The method for measuring a direct current magnetic field according to [26], including the step of optimizing the two ratios so as to match the measurement results when using a coil.

The DC magnetic field measuring device of the present invention includes the following embodiments [29] to [49].
[29] A device for measuring a direct current magnetic field, comprising:
a cantilever having a superparamagnetic probe at one end that generates a magnetic moment in the direction of an applied magnetic field;
an exciter that excites the cantilever;
an alternating current magnetic field generator that frequency-modulates the excitation vibration of the cantilever by applying an alternating magnetic field to the probe and periodically varying the magnetization of the probe;
a vibration sensor that detects vibrations of the probe;
a scanning mechanism that causes the probe to scan a scanning area set within a plane intersecting the vibration direction of the probe;
a demodulator that frequency demodulates the detection signal of the vibration sensor;
a detector that measures a frequency component of the alternating magnetic field included in the demodulated signal from the demodulator;
a storage device that stores a measurement value corresponding to a measurement signal of the detector for each in-plane coordinate in the scanning area;
a Fourier transformer that performs a two-dimensional Fourier transform on the measured values for each in-plane coordinate of the scanning area stored in the storage device with respect to the in-plane coordinate;
From the Fourier transform information output from the Fourier transformer, it is possible to extract information corresponding to a two-dimensional Fourier transform of a component of the DC magnetic field parallel to the alternating current magnetic field in an in-plane direction of the scanning area. a first wave number filter computing unit configured to;
Each in-plane coordinate in the scanning area is determined by two-dimensional inverse Fourier transformation based on information corresponding to the two-dimensional Fourier transformation of the component of the DC magnetic field parallel to the alternating current magnetic field in the in-plane direction of the scanning area. an inverse Fourier transformer configured to be able to obtain a value corresponding to a component parallel to the alternating current magnetic field of the direct current magnetic field,
The extraction in the first wave number filter calculator includes: the amplitude of the alternating magnetic field at the position of the probe; the first-order differential of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe; and the second derivative of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe, or two ratios therebetween, and two wave numbers in the in-plane direction within the scanning region. It is done based on a combination of
A DC magnetic field measuring device, wherein the amplitude of the AC magnetic field at the position of the probe and the value of the second derivative of the amplitude with respect to the vibration direction of the probe are non-zero.

[30] When the probe scans each in-plane coordinate within the scanning region, the probe receives an external DC magnetic field whose intensity of a component parallel to the AC magnetic field from the AC magnetic field generator has a predetermined value. The DC magnetic field measuring device according to [29], further comprising an external DC magnetic field generator configured to be able to apply an external DC magnetic field.

[31] From the Fourier transform information output from the Fourier transformer, determine the in-plane direction of the scanning region of the second derivative of the component of the DC magnetic field parallel to the AC magnetic field with respect to the vibration direction of the probe. further comprising a second wave number filter calculator configured to be able to extract information corresponding to a two-dimensional Fourier transform of
The extraction in the second wave number filter calculator includes the amplitude of the alternating magnetic field at the position of the probe, and the first-order differential of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe. and the second derivative of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe, and a combination of two wave numbers in the in-plane direction within the scanning region. The DC magnetic field measuring device according to [29] or [30], which is carried out based on [29] or [30].

[32] The second derivative of the component of the direct current magnetic field parallel to the alternating current magnetic field, extracted by the second wave number filter calculator, with respect to the vibration direction of the probe, with respect to the in-plane direction of the scanning region. The device is configured to be able to convert information corresponding to a two-dimensional Fourier transform into information corresponding to a two-dimensional Fourier transform of a component of the DC magnetic field parallel to the alternating current magnetic field in an in-plane direction of the scanning area. , further including a first integral filter calculator,
The DC magnetic field measurement device according to [31], wherein the conversion in the first integral filter calculator is performed based on a combination of two wave numbers in an in-plane direction within the scanning region.

[33] The inverse Fourier transformer is capable of performing a two-dimensional Fourier transform of a second-order differential of a component of the direct current magnetic field parallel to the alternating current magnetic field with respect to the vibration direction of the probe in an in-plane direction of the scanning area. Based on the information, the second derivative of the component of the direct current magnetic field parallel to the alternating current magnetic field with respect to the vibration direction of the probe is determined for each in-plane coordinate within the scanning region by two-dimensional inverse Fourier transform. The DC magnetic field measuring device according to [31] or [32], further configured to be able to obtain a value for which

[34] The second derivative of the component of the direct current magnetic field parallel to the alternating current magnetic field, extracted by the second wave number filter calculator, with respect to the vibration direction of the probe, with respect to the in-plane direction of the scanning region. The information corresponding to the two-dimensional Fourier transform is converted into a two-dimensional Fourier transform of the first derivative of the component of the DC magnetic field parallel to the AC magnetic field with respect to the vibration direction of the probe in the in-plane direction of the scanning area. further including a second integral filter calculator configured to be able to convert into corresponding information;
The DC magnetic field measuring device according to any one of [31] to [33], wherein the conversion in the second integral filter calculator is performed based on a combination of two wave numbers in an in-plane direction within the scanning region. .

[35] From the Fourier transform information output from the Fourier transformer, determine the in-plane direction of the scanning region of the first derivative of the component of the DC magnetic field parallel to the AC magnetic field with respect to the vibration direction of the probe. further including a third wave number filter calculator configured to be able to extract information corresponding to a two-dimensional Fourier transform of;
The extraction in the third wave number filter calculator includes the amplitude of the alternating magnetic field at the position of the probe, and the first-order differential of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe. and the second derivative of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe, and a combination of two wave numbers in the in-plane direction within the scanning region. It is carried out based on
The DC magnetic field measurement device according to any one of [29] to [34], wherein the value of the first derivative of the amplitude of the AC magnetic field at the position of the probe with respect to the vibration direction of the probe is non-zero.

[36] The first derivative of the component parallel to the alternating current magnetic field of the direct current magnetic field extracted by the third wave number filter calculator with respect to the vibration direction of the probe, with respect to the in-plane direction of the scanning region. The device is configured to be capable of converting information corresponding to a two-dimensional Fourier transform into information corresponding to a two-dimensional Fourier transform of a component of the DC magnetic field parallel to the alternating current magnetic field in an in-plane direction of the scanning area. , further including a third integral filter calculator,
The DC magnetic field measuring device according to [35], wherein the conversion in the third integral filter calculator is performed based on a combination of two wave numbers in an in-plane direction within the scanning region.

[37] The inverse Fourier transformer converts a first-order differential of a component of the direct current magnetic field parallel to the alternating current magnetic field with respect to the vibration direction of the probe into a two-dimensional Fourier transform with respect to the in-plane direction of the scanning area. Based on the corresponding information, a two-dimensional inverse Fourier transform is used to calculate the first derivative of the component of the DC magnetic field parallel to the AC magnetic field with respect to the vibration direction of the probe for each in-plane coordinate in the scanning area. The DC magnetic field measuring device according to any one of [34] to [36], further configured to be able to obtain a corresponding value.

[38] The alternating current magnetic field applied to the probe by the alternating current magnetic field generator is parallel to the vibration direction of the probe,
The DC magnetic field measurement device includes:
Information corresponding to a two-dimensional Fourier transform of a component of the DC magnetic field parallel to the AC magnetic field in the in-plane direction of the scanning area, based on a combination of two wave numbers in the in-plane direction within the scanning area, further comprising a direction conversion filter calculator configured to be able to convert the in-plane direction component of the DC magnetic field into information corresponding to a two-dimensional Fourier transform in the in-plane direction of the scanning area,
The inverse Fourier transformer transforms the scanning area by two-dimensional inverse Fourier transformation based on information corresponding to two-dimensional Fourier transformation of the in-plane direction component of the DC magnetic field in the in-plane direction of the scanning area. The DC magnetic field measurement according to any one of [29] to [37], further configured to be able to obtain a value corresponding to the in-plane direction component of the DC magnetic field for each in-plane coordinate within Device.

[39] The direction conversion filter calculator performs a two-dimensional Fourier transform of a second-order differential of a component of the DC magnetic field parallel to the AC magnetic field with respect to the vibration direction of the probe in the in-plane direction of the scanning area. Based on the combination of two wave numbers in the in-plane direction within the scanning region, information corresponding to the second differential of the in-plane direction component of the DC magnetic field with respect to the vibration direction of the probe is It is further configured to be capable of converting into information corresponding to two-dimensional Fourier transform in the in-plane direction of the scanning area,
The inverse Fourier transformer converts the in-plane direction component of the DC magnetic field into information corresponding to the two-dimensional Fourier transform of the second-order differential with respect to the vibration direction of the probe in the in-plane direction of the scanning area. Based on the two-dimensional inverse Fourier transform, for each in-plane coordinate in the scanning region, a value corresponding to the second derivative of the in-plane direction component of the DC magnetic field with respect to the vibration direction of the probe is obtained. The DC magnetic field measuring device according to [38], further configured to enable the following.

[40] The direction conversion filter calculator performs a two-dimensional Fourier transform of a first-order differential of a component of the DC magnetic field parallel to the AC magnetic field with respect to the vibration direction of the probe in the in-plane direction of the scanning area. Based on the combination of two wave numbers in the in-plane direction within the scanning region, information corresponding to It is further configured to be capable of converting into information corresponding to two-dimensional Fourier transform in the in-plane direction of the scanning area,
The inverse Fourier transformer converts information corresponding to a two-dimensional Fourier transform in the in-plane direction of the scanning region of a first-order differential of the in-plane direction component of the DC magnetic field with respect to the vibration direction of the probe. Based on the two-dimensional inverse Fourier transform, for each in-plane coordinate in the scanning region, a value corresponding to the first-order differential of the in-plane direction component of the DC magnetic field with respect to the vibration direction of the probe is obtained. The DC magnetic field measuring device according to [38] or [39], further configured to enable the above-mentioned.

[41] Two-dimensional Fourier transform of a component of the direct current magnetic field parallel to the alternating current magnetic field, in the in-plane direction of the scanning region, obtained by measurement at a first probe position in the vibration direction of the probe. information corresponding to the scanning area of the component parallel to the alternating current magnetic field of the direct current magnetic field at a virtual second probe position shifted from the first probe position in the vibration direction of the probe. further includes a distance conversion filter calculator configured to be able to convert information into information corresponding to a two-dimensional Fourier transform in an in-plane direction;
The conversion in the distance conversion filter calculator calculates two values: the distance of the second probe position from the first probe position in the vibration direction of the probe, and the distance in the in-plane direction within the scanning area. The DC magnetic field measurement device according to any one of [29] to [40], which is carried out based on a combination of wave numbers.

[42] The distance conversion filter calculator converts a component of the direct current magnetic field parallel to the alternating current magnetic field of the probe obtained by measurement at the first probe position in the vibration direction of the probe. Information corresponding to the two-dimensional Fourier transform of the second-order differential with respect to the vibration direction in the in-plane direction of the scanning area is obtained by converting information corresponding to the two-dimensional Fourier transform of the second-order differential with respect to the vibration direction into a component of the direct current magnetic field parallel to the alternating current magnetic field at the second probe position. It is further configured to be capable of converting a second differential with respect to the vibration direction of the probe into information corresponding to a two-dimensional Fourier transform in an in-plane direction of the scanning area,
The conversion of information corresponding to the two-dimensional Fourier transform of the second order differential in the distance conversion filter calculation unit is based on the distance of the second probe position from the first probe position in the vibration direction of the probe. and a combination of two wave numbers in the in-plane direction within the scanning area, the DC magnetic field measuring device according to [41].

[43] The distance conversion filter calculator converts a component of the direct current magnetic field parallel to the alternating current magnetic field of the probe obtained by measurement at the first probe position in the vibration direction of the probe. Information corresponding to the two-dimensional Fourier transform of the first-order differential with respect to the vibration direction in the in-plane direction of the scanning area is converted into information of the component of the DC magnetic field parallel to the AC magnetic field at the second probe position. It is configured to be capable of converting a first-order differential with respect to the vibration direction of the probe into information corresponding to a two-dimensional Fourier transform in the in-plane direction of the scanning area,
The conversion of the two-dimensional Fourier transform of the first-order differential in the distance conversion filter calculator calculates the distance of the second probe position from the first probe position in the vibration direction of the probe, and the scanning direction. The DC magnetic field measuring device according to [41] or [42], wherein the measurement is performed based on a combination of two wave numbers in an in-plane direction within a region.

[44] The alternating current magnetic field generator,
air core coil,
an alternating current source that supplies alternating current to the air-core coil;
The DC magnetic field measuring device according to any one of [29] to [43], comprising:

[45] The DC magnetic field measuring method according to [44], wherein the probe is placed in a cavity of the air-core coil.

[46] The DC magnetic field measuring device according to [44] or [46], wherein the probe is arranged on the central axis of the air-core coil.

[47] The alternating current magnetic field generator,
an electromagnet comprising an electromagnetic core and a coil wound around the electromagnetic core;
an alternating current source that supplies alternating current to the electromagnet;
The DC magnetic field measuring device according to any one of [29] to [46], comprising:

[48] The measurement results of the component of the DC magnetic field parallel to the AC magnetic field when the electromagnet is used as the AC magnetic field generator are the measurement results when an air-core coil is used as the AC magnetic field generator. The amplitude of the alternating magnetic field at the position of the probe, the first derivative of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe, and the a parameter fitting operation configured to be capable of determining two ratios by optimizing two ratios between the amplitude of the alternating magnetic field and the second derivative with respect to the vibration direction of the probe; The DC magnetic field measuring device according to [47], further comprising a device.

[49] When the electromagnet is used as the alternating current magnetic field generator, the measurement result of the second-order differential in the vibration direction of the probe of the component of the direct current magnetic field parallel to the alternating current magnetic field is measured as the second order differential in the vibration direction of the probe. In order to match the measurement result when an air-core coil is used as determining the two ratios by optimizing the two ratios between a first derivative and a second derivative of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe; The DC magnetic field measuring device according to [47], further comprising a parameter fitting calculator configured to be able to perform the following operations.

The DC magnetic field measuring device of the present invention will be explained along with each step of the DC magnetic field measuring method. FIG. 5 is a diagram schematically explaining a DC magnetic field measuring device 1000 according to one embodiment of the present invention. The DC magnetic field measuring device 1000 is a device that observes a DC magnetic field generated from a sample 20. The DC magnetic field measuring device 1000 includes a cantilever 100, an exciter 200, an AC magnetic field generator 300, a vibration sensor 400, a demodulator 430, a detector 440, a scanning mechanism 500, a signal processing device 600, and an external DC magnetic field generator 700. We are prepared.

(Magnetic sample 20)
The magnetic sample 20 that is the measurement target of the DC magnetic field measuring device 1000 is a sample that generates a DC magnetic field. A specific example of the magnetic sample 20 is a permanent magnet.

(probe 10 and cantilever 100)
A probe 10 is provided at one end of the cantilever 100. The probe 10 is the magnetic force microscope probe 10 described above. The probe 10 is a magnetic probe that generates a magnetic moment in the direction of the applied magnetic field, and is characterized in that the magnetism does not saturate when an external magnetic field with a strength of 20 kOe is applied over a temperature range of at least 10 to 30°C. .
If a probe made of ferromagnetic or ferrimagnetic material with magnetic saturation is used, the magnetization of the probe will be saturated due to the strong DC magnetic field leaking from the magnetic sample 20, making it impossible to apply an AC magnetic field. However, since the magnetization of the probe cannot be varied even if the probe is moved, frequency modulation cannot be caused in the excitation vibration of the cantilever.

Note that as long as the probe 10 contains a magnetic material that has no magnetic saturation and generates a magnetic moment in the direction of the applied magnetic field, and the probe 10 is not attracted to the magnetic sample 20 and the problem of inability to measure occurs. , the tip may include a ferromagnetic material (ie, a material with magnetic saturation). Even if the magnetization of the ferromagnetic material is saturated by the DC magnetic field from the magnetic sample 1, the magnetization of the magnetic material without magnetic saturation can be changed by applying an AC magnetic field. It can be varied by applying . In the case of a probe whose magnetic coating contains a ferromagnetic material, the residual magnetization is not zero and has hysteresis, but as long as a strong DC magnetic field such as a permanent magnet is observed, the magnetization of the entire probe has hysteresis. It will fluctuate in a reversible area outside of this area. Therefore, unless the probe 10 is attracted to the magnetic sample 20 and the measurement itself becomes impossible, a probe containing a ferromagnetic material in addition to a magnetic material that has no magnetization saturation and generates a magnetic moment in the direction of the applied magnetic field can also be used. Can be used in the invention.
However, from the viewpoint of measurement accuracy, it is preferable that the probe 10 does not have magnetic hysteresis.

As the magnetic material used for the probe 10 that has no magnetic saturation and generates a magnetic moment in the direction of the applied magnetic field, it is preferable to use a material that exhibits paramagnetism or superparamagnetism, and it is preferable to use a material that exhibits superparamagnetism (superparamagnetic material). is particularly preferred. Superparamagnetic materials exhibit higher magnetic susceptibility than paramagnetic materials, so they are advantageous for detecting magnetic fields with high sensitivity.

The thickness of the coating of the magnetic material on the probe 10 is not particularly limited, and can be appropriately determined in consideration of the trade-off between magnetic field measurement sensitivity and spatial resolution, and can be, for example, 10 to 100 nm.

A preferred example of the paramagnetic material that can be used in the probe 10 is a multi-component paramagnetic material containing one or more ferromagnetic elements and one or more non-magnetic elements. Paramagnetic materials exhibit the highest magnetic susceptibility near the Curie temperature (Hopkinson effect), so with multicomponent paramagnetic materials, by changing the composition and adjusting the Curie temperature, the magnetic susceptibility at the measurement temperature can be adjusted. It is possible to increase the measurement sensitivity of the magnetic force microscope. Specifically, as the multi-component paramagnetic material, the above (a) solid solution type paramagnetic material and the above (b) amorphous type paramagnetic material can be preferably employed.

As the superparamagnetic material that can be used for the probe 10, the above-mentioned (c) granular superparamagnetic material (sufficiently small particles of ferromagnetic material are dispersed in a non-magnetic matrix, and ferromagnetic material particles account for 10 to 45 of the total % by volume, preferably 15 to 40% by volume). When ferromagnetic material particles occupy 10 to 45% by volume of the whole, percolation (in a sphere approximation model, when two types of spheres are mixed, the spheres of the same type do not come into contact with each other) occurs, so ferromagnetic material Strong magnetic interaction (exchange interaction) between particles can be suppressed. As the size of ferromagnetic material particles decreases, thermal energy randomizes the direction of magnetization of the particles, and in the absence of a magnetic field, the magnetization of individual particles cancel each other out, so the magnetization of the entire material becomes zero on average, changing from ferromagnetic to supernormal. Transfer to magnetism. Since magnetization is zero under no magnetic field, residual magnetization and coercive force are also zero at the same time. When a magnetic field is applied to a superparamagnetic material, magnetization occurs only in the direction of the magnetic field, and magnetization in the direction orthogonal to the magnetic field cancels out between individual particles, so the superparamagnetic material does not have a magnetization component perpendicular to the direction of the applied magnetic field. .

Superparamagnetic materials transition from superparamagnetism to ferromagnetism as the temperature decreases, and the transition temperature is called the blocking temperature. When a superparamagnetic material is used for the probe, the temperature of the probe during use is kept above the blocking temperature.

(Exciter 200)
The probe 10 is provided near one end (free end) of the cantilever 100, and the other end (fixed end) of the cantilever 100 is fixed. The exciter 200 excites the cantilever 100 (step (a)).

The configuration of the exciter 200 is not particularly limited as long as the cantilever 100 can be excited. The exciter 200 can be configured, for example, by an excitation actuator (for example, a piezo element, etc.) attached to the vicinity of the fixed end of the cantilever 100, and an AC voltage power supply connected to the excitation actuator. The frequency at which the exciter 200 excites the cantilever 100 is not particularly limited as long as excitation is possible, but a frequency near the resonant frequency of the cantilever 100 is usually preferably employed as the excitation frequency.

(AC magnetic field generator 300)
The AC magnetic field generator 300 is a device that applies an AC magnetic field to the probe 10. The alternating current magnetic field applied to the probe 10 by the alternating current magnetic field generator 300 preferably has an intensity that does not cause the magnetization of the magnetic sample 20 to be reversed. Further, it is preferable that the alternating magnetic field has an intensity that does not saturate the magnetization of the probe 10. In the DC magnetic field measurement device 1000 of FIG. 4, the AC magnetic field generator 300 includes an air-core coil 310 and an AC current source 320 that supplies an AC current to the air-core coil 310. By supplying an alternating current from the alternating current source 320 to the air-core coil 310, an alternating magnetic field parallel to the vibration direction of the probe (that is, the direction perpendicular to the sample surface) is applied to the probe 10 (step ( b)).

Note that the frequency of the AC magnetic field generated by the AC magnetic field generator 300 is not particularly limited as long as the frequency modulation of the vibration of the probe 10 can be detected, and may be, for example, 10 Hz to 1 kHz. For example, when the exciter 200 excites the cantilever 100 at its resonant frequency or a frequency near the resonant frequency, the sideband frequency generated by frequency modulating the excitation vibration can obtain the necessary gain in the resonance curve. A frequency within the range can be selected as appropriate.

The strength of the alternating current magnetic field applied to the probe 10 by the alternating current magnetic field generator 300 is adjusted as appropriate within a range in which the probe 10 is not attracted to the magnetic sample 20 and a desired magnetic field measurement sensitivity is obtained. be able to.

The installation positions of the elements constituting the AC magnetic field generator 300 are determined so that the amplitude of the AC magnetic field from the AC magnetic field generator 300 and the value of the second-order differential in the vibration direction of the probe 10 (z-axis direction in FIG. 4) are determined. There is no particular limitation as long as it is non-zero. For example, in the DC magnetic field measuring device 1000 shown in FIG. 4, the probe 10 is preferably disposed in a hollow portion of the air-core coil 310, and preferably on the central axis of the air-core coil 310. In one preferred embodiment, the probe 10 is placed on the central axis of the air-core coil 310 and at the center of the thickness of the air-core coil 310. At this position, the magnetic field generated from the air-core coil 310 is at its maximum, so by arranging the probe 10 at this position, it is possible to further increase the measurement sensitivity.

(Vibration sensor 400, demodulator 430, detector 440)
Due to the magnetic interaction between the magnetic field vector formed by the superposition of the DC magnetic field from the magnetic sample 20 and the AC magnetic field from the AC magnetic field generator 300 and the magnetic moment of the probe 10, the probe 10 has a periodic strength. subject to varying magnetic forces. The gradient of the magnetic force whose strength periodically varies causes the effective spring constant of the cantilever 100 to vary periodically, thereby causing the frequency of vibration of the probe 10 to vary periodically. Vibration sensor 400, demodulator 430, and detector 440 can extract information corresponding to the amplitude of the magnetic force gradient at the position of probe 10 from this frequency-modulated vibration of probe 10.

(Vibration sensor 400)
In the DC magnetic field measuring device 1000, the vibration sensor 400 includes a light source 410 that irradiates the free end side tip of the cantilever 100 with laser light, and an optical displacement sensor 420 that detects the laser light reflected by the cantilever 100. ing. By detecting the laser beam emitted from the light source 410 and reflected by the free end of the cantilever 100 with the optical displacement sensor 420, the displacement of the probe 10 can be extracted as an output. It is obtained by scanning each in-plane (x, y) coordinate of a scanning area set in a plane intersecting the vibration direction (z-axis direction) of the probe 10 with the probe 10 using a scanning mechanism 500 described later. , the output from optical displacement sensor 420 is input to demodulator 430.

(Demodulator 430)
The detection signal of the vibration sensor 400 is a signal obtained by frequency-modulating the excitation vibration of the cantilever 100 by the alternating current component of the magnetic force acting on the probe 10. The demodulator 430 frequency demodulates the detection signal of the vibration sensor 400 (step (c)) to obtain a signal corresponding to the alternating current component of the magnetic force acting on the probe 10. In the DC magnetic field measuring device 1000 of FIG. 4, the demodulator 430 is an FM demodulator that demodulates the frequency of the detection signal of the vibration sensor 400. As the demodulator 430, any circuit known as an FM demodulator, such as a PLL (Phase Locked Loop) circuit, a Foster-Seeley detection circuit, a ratio detection circuit, a quadrature detection circuit, etc., can be employed without particular limitation. The signal frequency demodulated by demodulator 430 is input to detector 440 .

(Detector 440)
The detector 440 measures the intensity (amplitude) of a frequency component that is included in the demodulated signal input from the demodulator 430 and has a frequency corresponding to the alternating current magnetic field generated from the alternating current magnetic field generator 300 (step (d) )). As will be described later, the measurement signal of the detector 440 corresponds to the amplitude of the gradient in the vibration direction of the probe 10 of the component of the magnetic force acting on the probe 10 in the vibration direction of the probe 10 . Such a detector 440 can also be configured, for example, by a combination of a narrowband bandpass filter capable of extracting a specific frequency component (i.e., a frequency component having the frequency of an alternating magnetic field) and an amplitude demodulator. It is also possible, for example, to configure it using a spectrum analyzer that measures the intensity of the sideband spectrum corresponding to the frequency of the alternating magnetic field. In the DC magnetic field measuring device of FIG. 4, the detector 440 uses the voltage signal or current signal of the AC current source 320 included in the AC magnetic field generator 300 as a reference signal, and detects the frequency corresponding to the AC magnetic field in the input signal. Detects the frequency components that have the same characteristics and measures their intensity (amplitude). Such a detector 440 can be configured with a lock-in amplifier or a synchronous detector.

(Scanning mechanism 500)
The scanning mechanism 500 is a mechanism that can relatively change the positions of the probe 10 and the magnetic sample 20. The scanning mechanism 500 scans a scanning area (for example, a scanning area set on the surface of the magnetic sample 20) set in a plane (x, y directions) intersecting the vibration direction (z direction) of the probe 10. The probe 10 scans, and the measurement results output from the detector 440 are stored in the memory 610 of the signal processing device 600 for each in-plane coordinate (x, y) set within the scanning area (step (e) )). In-plane coordinates (measurement points) (x, y) for performing measurements within the scanning area are preferably arranged in a grid pattern (that is, so as to constitute Cartesian coordinates). The number of measurement points in the scanning area can be set to an integer power of 2 in each of the x direction and the y direction, for example, so that the two-dimensional Fourier transform described later is easy. As a scanning mechanism, for example, the probe 10 can be moved by moving the sample platform on which the magnetic sample 20 is placed using a drive device to change the position of the sample platform relative to the probe 10. A mechanism that can relatively change the positions of the magnetic sample 20 and the magnetic sample 20 can be preferably used. Examples of such mechanisms include an XY two-axis stage, an XYZ three-axis stage, and the like. In addition, it is also possible to employ a scanning mechanism in which the relative positional relationship between the probe 10 and the magnetic sample 20 is changed by moving the probe 10 with a drive device. Further, as the scanning mechanism 500, it is also possible to use a known mechanism (for example, a piezo element, etc.) used in a conventional scanning probe microscope.

(External DC magnetic field generator 700)
The external DC magnetic field generator 700 maintains the intensity of the component parallel to the AC magnetic field from the AC magnetic field generator 300 at a predetermined value when the probe 10 scans each in-plane coordinate (x, y) within the scanning area. It is configured to be able to apply a certain external DC magnetic field to the probe 10. In the DC magnetic field measuring device 1000 of FIG. 4, the external DC magnetic field generator 700 supplies a predetermined DC current to the electromagnet including an electromagnetic core 710 and a coil 720 wound around the electromagnetic core 710, and to the coil 720 of the electromagnet. and a direct current source 730 configured to be able to do so. The external DC magnetic field generator 700 is used when calibrating the measured value of magnetic field information using the DC magnetic field measuring device 1000. Details of the calibration method will be described later.

(Signal processing device 600)
FIG. 5 is a diagram illustrating the configuration of the signal processing device 600 and the flow of data processing in the signal processing device 600. The signal processing device 600 includes a memory 610, a Fourier transformer 620, a first wavenumber filter calculator 631, a second wavenumber filter calculator 632, a third wavenumber filter calculator 633, and an inverse Fourier transformer. 640, a first integral filter calculator 651, a second/third integral filter calculator 652, a direction conversion filter calculator 660, and a distance conversion filter calculator 670.

The memory 610 is a storage device that stores measurement values corresponding to the measurement signals of the detector 440 for each in-plane coordinate (x, y) within the scanning area. Memory 610 can be configured by a known storage device.

The Fourier transformer 620 performs a two-dimensional Fourier transform on the measured values for each in-plane coordinate (x, y) of the scanning area stored in the storage device 610, and converts the result into a two-dimensional Fourier transform for the in-plane coordinate (x, y). Output (step (f)). The Fourier transformer 620 can be configured by a known computer capable of performing two-dimensional discrete Fourier transform. The Fourier transformer 620 may be configured by a combination of a computer and a program implementing a known algorithm for performing two-dimensional discrete Fourier transform.

The first wave number filter calculator 631 scans the component (here, the z component) of the DC magnetic field parallel to the AC magnetic field from the AC magnetic field generator 300 based on the Fourier transform information output from the Fourier transformer 620. It is configured to be able to extract information corresponding to the two-dimensional Fourier transform H _z ^dc(sample) (k _x , k _y , z) in the in-plane direction of the region (step (g0)). The extraction calculation in the first wave number filter calculator 631 is performed on the amplitude H ^ac of the alternating magnetic field at the position of the probe 10 and the amplitude of the alternating magnetic field at the position of the probe 10 in the vibration direction of the probe 10 (here, in the z direction). ), and the second derivative of the amplitude of the alternating magnetic field at ^the position of the probe 10 with respect to the vibration direction of the probe 10 (here, the z direction) ∂ ² H ^ac /∂z ² and the combination of two wave numbers (k _x , k _y ) in the in-plane (x, y) direction within the scanning area. Further details will be discussed below.

The second wave number filter calculator 632 searches for a component of the DC magnetic field parallel to the AC magnetic field from the AC magnetic field generator 300 (here, the z component) from the Fourier transform information output from the Fourier transformer 620. Two-dimensional Fourier transform of the second differential with respect to the vibration direction of the needle 10 (here, the z direction) in the in-plane direction of the scanning area ∂ ² _Hz ^dc(sample) /∂z ² (k _x , k _y , z) is configured to be able to extract information corresponding to (step (g2)). The extraction calculation in the second wave number filter calculator 632 is performed on the amplitude H ^ac of the alternating magnetic field at the position of the probe 10 and the amplitude of the alternating magnetic field at the position of the probe 10 in the vibration direction of the probe 10 (here, in the z direction). ), and the second derivative of the amplitude of the alternating magnetic field at ^the position of the probe 10 with respect to the vibration direction of the probe 10 (here, the z direction) ∂ ² H ^ac /∂z ² and the combination of two wave numbers (k _x , k _y ) in the in-plane (x, y) direction within the scanning area. Further details will be discussed below.

The third wave number filter calculator 633 calculates, from the Fourier transform information output from the Fourier transformer 620, the vibration direction of the probe 10 ( Here _, the two-dimensional Fourier transform ∂H _z ^{dc (sample)} /∂z ( _k The configuration is such that it is possible to extract corresponding information (step (g3)). The extraction calculation in the third wave number filter calculator 633 is performed on the amplitude H ^ac of the alternating magnetic field at the position of the probe 10 and the amplitude of the alternating magnetic field at the position of the probe 10 in the vibration direction of the probe 10 (here, in the z direction). ), and the second derivative ∂ 2 H ^ac /∂z of the amplitude of the alternating magnetic field at the position of the probe 10 with respect to the vibration direction of the probe 10 (here, ^{the z} direction). ² and a combination of two wave numbers (k _x , k _y ) in the in-plane (x, y) direction within the scanning area. Further details will be discussed below. However, the third wave number filter calculator 633 functions based on the first-order differential ∂H ^ac /∂ of the amplitude of the alternating current magnetic field at the position of the probe 10 with respect to the vibration direction of the probe 10 (here, the z direction). Only if the value of z is non-zero.

The inverse Fourier transformer 640 generates information about the two-dimensional Fourier transform in the in-plane ( _x , _y ) direction of the scanning area (i.e., the value F(k _x , k _y )), the value (f(x, y)) in real space corresponding to the input is obtained for each in-plane (x, y) coordinate in the scanning area by two-dimensional inverse Fourier transformation (step (i0), (i2-0), (i2-2), (i1-0), (i1), (l0), (l2), (l1), (n0), (n2), (n1)) It is configured to be possible. For example, the in-plane (x, y) direction of the scanning area of the component (here, the z ^component ) of the _DC magnetic field parallel to the AC magnetic field from the AC magnetic field generator 300 (x, y, z) When the information corresponding to the two-dimensional Fourier transform H _z ^dc(sample) (k _x , k _y , z) is input to the inverse Fourier transformer 640, the inverse Fourier transformer 640 converts the input information into Through Fourier transformation, for each in-plane coordinate (x, y) within the scanning area, the value _Hz ^dc(sample) (x, y, z) corresponding to the component of the DC magnetic field parallel to the AC magnetic field is obtained ( Step (i0)). Such an inverse Fourier transformer 640 can be configured by a known computer capable of performing two-dimensional discrete inverse Fourier transform. The inverse Fourier transformer 640 may be configured by a combination of a computer and a program implementing a known algorithm for performing two-dimensional discrete inverse Fourier transform.

The first integral filter calculator 651 performs an operation of integrating the input two-dimensional Fourier transform twice in the vibration direction of the probe 10 (here, the z direction) in Fourier space. Scanning of the second-order differential with respect to the vibration direction of the probe 10 (here, the z-direction) of the component (here, the z-component) of the DC magnetic field parallel to the alternating-current magnetic field, extracted by the second wave number filter calculator 632 The information corresponding to the two-dimensional Fourier transform ∂ ² _Hz ^dc(sample) _/ ∂z ² ₍ k 651, the input information is a two-dimensional Fourier transform H _z ^{dc (sample )} (k _x , k _y , z) is converted into information and output (step (h2-0)). The above conversion in the first integral filter calculator 651 is performed based on a combination of two wave numbers (k _x , k _y ) in the in-plane (x, y) direction within the scanning area. Such an operation is to multiply the input value by 1/(k _x ² + k _y ² ) for each combination of wave numbers (k _x , k _y ) except for (k _x , _ky ) = (0, 0). This can be done by:

The second/third integral filter calculator 652 performs an operation (step (h2-1 ), (h1-0)). For example, regarding the in-plane (x, y) direction of the scanning region, the second derivative of the component (here, the z component) of the DC magnetic field parallel to the alternating current magnetic field with respect to the vibration direction of the probe 10 (here, the z direction) When information corresponding to the two-dimensional Fourier transform ∂ ² H _z ^dc(sample) /∂z ² (k _x , k _y , z) is input to the second/third integral filter calculator 652, the input The information is the in-plane (x, y) direction of the scanning region of the first derivative of the component (here, the z component) of the DC magnetic field parallel to the alternating current magnetic field with respect to the vibration direction of the probe 10 (here, the z direction). The information is converted into information corresponding to the two-dimensional Fourier transform ∂H _z ^dc(sample) /∂z(k _x , k _y , z) and output (step (h2-1)). For example, the first derivative of the component (here, the z component) of the DC magnetic field parallel to the alternating current magnetic field with respect to the vibration direction of the probe 10 (here, the z direction) in the in-plane (x, y) direction of the scanning region When information corresponding to the two-dimensional Fourier transform ∂H _z ^dc(sample) /∂z(k _x , k _y , z) is input to the second/third integral filter calculator 652, the input information is the two-dimensional Fourier transform H _z ^dc(sample) (k _x , k _y , z ) is converted into information corresponding to and output (step (h1-0)). Specifically, the above conversion in the second/third integral filter calculator 652 is performed based on a combination of two wave numbers (k _x , k _y ) in the in-plane (x, y) direction within the scanning region. For each combination of wavenumbers (k _x , k _y ) except (k _x , k _y )=(0,0), such an operation adds −1/(k _x ² +k _{y )} to the input value. ² ) This can be done by multiplying by ^1/2 .

The direction conversion filter calculator 660 uses DC magnetic field information (which may be the DC magnetic field itself, or information about the DC magnetic field in the vibration direction of the probe 10 (in the z direction) of a component (z component here) parallel to the vibration direction of the probe 10. ) may be the first-order differential with respect to the direction of vibration (z-direction) of the probe 10 of the DC magnetic field. ), in the in-plane (x, y) direction of the scanning area. An operation is performed to convert the information corresponding to the two-dimensional Fourier transform into the DC magnetic field information of the in-plane (x, y) direction component (here, the z component) of the scanning area (steps (k0) and (k2) , (k1)). For example, the two-dimensional Fourier transform H _z ^dc(sample) (k _x , k _y , z ) is input to the direction conversion filter calculator 660, the two-dimensional Fourier transform H of the in-plane (x, y) direction component of the DC magnetic field in the in-plane (x, y) direction of the scanning area is input. Information corresponding to _x ^dc(sample) (k _x , k _y , z) and H _y ^{dc (sample)} (k _x , _ky , z) is output (step (k0)). Also, for example, the two-dimensional Fourier transform ∂ ² of the second-order differential of the component (z component) of the DC magnetic field parallel to the AC magnetic field with respect to the vibration direction of the probe 10 in the in-plane (x, y) direction of the scanning region When information corresponding to H _z ^dc(sample) /∂z ² (k _x , k _y , z) is input to the direction conversion filter calculator 660, the in-plane (x, y) direction component of the DC magnetic field is Two-dimensional Fourier transform of the second differential with respect to the vibration direction (z direction) of the probe 10 in the in-plane (x, y) direction of the scanning region ∂ ² H _x ^dc(sample) /∂z ² (k _x , k _y , z), ∂ ² H _y ^dc(sample) / ∂z ² (k _x , k _y , z) is output (step (k2)). Also, for example, the first derivative of the component (z component) of the DC magnetic field parallel to the AC magnetic field with respect to the vibration direction (z direction) of the probe 10, and the two-dimensional difference in the in-plane (x, y) direction of the scanning region. When information corresponding to the Fourier transform ∂H _z ^dc(sample) /∂z(k _x , k _y , z) is input to the direction conversion filter calculator 660, the in-plane (x, y) direction component of the DC magnetic field is The two-dimensional Fourier transform of the first-order differential with respect to the vibration direction (z direction) of the probe 10 in the in-plane (x, y) direction of the scanning region ∂H _x ^dc(sample) /∂z(k _x , k _y , z), ∂H _y ^dc(sample) /∂z(k _x , k _y , z) is output (step (k1)). Each of the above conversions in the direction conversion filter calculator 660 is performed based on a combination (k _x , k _y ) of two wave numbers in the in-plane (x, y) direction within the scanning region. Specifically, the conversion from the z (vertical direction) component to the x component is performed by adding -ik _x / (k _x ² + k _y ² ) ¹ to the input value for each wave number combination (k _x , k _y ). ^/2 (i is an imaginary unit), and the conversion from the z (vertical direction) component to the y component can be performed by multiplying each wave number combination by (k _x , k _y ) = (0, 0). For (k _x , k _y ), this can be done by multiplying the input value by -ik _y /(k _x ² +k _y ² ) ^1/2 . Note that when the input magnetic field information is information on a vertical magnetic field component (z component), the direction conversion filter calculator 660 is configured such that when the input magnetic field information is information on a vertical magnetic field component (z component), that is, when the direction of application of the alternating magnetic field is in the vibration direction of the probe 10 (the z direction, that is, the vertical direction ).

The distance conversion filter calculator 670 receives magnetic field information (information about the DC magnetic field itself) obtained by measurement at the first probe position (z=z') in the vibration direction of the probe 10 (here, the z direction). It may be information on the first-order differential with respect to the vibration direction (z-direction) of the probe 10 in the DC magnetic field, or information on the second-order differential with respect to the vibration direction (z-direction) of the probe 10 in the DC magnetic field. It may also be information in the vibration direction of the probe 10 (z direction, that is, vertical direction), or information in the in-plane direction (x, y direction). Information corresponding to the two-dimensional Fourier transform in the in-plane (x, y) direction of the scanning area is transferred from the first probe position to a virtual second probe position ( An operation of converting into magnetic field information at z=z'+Δz) is performed (steps (m0), (m2), (m1)).
For example, the two-dimensional Fourier transform H _z ^{dc (sample} ) of the component (here z component) of the DC magnetic field parallel to the AC magnetic field at the probe position z = z' in the in-plane (x, y) direction of the scanning area. When information corresponding to (k _x , k _y , z') and Δz are input to the distance conversion filter calculator 670, the component (here, z component) in the in-plane ( _x , y) direction of the scanning area. Information corresponding to the two-dimensional Fourier transform _{H z} ^{dc (sample} ) (k m0)). For example, the two-dimensional Fourier transform H _x ^dc(sample) (k _x , k _y , z'), H _y ^dc(sample) (k _x , k _y , z') and Δz are input to the distance conversion filter calculator 670, the probe position z=z Two-dimensional Fourier transform H _x ^{dc (sample} ) (k _x , k _y , z' + Δz ), H _y ^dc(sample) (k _x , k _y , z'+Δz) is output. Further, for example, the second derivative of the component (z component) of the DC magnetic field parallel to the AC magnetic field at the probe position z=z' with respect to the vibration direction (z direction) of the probe 10 in the plane of the scanning region (x , y), when information corresponding to the two-dimensional Fourier transform ∂ ² _Hz ^dc(sample) /∂z ² (k _x , k _y , z') and Δz are input to the distance conversion filter calculator 670. , the second derivative of the component (z component) of the direct current magnetic field parallel to the alternating current magnetic field at the probe position z=z'+Δz with respect to the vibration direction (z direction) of the probe 10, in the plane of the scanning region (x, Information corresponding to the two-dimensional Fourier transform ∂ ² _Hz ^dc(sample) /∂z ² (k _x , k _y , z′+Δz) in the y) direction is output (step (m2)). Further, for example, the second derivative of the in-plane components (x, y components) of the DC magnetic field at the probe position z=z' with respect to the vibration direction (z direction) of the probe 10 in the plane (x, y) of the scanning region y) two-dimensional Fourier transform in the direction ∂ ² H _x ^{dc (sample)} / ∂z ² (k _x , k _y , z'), ∂ ² H _y ^{dc (sample)} / ∂z ² (k _x , k _y When the information corresponding to Two-dimensional Fourier transform of the second derivative with respect to the vibration direction (z direction) in the in-plane (x, y) direction of the scanning area ∂ ² H _x ^dc(sample) /∂z ² (k _x , k _y , z '+Δz), ∂ ² H _y ^dc(sample) /∂z ² (k _x , k _y , z'+Δz) is output. For example, the first derivative of the component (z component) of the DC magnetic field parallel to the AC magnetic field at the probe position z=z' with respect to the vibration direction (z direction) of the probe 10 in the plane of the scanning region (x , y) direction, the information corresponding to the two-dimensional Fourier transform ∂H _z ^dc(sample) /∂z(k _x , k _y , z') and Δz are input to the distance transform filter calculator 670. The first derivative of the component (z component) of the DC magnetic field parallel to the AC magnetic field at needle position z = z' + Δz with respect to the vibration direction (z direction) of the probe 10 in the plane of the scanning region (x, y) Information corresponding to the two-dimensional Fourier transform ∂H _z ^dc(sample) /∂z(k _x , k _y , z′+Δz) regarding the direction is output (step (m1)). Further, for example, the first derivative of the in-plane components (x, y components) of the DC magnetic field at the probe position z=z' with respect to the vibration direction (z direction) of the probe 10 in the plane (x, y) of the scanning region y) two-dimensional Fourier transform in the direction ∂H _x ^dc(sample) /∂z(k _x , k _y , z'), ∂H _y ^dc(sample) /∂z(k _x , k _y , z') When the information corresponding to Two-dimensional Fourier transform ^of _the first derivative with respect to the direction) in the in-plane ( _x , _y ) direction of the scanning area ∂H Information corresponding to _y ^{dc (sample)} / ∂z (k _x , k _y , z'+Δz) is output.
Each of the above conversions in the distance conversion filter calculator 670 is performed based on a combination (k _x , k _y ) of two wave numbers in the in-plane (x, y) direction within the scanning region. _Specifically , _such conversion of _the tip position is performed by adding _exp ( This can be done by multiplying by -(k _x ² + k _y ² ) ^1/2 Δz).

FIG. 6 is a diagram schematically explaining a DC magnetic field measuring device 2000 according to another embodiment. In FIG. 6, elements that have already appeared in FIGS. 1 to 5 are given the same reference numerals as those in FIGS. 1 to 5, and their explanations may be omitted. The DC magnetic field measuring device 2000 has an AC magnetic field generator 2300 instead of the AC magnetic field generator 300, and is configured so that the AC magnetic field generator 2300 can also function as an external DC magnetic field generator, as shown in FIG. This is different from the DC magnetic field measuring device 1000 of . That is, the DC magnetic field measuring device 2000 includes an AC/DC current source 2330 instead of the AC current source 320 and the DC current source 730. The AC/DC current source 2330 is a current source that can supply not only an AC current but also a current in which a DC current is superimposed on an AC current, if necessary. The alternating current magnetic field generator 2300 includes an electromagnet including an electromagnetic core 2320 and a coil 2310 wound around the electromagnetic core 2320, and an alternating current/direct current that supplies alternating current and optionally direct current to the coil 2310 of the electromagnet. A current source 2330 is provided. The AC/DC current source 2330 supplies a voltage or current signal of the AC component of the supplied current to the detector 440 as a reference signal. The AC magnetic field generator 2300 further includes a changeover switch 2340, which allows the user to switch between supplying the current from the AC/DC current source 2330 to the electromagnetic coil 2320 or to the air core coil 310. can. The DC magnetic field measuring device 2000 further includes a parameter fitting calculator 2800. In one embodiment, the parameter fitting calculator 2800 calculates the following when the electromagnet is used as the AC magnetic field generator 2300 (that is, when the AC/DC current source 2330 supplies AC current to the electromagnetic coil 2320): The measurement results of the component of the DC magnetic field parallel to the AC magnetic field are obtained when the air-core coil 310 is used as an AC magnetic field generator (that is, when AC current from the AC/DC current source 2330 is supplied to the air-core coil 310). In order to match the ^measurement results of Optimize the two ratios between H ^ac /∂z and the second derivative of the amplitude of the alternating magnetic field at the position of the probe 10 with respect to the vibration direction of the probe 10 ∂ ² H ^ac /∂z ² Accordingly, it may be possible to determine the ratio between the two. In another embodiment, the parameter fitting calculator 2800 uses the electromagnet described above as the AC magnetic field generator 2300 (that is, when the AC/DC current source 2330 supplies AC current to the electromagnetic coil 2320). When the air-core coil 310 is used as an AC magnetic field generator (i.e., when the air-core coil 310 is used as an AC magnetic field generator, The amplitude H ^ac of the alternating magnetic field at the position of the probe 10 and the amplitude of the alternating magnetic field at the position of the probe 10 are adjusted to match the measurement result when the alternating current from the direct current source 2330 is supplied to the air-core coil 310. The first derivative ∂H ^ac /∂z with respect to the vibration direction (z direction) of the probe 10 and the second derivative ∂ ² of the amplitude of the alternating current magnetic field at the position of the probe 10 with respect to the vibration direction of the probe 10. It may be possible to determine the two ratios by optimizing the two ratios between H ^ac /∂z ² . Even with the DC magnetic field measuring device 2000 having such a configuration, the effects of the DC magnetic field measuring device and method of the present invention can be obtained.

In the above description of the present invention, the DC magnetic field measurement apparatuses 1000 and 2000 and the DC magnetic field measurement method in which the processing by the direction conversion filter calculation unit 660 is applied before the processing by the distance conversion filter calculation unit 670 are taken as examples. However, the present invention is not limited to this form. For example, it is also possible to provide a DC magnetic field measurement device and a DC magnetic field measurement method in which the processing by the distance conversion filter calculation unit 670 is first applied, and then the processing by the direction conversion filter calculation unit 660 is applied.

(Principle of measurement: measurement of DC magnetic field)
The operating principle of the DC magnetic field measuring device of the present invention and the measurement principle of the DC magnetic field measuring method of the present invention will be explained.
In the xyz coordinate system, the vibration direction of the probe is assumed to be the z direction. When a superparamagnetic probe is magnetized in response to the alternating magnetic field by applying an alternating magnetic field (for example, from an air-core coil) in the direction of vibration of the probe, the tip will be magnetized by the interaction between the magnetic moment of the tip and the alternating magnetic field. Due to the magnetic force acting on the cantilever, the spring constant of the cantilever changes periodically. The effective spring constant k _eff of the cantilever is

（ｋ_０：カンチレバー固有のバネ定数、Δｋ：実効的バネ定数の周期的変化の振幅、ω_ｍ：交流磁場の角周波数）
で表される。フックの法則Ｆ＝－ｋｚから

( _k0 : spring constant specific to the cantilever, Δk: amplitude of periodic change in effective spring constant, _ωm : angular frequency of alternating magnetic field)
It is expressed as From Hooke's law F=-kz

であるから、実効的バネ定数の変化は磁気力の勾配に対応する。実効的バネ定数が角周波数ω_ｍで周期的に変化するカンチレバーを、カンチレバーの固有共振周波数ω_０（＝（ｋ_０／ｍ）^１／２、ｍはカンチレバーの質量）で強制振動させると、カンチレバーのｚ方向の運動方程式は

Therefore, the change in the effective spring constant corresponds to the gradient of the magnetic force. When a cantilever whose effective spring constant changes periodically at an angular frequency ω _m is forced to vibrate at the cantilever's natural resonance frequency ω ₀ (=(k ₀ /m) ^1/2 , where m is the mass of the cantilever), the cantilever The equation of motion in the z direction is

（ｍ：探針質量、γ：減衰係数、Ｆ_０：加振力の振幅、ｚ：探針の座標）
で表される。Δｋ＜ｋ_０かつΔｋ＜＜ｍγω_０のとき、解は

(m: tip mass, γ: attenuation coefficient, F ₀ : amplitude of excitation force, z: tip coordinates)
It is expressed as When Δk<k ₀ and Δk<<mγω ₀ , the solution is

となり、探針振動に狭帯域の周波数変調（ＦＭ変調）が発生する。探針振動の検出信号を周波数復調（ＦＭ復調）した信号（ＦＭ復調信号：）から、角周波数ω_ｍで振動する成分（ω_ｍｔ成分）を抽出すると、実効的バネ定数の変化に対応する磁気力勾配を測定することができる。ＦＭ復調信号からのω_ｍｔ成分の抽出は、例えば、ＦＭ復調信号を、交流磁場発生器（例えば空芯コイル）の交流電流源の電圧信号を参照信号に用いてロックイン検出（同期検波）することにより行うことができる。以下、ω＝ω_ｍとする。探針位置の磁場Ｈは

Therefore, narrowband frequency modulation (FM modulation) occurs in the tip vibration. When a component that vibrates at an angular frequency ω _m (ω _m t component) is extracted from a signal obtained by frequency demodulating (FM demodulating) the probe vibration detection signal (FM demodulated signal: ), it corresponds to a change in the effective spring constant. Magnetic force gradients can be measured. To extract the ω _m t component from the FM demodulated signal, for example, the FM demodulated signal is subjected to lock-in detection (synchronous detection) using a voltage signal of an AC current source of an AC magnetic field generator (for example, an air-core coil) as a reference signal. This can be done by Hereinafter, ω=ω _m . The magnetic field H at the probe position is

（Ｈ^ｄｃ：試料からの直流磁場、Ｈ^ａｃ：交流磁場発生器からの交流磁場の振幅）
で表される。本明細書において、数式中の太字はベクトル量を意味し、数式中でベクトルを太字で表記しない場合は当該ベクトルのノルムを意味する。超常磁性探針に誘起される磁気モーメントｍは

(H ^dc : DC magnetic field from the sample, H ^ac : amplitude of the AC magnetic field from the AC magnetic field generator)
It is expressed as In this specification, boldface in the formula means a vector quantity, and when a vector is not written in boldface in the formula, it means the norm of the vector. The magnetic moment m induced in the superparamagnetic tip is

（χ：超常磁性探針の磁化率）
で表される。磁場Ｈ中に存在する磁気モーメントｍの位置エネルギーＵは

(χ: Magnetic susceptibility of superparamagnetic tip)
It is expressed as The potential energy U of the magnetic moment m existing in the magnetic field H is

で表される。探針に作用する磁気力Ｆのｚ方向成分Ｆ_ｚの勾配Ｆ_ｚ’は

It is expressed as The gradient _Fz ' of the z-direction component _Fz of the magnetic force F acting on the probe is

であるから、その角周波数ωで振動する成分（ωｔ成分）Ｆ_ｚ’（ωｔ）は

Therefore, the component that vibrates at the angular frequency ω (ωt component) F _z '(ωt) is

である。直流磁場が試料から発生することを想定し、Ｈ^ｄｃをＨ^{ｄｃ（ｓａｍｐｌｅ）}と書き直す。探針位置の交流磁場がｚ軸方向であるとき（例えば空芯コイルの平面内の中心からの交流磁場は、空芯コイルの軸方向である。空芯コイルの平面内の中心に探針が配置され、空芯コイルの軸方向がｚ軸方向であるならば、探針位置の交流磁場もｚ軸方向となる。）、探針位置の磁場Ｈは、ｚ軸方向の単位ベクトルｋ_ｚおよび交流磁場Ｈ^ａｃのｚ成分の振幅Ｈ_ｚ ^ａｃを用いて

It is. Assuming that a DC magnetic field is generated from the sample, H ^dc is rewritten as H ^{dc (sample)} . When the AC magnetic field at the probe position is in the z-axis direction (for example, the AC magnetic field from the center in the plane of the air-core coil is in the axial direction of the air-core coil. (If the axial direction of the air-core coil is in the z-axis direction, the alternating current magnetic field at the probe position will also be in the z-axis direction.), The magnetic field H at the probe position is expressed by the unit vector k _z in the z-axis direction and Using the amplitude H ^{z ac} of the z component of the alternating current magnetic field _H ^ac

で表され、超常磁性探針に誘起される磁気モーメントｍは

The magnetic moment m induced in the superparamagnetic tip is expressed as

となるから、磁気力勾配のωｔ成分において、試料からの直流磁場Ｈ^{ｄｃ（ｓａｍｐｌｅ）}のうちｚ成分Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}だけが関与して、測定可能量Ｆ_ｚ’（ωｔ）は

Therefore, in the ωt component of the magnetic force gradient, only the z component H _z ^{dc (sample)} of the DC magnetic field H ^{dc (sample)} from the sample is involved, and the measurable quantity F _z '(ωt) is

となる。本発明では、測定可能量Ｆ_ｚ’（ωｔ）から、試料からの直流磁場のｚ成分Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}並びにその１階微分∂Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ及び２階微分∂^２Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２を分離して抽出する方法を提案する。

becomes. In the present invention, from the measurable quantity F _z '(ωt), the z component of the DC magnetic field from the sample H _z ^{dc (sample)} , its first derivative ∂H _z ^{dc (sample)} /∂z, and the second derivative ∂ ² We propose a method to separate and extract H _z ^dc(sample) /∂z ² .

Consider a case where an air-core coil is used as an AC magnetic field source and an AC magnetic field H _z ^{ac (coil)} in the axial direction (z direction) centered on the air-core coil is applied to a superparamagnetic probe. The vibration amplitude of the probe is at most a few tens of nanometers, which is much smaller than the size of the air-core coil, so the magnetic field and magnetic field gradient applied to the vibrated probe are expressed as coil constants C ₁ , C ₂ , and C ₃ ,

とおくことができる。探針の振動振幅は定数Ｃ_１、Ｃ_２、Ｃ_３に含まれるＨ_ｚ ^{ａｃ（ｃｏｉｌ）}並びにその１階微分∂Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}／∂ｚおよび２階微分∂^２Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}／∂ｚ^２は、空芯コイルの形状から解析的に求めることができる。例えば、軸方向（厚み方向）がｚ軸方向、面内方向がｘｙ方向であり、巻線の太さがゼロの１回巻と見なせる半径ａの理想的な空芯コイルに電流Ｉが流れる場合についてビオー・サバールの法則を適用すると、コイル中心からｚ方向にｚだけ離れた位置における磁場（これはｚ軸方向である。）、並びにその１階微分および２階微分は

You can leave it as The vibration amplitude of the tip is determined by the constants C ₁ , C ₂ , and C ₃ including Hz _ac ^(coil) , its first derivative ∂H _z ^ac(coil) /∂z, and its second derivative ∂ ² _Hz ^{ac(coil) )} /∂z ² can be analytically determined from the shape of the air-core coil. For example, when a current I flows through an ideal air-core coil with radius a, which can be considered as one turn with zero thickness, where the axial direction (thickness direction) is the z-axis direction, the in-plane direction is the xy direction, and the winding thickness is zero. Applying the Biot-Savart law to

である。したがって、Ｃ_１はｚ座標によらず同符号である、Ｃ_２はｚ＞０においてＣ_１と異符号、ｚ＜０においてＣ_１と同符号である。Ｃ_３は０≦ｚ＜ａ／２においてＣ_１と異符号、ｚ＞ａ／２においてＣ_１と同符号である。現実の空芯コイルは、内半径ａ_１、外半径ａ_２、長さ２ｌの多層円筒ソレノイドとみなすことができる。該多層円筒ソレノイドに全巻数Ｎが均等に巻かれていて、電流Ｉが流れると仮定し、コイルの中心をｚ＝０とする。中心軸上一端からｚ＋ｌの距離の点Ｐの磁界Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}は

It is. Therefore, C ₁ has the same sign regardless of the z coordinate, C ₂ has a different sign from C ₁ when z>0, and has the same sign as C ₁ when z<0. C ₃ has _a different sign from C 1 when 0≦z _{<a/2, and has the same sign as C 1 when z>} a/2. An actual air-core coil can be regarded as a multilayer cylindrical solenoid with an inner radius a ₁ , an outer radius a ₂ , and a length of 2 l. Assume that the multilayer cylindrical solenoid has a total number of turns N evenly wound, a current I flows through it, and the center of the coil is set to z=0. The magnetic field H _z ^{ac (coil)} at a point P at a distance of z+l from one end on the central axis is

で表される。これをｚで偏微分することにより１階微分∂Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}／∂ｚおよび２階微分∂^２Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}／∂ｚ^２が得られる。実際の計算にあたっては数値微分を好ましく用いることができる。該多層円筒ソレノイドにおいても、Ｃ_１はｚ座標によらず同符号であり、ｚ＞０においてＣ_１に対してＣ_２は異符号であり、Ｃ_３はｚが０から正に増加するとき異符号から０を経由して同符号に変化する。探針を空芯コイルの面内（ｘｙ）方向の中心かつ軸方向のｚ＞０の位置に配置するとき、式（１２）は

It is expressed as By partially differentiating this with respect to z, a first-order differential ∂H _z ^ac(coil) /∂z and a second-order differential ^{∂ 2} H _z ^ac(coil) /∂z ² are obtained. Numerical differentiation can be preferably used in actual calculations. In this multilayer cylindrical solenoid, C ₁ has the same sign regardless of the z coordinate, C 2 has a different sign with respect to C ₁ when z>0, and _{C 3 has} a different sign when z increases positively from 0. It changes from the sign to the same sign via 0. When the probe is placed at the center of the air-core coil in the in-plane (xy) direction and at a position where z>0 in the axial direction, equation (12) is

となる。振幅を比較することにより

becomes. By comparing the amplitude

が得られる。式（１７）において左辺が測定可能量である。空芯コイルの中心軸上においてＣ_１の符号は不変であるので、ここではＣ_１＞０を仮定している。式中、σ（Ｃ_３）はＣ_３がＣ_１と同符号か異符号かを表す関数であり、

is obtained. In equation (17), the left side is the measurable quantity. Since the sign of C ₁ does not change on the central axis of the air-core coil, it is assumed here that C ₁ >0. In the formula, σ(C ₃ ) is a function indicating whether C ₃ has the same sign as C ₁ or a different sign,

で定義される。すなわちＣ_３がＣ_１と同符号のときσ（Ｃ_３）＝＋１、異符号のときσ（Ｃ_３）＝－１である。探針の振動方向（ｚ軸方向）に交差する面内（ｘｙ面内方向）に定められた走査領域を探針で走査しながら測定を行う、すなわち、走査領域内の各（ｘ，ｙ）座標について測定を行うことにより、測定可能量

Defined by That is, when C ₃ has the same sign as C ₁ , σ(C ₃ )=+1, and when they have different signs, σ(C ₃ )=−1. Measurement is performed while the probe scans a scanning area defined in a plane (xy plane direction) that intersects the vibration direction (z-axis direction) of the probe, that is, each (x, y) within the scanning area Measurable quantities by making measurements on coordinates

（すなわち式（１７）の左辺）の走査領域内（ｘｙ面内）における分布：

(i.e., the left side of equation (17)) within the scanning area (in the xy plane):

が得られる。その面内方向（ｘ及びｙ）についてのフーリエ変換（二次元フーリエ変換）は、式（１７）及びフーリエ変換の線型性から、

is obtained. The Fourier transform (two-dimensional Fourier transform) in the in-plane direction (x and y) is given by equation (17) and the linearity of the Fourier transform.

を満たす。式中、ｋ_ｘ及びｋ_ｙは面内方向における波数である。フーリエ変換により、（ｘ，ｙ）空間が波数空間（ｋ_ｘ，ｋ_ｙ）に写されている。式中、

satisfy. In the formula, k _x and k _y are wave numbers in the in-plane direction. The (x, y) space is mapped to the wavenumber space (k _x , k _y ) by Fourier transformation. During the ceremony,

はそれぞれ、

are each

の面内方向（ｘ及びｙ）についてのフーリエ変換である。ここで、Ｓａｉｔｏら（H. Saito, et al., Journal of Magnetism and Magnetic Materials 191 (1999) 153-161）は、座標ｒ’に分布する磁荷分布ρ（ｒ’）により座標ｒに発生する磁場Ｈ（ｒ）が、座標ｒに存在する磁気モーメントｍに及ぼす磁気力Ｆのｚ方向成分Ｆ_ｚの勾配Ｆ_ｚ’（ｒ）

This is the Fourier transform in the in-plane direction (x and y) of . Here, Saito et al. (H. Saito, et al., Journal of Magnetism and Magnetic Materials 191 (1999) 153-161) explained that the magnetic charge distribution ρ(r') distributed at the coordinate r' causes the magnetic charge to be generated at the coordinate r. Gradient Fz'(r) of the z-direction component _Fz of the magnetic force F exerted by the magnetic field H(r) on the magnetic moment m existing at coordinate _r

を、積分

, the integral

で与える伝達関数Ｇ_ρ（ｒ）の解析解を報告しており、そのｘ及びｙに関するフーリエ変換が

We report the analytical solution of the transfer function G _ρ (r) given by , and its Fourier transform with respect to x and y is

（ｋ_ｘ，ｋ_ｙは波数（空間周波数））
で表されることを報告している。Ｓａｉｔｏの結果（式（２６））を用いると、式（２１）において

(k _x , k _y are wave numbers (spatial frequencies))
It is reported that it is expressed as Using Saito's result (Equation (26)), in Equation (21),

である。式中、ρ（ｋ_ｘ，ｋ_ｙ，ｚ_０）は、ｚ＝ｚ_０における（仮想的な）磁荷分布のｘ及びｙについてのフーリエ変換である。ｍ_ｚ／（２μ_０）＝１で規格化すると、式（２１）から

It is. In the formula, ρ(k _x , k _y , z ₀ ) is the Fourier transform of the (virtual) magnetic charge distribution at z=z ₀ with respect to x and y. When normalized by m _z /(2μ ₀ )=1, from equation (21),

であるから、Ｃ_１について

Therefore, for C ₁

である。以下Ｃ_２、Ｃ_３についても同様にして、

It is. Similarly for C ₂ and C ₃ below,

を得る。すなわち、測定可能量の面内方向についてのフーリエ変換（式（２１）左辺、式（３０ａ）～（３０ｃ）右辺第２項）から、コイル定数Ｃ_１、Ｃ_２、Ｃ_３、及び面内方向の波数ｋ_ｘ、ｋ_ｙに基づいて、探針位置における試料からの直流磁場のｚ成分Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}並びにその１階微分（勾配）∂Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ}／∂ｚ及び２階微分∂^２Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ}／∂ｚ^２の、それぞれの面内方向（ｘ及びｙ）についてのフーリエ変換（左辺）を分離抽出することができる（以下においてこの分離抽出処理を「波数フィルタ」ということがある。）。分離抽出された各左辺をｋ_ｘ、ｋ_ｙについて二次元逆フーリエ変換することにより、探針位置における試料からの直流磁場のｚ成分Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ）並びにその１階微分（勾配）∂Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ}／∂ｚ（ｘ，ｙ，ｚ）及び２階微分∂^２Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ}／∂ｚ^２（ｘ，ｙ，ｚ）を復元することができる。
Ｃ_３がＣ_１と同符号（Ｃ_３＞０）である場合には、σ（Ｃ_３）＝＋１であるので、式（３０ａ）～（３０ｃ）は

get. That is, from the Fourier transform of the measurable quantity in the in-plane direction (the left side of equation (21), the second term on the right side of equations (30a) to (30c)), the coil constants C ₁ , C ₂ , C ₃ and the in-plane direction Based on ^the wavenumbers k _{x and k y} ^of The Fourier transform (left side) of ∂ ² _Hz ^{dc (sample} / ∂z ² in each in-plane direction (x and y) can be separated and extracted (hereinafter, this separation and extraction process will be referred to as a "wavenumber filter"). ).By performing a two-dimensional inverse Fourier transform on each separated _and extracted _left side with ^respect to _k , z) and its first derivative (gradient) ∂H _z ^dc(sample /∂z(x, y, z) and second derivative ∂ ² H _z ^dc(sample /∂z ² (x, y, z)) Can be restored.
When C ₃ has the same sign as C ₁ (C ₃ >0), σ(C ₃ )=+1, so equations (30a) to (30c) are

となる。Ｃ_３がＣ_１と異符号（Ｃ_３＜０）である場合には、σ（Ｃ_３）＝－１であるので、式（３０ａ）～（３０ｃ）は

becomes. When C ₃ has a different sign from C ₁ (C ₃ <0), σ(C ₃ )=-1, so equations (30a) to (30c) are

となる。
Ｃ_３がＣ_１と同符号（Ｃ_３＞０）である場合（式（３１ａ）～（３１ｃ））には、全ての（ｋ_ｘ，ｋ_ｙ）について右辺の分母が正であるので、計算に支障は生じない。これに対し、Ｃ_３がＣ_１と異符号（Ｃ_３＜０）である場合（式（３２ａ）～（３２ｃ））には、

becomes.
When C ₃ has the same sign as C ₁ (C ₃ >0) (Equations (31a) to (31c)), the denominator on the right side is positive for all (k _x , k _y ), so the calculation There will be no problem. On the other hand, when C ₃ has a different sign from C ₁ (C ₃ <0) (Equations (32a) to (32c)),

を満たす特異点（ｋ_ｘ，ｋ_ｙ）において式（３２ａ）～（３２ｃ）右辺の分母がゼロ：

At the singular point (k _x , k _y ) that satisfies the following, the denominator on the right side of equations (32a) to (32c) is zero:

になるので、式（３２ａ）～（３２ｃ）の計算が行えない場合があり得る。この波数（ｋ_ｘ，ｋ_ｙ）では、測定可能量のフーリエ変換（式（２８））が次のようにゼロになる。

Therefore, calculations of equations (32a) to (32c) may not be possible. At this wave number (k _x , k _y ), the Fourier transform of the measurable quantity (Equation (28)) becomes zero as follows.

この現象は、２χ∂^２Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}Ｈ_ｚ ^ａｃ／∂ｚ^２像の内訳において、∂^２Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２像成分および∂Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ像成分の和からＨ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}像成分が差し引かれることで、像が相互にキャンセルする現象である。この場合には、式（３２ａ）～（３２ｃ）の波数フィルタの分母もゼロになるので、式（３２ａ）～（３２ｃ）そのままでは、各成分の分離抽出を行うことはできない。そこで、信号に位相が９０°進んだ十分小さいノイズｉε（εは実数）が含まれているものとして、すなわち、式（２８）を

This phenomenon is explained by the following _two image components: 2χ∂ ² H _z ^dc(sample) H _z ^ac /∂z ² image components and ∂ ² H _z ^{dc(sample )} /∂z ² image components This is a phenomenon in which the images cancel each other out by subtracting the H _z ^{dc (sample)} image component from the sum of the image components. In this case, since the denominators of the wave number filters in equations (32a) to (32c) also become zero, it is not possible to separate and extract each component using equations (32a) to (32c) as they are. Therefore, assuming that the signal contains a sufficiently small noise iε (ε is a real number) whose phase is advanced by 90°, that is, equation (28) is

に変更して、波数フィルタを次のように構成する。

and configure the wavenumber filter as follows.

式中、「ＲＥ」は引数の実部を与える関数である。Ｃ_１について波数フィルタの分母を実数化すると

In the formula, "RE" is a function that gives the real part of the argument. When converting the denominator of the wave number filter into a real number for C ₁ ,

となる。以下Ｃ_２、Ｃ_３についても同様にして、

becomes. Similarly for C ₂ and C ₃ below,

となる。式（３７ａ）～（３７ｃ）及び（３９ａ）～（３９ｃ）より、Ｃ_３がＣ_１と異符号である（σ（Ｃ_３）＝－１）場合の新たな波数フィルタが次のように得られる。

becomes. From equations (37a) to (37c) and (39a) to (39c), a new wavenumber filter when C ₃ has a different sign from C ₁ (σ(C ₃ )=-1) is obtained as follows. It will be done.

なお波数フィルタの分母と分子を｜Ｃ_１｜で規格化している。式中、ε’はεに対応する非ゼロの微小実定数であり、その値としては、ε’^２が

Note that the denominator and numerator of the wave number filter are normalized by |C ₁ |. In the formula, ε' is a non-zero infinitesimal real constant corresponding to ε, and its value is ε' ²

のゼロ点近傍を除く値に対して十分小さくなる値を適宜選択できる。そのようなε’としては、例えば、｜ε’｜が式（４１）のゼロ点すなわち式（３４）の解をなす波数（ｋ_ｘ ^２＋ｋ_ｙ ^２）^１／２（式（３３））に対して十分小さい値、例えば、｜ε’｜の当該波数に対する比：

A value that is sufficiently smaller than the value near the zero point of can be appropriately selected. As such ε', for example, |ε'| is the zero point of equation (41), that is, the wave number (k _x ² + k _y ² ) ^1/2 (equation (33)) that forms the solution to equation (34). For example, the ratio of |ε'| to the corresponding wavenumber:

が０．１未満である非ゼロの実定数ε’を好ましく採用できる。波数フィルタの精度の観点からは、当該比（式（４２））の値はより好ましくは１０^－２未満、さらに好ましくは１０^－３未満、特に好ましくは１０^－４未満である。なお、式（４１）がゼロになる（すなわち式（３４）の左辺がゼロになる）波数（ｋ_ｘ，ｋ_ｙ）においては、波数フィルタの入力である式（３５）の左辺がそもそもゼロになるので、ε’の選び方は実用上の問題をもたらすことはないと考えられ、当業者は波数フィルタの計算が所望の精度を得られるようにε’を適切に選択することができる。また、抽出フィルタによる分離抽出の計算を行う計算機の精度を考慮すると、εは

A non-zero real constant ε′ in which is less than 0.1 can be preferably employed. From the viewpoint of accuracy of the wave number filter, the value of the ratio (formula (42)) is more preferably less than 10 ⁻² , still more preferably less than 10 ⁻³ , particularly preferably less than 10 ⁻⁴ . Note that at wavenumbers (k _x , k _y ) where equation (41) becomes zero (that is, the left side of equation (34) becomes zero), the left side of equation (35), which is the input of the wave number filter, becomes zero in the first place. Therefore, the selection of ε' is not considered to pose any practical problems, and those skilled in the art can appropriately select ε' so that the calculation of the wave number filter can obtain the desired accuracy. Also, considering the accuracy of the computer that calculates the separation and extraction using the extraction filter, ε is

（式中、δは抽出フィルタの処理を行う計算機のマシンイプシロンを表す。）
を満たすことが好ましい。

(In the formula, δ represents the machine epsilon of the computer that processes the extraction filter.)
It is preferable to satisfy the following.

According to this new wavenumber filter (Equations (40a) to (40c)), the denominator on the right side is always kept positive. In other words, in the wavenumber filters of Equations (32a) to (32c), the denominator on the right side is zero. Since the denominator on the right _side is kept non- _zero even at the singular point (k _x , _{k y} ) where it becomes can be processed without any problems.

Calculating the magnetic field in real space from the wavenumber filter extraction results is as follows:
(a) Integrating the second-order differential extraction result (Equation (31a) or (40a)) in the z-direction of the magnetic field (the vibration direction of the tip) by the wave number filter twice in the z-direction in Fourier space. After obtaining information on the Fourier transform of the magnetic field by (step (h2-0)), subjecting it to two-dimensional inverse Fourier transform for k _x and k _y (step (i2-0));
(b) Integrate the first-order differential extraction result (Equation (31b) or (40b)) in the z-axis direction of the magnetic field (the vibration direction of the tip) by the wave number filter once in the z-direction in Fourier space. After obtaining information on the Fourier transform of the magnetic field by (step (h1-0)), this is subjected to two-dimensional inverse Fourier transform for k _x and k _y (step (i1-0)), or
(c) Two-dimensional inverse Fourier transform of the magnetic field extraction result (Equation (31c) or (40c)) by the wave number filter with respect to k _x and k _y (step (i0));
This can be done by When an air-core coil is used as an external AC magnetic field generator, (a) or (c) is preferable from the viewpoint of increasing signal strength. Further, among the components extracted by the wave number filter, the second-order differential has the richest amount of information, so (a) is preferable from the viewpoint of making use of the amount of information included in the second-order differential. However, the magnetic field obtained by integrating the second-order differential twice in Fourier space does not include the component (k _x , k _y ) = (0, 0) (a constant value component that does not depend on in-plane coordinates), so The component of (k _x , k _y )≠(0,0) is obtained by (a), and the measurement sensitivity and the calibration of the constant value component of (k _x , k _y )=(0,0) are obtained by (c). It is particularly preferable to carry out by.

The above case (c) is expressed as follows.

ここで、関数ＩＦＴは、引数の逆フーリエ変換を意味する。上記（ｃ）の場合においては、面内座標（ｘ，ｙ）に依存しない一定値成分（すなわち（ｋ_ｘ，ｋ_ｙ）＝（０，０）の成分）の情報も波数フィルタの抽出結果に含まれているので、逆フーリエ変換により一定値成分を含む磁場像を直接得ることができる。

Here, the function IFT means inverse Fourier transform of the argument. In case (c) above, information on constant value components that do not depend on in-plane coordinates (x, y) (i.e., components of (k _x , k _y ) = (0, 0)) is also included in the extraction results of the wave number filter. Therefore, a magnetic field image containing a constant value component can be directly obtained by inverse Fourier transform.

In the case of (a) above, the operation (step (h2-0)) of integrating the extraction result of the second derivative of the magnetic field by the wave number filter (Equation (31a) or (40a)) twice in the z direction in Fourier space is , can be done using the following relationship.

このスペクトルを二次元逆フーリエ変換することにより、磁場の一定値成分を含まない磁場像を得ることができる（工程（ｉ２－０））。これを式に表すと次の通りである。

By subjecting this spectrum to two-dimensional inverse Fourier transformation, a magnetic field image that does not include a constant value component of the magnetic field can be obtained (step (i2-0)). This can be expressed as follows.

In the case of (b) above, the operation (step (h1-0) ) can be done using the following relationship.

上記（ａ）の場合と同様に、このスペクトルを二次元逆フーリエ変換することにより、磁場の一定値成分を含まない磁場像を得ることができる（工程（ｉ１－０））。これを式に表すと次の通りである。

As in the case of (a) above, by subjecting this spectrum to two-dimensional inverse Fourier transform, a magnetic field image that does not contain a constant value component of the magnetic field can be obtained (step (i1-0)). This can be expressed as follows.

The magnetic field image H _z ^dc(sample) (x, y, z) obtained by the above equation (44) and the magnetic field image H _z ^dc(sample) (x, y, z; (k _x , k _y )≠(0,0)) is that the constant value component of the magnetic field ((k _x , k _y )=(0,0) component) is not included in the former. However, the latter is not included.

Calibration of the magnetic field value in the H _z ^dc(sample) (x, y, z) image (step (j)) can be performed, for example, as follows. In the H _z ^{dc (sample)} (x, y, z) image obtained by the above formula (44),

を満たす面内座標（ｘ’，ｙ’）の集合が、測定試料からの磁場がゼロである等値線を形成する（工程（ｊ３））。実際に測定を行った測定点（格子点）において値がゼロにならず、隣接する２つの測定点において値が異符号である場合には、式（４９）を満たす面内座標（ｘ’，ｙ’）を補間により求めることができる。
外部交流磁場Ｈ_ｚ ^ａｃに平行な方向の外部直流磁場であって、各面内座標について同一の強度を有する、強度のわかった外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ）}を、探針に印加した条件で、各面内座標（ｘ，ｙ）について測定を行う。そのような測定は、外部直流磁場源（例えば磁心と該磁心に巻回されたコイルとを備える電磁石等）から一様な外部直流磁場、すなわち

A set of in-plane coordinates (x', y') that satisfy the following form an isovalue line where the magnetic field from the measurement sample is zero (step (j3)). If the value is not zero at the actual measurement point (lattice point) and the values at two adjacent measurement points have different signs, then the in-plane coordinates (x', y') can be obtained by interpolation.
Conditions in which an external DC magnetic field H _z ^{dc (ex)} of known intensity, ^which is an external DC magnetic field in a direction parallel to the external AC magnetic field H _z ac and has the same intensity for each in-plane coordinate, is applied to the probe. Then, measurements are made for each in-plane coordinate (x, y). Such measurements are performed by applying a uniform external DC magnetic field from an external DC magnetic field source (e.g. an electromagnet with a magnetic core and a coil wound around the core), i.e.

である外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ）}を探針に印加することによって行ってもよい。外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ）}が「一様な外部直流磁場」であること、すなわち式（５０）を満たすことは、波数フィルタ処理を通じて得られる∂^２Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｘ，ｙ，ｚ）像のゼロクロス画素の集合（値がゼロとなる面内座標（ｘ，ｙ）の集合と、値が異符号となる隣接する２つの測定点の組み合わせ（（ｘ_１，ｙ_１）、（ｘ_２，ｙ_２））との和集合。）および、波数フィルタ処理を通じて得られる∂Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｘ，ｙ，ｚ）像のゼロクロス画素の集合が、外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ）}を印加しても変化しないことと言い換えることができる、これにより判断できる。∂^２Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｘ，ｙ，ｚ）像、及び、∂Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｘ，ｙ，ｚ）像は、ゼロクロス画素の空でない集合を必ず有していることを注記する。上記判断において、∂Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｘ，ｙ，ｚ）像としては、波数フィルタ処理により抽出された∂^２Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｋ_ｘ，ｋ_ｙ，ｚ）をフーリエ空間上でｚ方向に１回積分してから逆フーリエ変換することにより得られる∂Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｘ，ｙ，ｚ）像を好ましく用いることができる。また、そのような測定は、外部直流磁場発生器７００の電磁石のコイル７２０に供給する直流電流、及び、外部直流磁場発生器７００の電磁石と探針との位置関係を同一に保ちながら走査領域を探針で走査することにより行ってもよい。そのような走査は、例えば、外部直流磁場発生器７００の電磁石と探針との位置関係を固定して、試料のみを面内方向に移動させることにより、行うことができる。
外部交流磁場Ｈ_ｚ ^ａｃに平行な方向であって、強度のわかった一様な外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ）}を、探針に印加した条件で、各面内座標（ｘ，ｙ）について測定を行ったとき、上記式（４４）の右辺により得られる外部交流磁場Ｈ_ｚ ^ａｃに平行な方向の磁場像（ここでは垂直磁場像）は

This may be done by applying an external DC magnetic field H _z ^dc(ex) to the probe. The fact that the external DC magnetic field H _z ^dc(ex) is a "uniform external DC magnetic field", that is, it satisfies equation (50), is obtained through wave number filtering as ∂ ² H _z ^dc(sample) /∂z ² A set of zero-crossing pixels of the (x, y, z) image (a set of in-plane coordinates (x, y) whose value is zero, and a combination of two adjacent measurement points whose values have opposite signs ((x ₁ , y ₁ ), (x ₂ , y ₂ ))), and the set of zero-crossing pixels of the ∂H _z ^dc(sample) /∂z(x, y, z) image obtained through wave number filtering is , which can be said to mean that it does not change even if an external DC magnetic field H _z ^dc(ex) is applied, and can be determined based on this. The ∂ ² H _z ^dc(sample) /∂z ² (x, y, z) image and the ∂H _z ^dc(sample) /∂z (x, y, z) image are non-empty sets of zero-crossing pixels. Note that it must be included. In the above judgment, the ∂H _z ^dc(sample) /∂z(x, y, z) image is the ∂ ² H _z ^dc(sample) /∂z ² (k _x , k _{y .} ^_ In addition, such a measurement is performed by using a DC current supplied to the electromagnetic coil 720 of the external DC magnetic field generator 700 and a scanning area while keeping the same positional relationship between the electromagnet of the external DC magnetic field generator 700 and the probe. This may be done by scanning with a probe. Such scanning can be performed, for example, by fixing the positional relationship between the electromagnet of the external DC magnetic field generator 700 and the probe and moving only the sample in the in-plane direction.
For each in-plane coordinate (x, y) under the condition that a uniform external DC magnetic field H _z ^{dc (ex)} of known intensity is applied to the probe in a direction parallel to the external AC magnetic field H _z ^ac . When measuring, the magnetic field image in the direction parallel to the external alternating current magnetic field _Hz ^ac (here, the perpendicular magnetic field image) obtained from the right side of the above equation (44) is

に等しい。外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ）}が一様であるとは、観察する試料面上の全ての画素の位置で、Ｈ_ｚ ^{ｄｃ（ｅｘ）}の大きさが等しいと見なせ、なおかつ磁場の勾配、∂Ｈ_ｚ ^{ｄｃ（ｅｘ）}／∂ｚ（ｘ，ｙ，ｚ）、∂^２Ｈ_ｚ ^{ｄｃ（ｅｘ）}／∂ｚ^２（ｘ，ｙ，ｚ）がゼロ近傍であることと言い換えることができる。一様な外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ）}を印加すると、式（１２）は

be equivalent to. The external DC magnetic field H _z ^{dc (ex)} is uniform because it can be assumed that the magnitude of H _z ^{dc (ex)} is equal at all pixel positions on the sample surface to be observed, and the gradient of the magnetic field is In other words, ∂H _z ^dc(ex) /∂z(x, y, z) and ∂ ² H _z ^dc(ex) /∂z ² (x, y, z) are near zero. When applying a uniform external DC magnetic field H _z ^dc(ex) , equation (12) becomes

となる。Ｈ_ｚ ^{ｄｃ（ｅｘ）}が一様な場合、

becomes. If H _z ^dc(ex) is uniform,

（好ましくは例えば、それぞれ右辺が左辺の１／１０未満であり得る。）であるから、さらに

(Preferably, for example, each right side may be less than 1/10 of the left side.)

となる。式（３１ｃ）若しくは（４０ｃ）（又は後述する式（３１ｃ’）若しくは（４０ｃ’））により、磁場の均一成分すなわち（ｋ_ｘ，ｋ_ｙ）＝（０，０）成分に対応する情報を抽出すると、

becomes. Extract information corresponding to the uniform component of the magnetic field, that is, the (k _x , k _y ) = (0, 0) component using equation (31c) or (40c) (or equation (31c') or (40c') described later). Then,

が得られる（工程（ｊ１０））。式中、α_３は後述する測定感度係数（未知）である。外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ）}を印加しないとき、すなわちＨ_ｚ ^{ｄｃ（ｅｘ）}＝０での測定結果に基づく抽出結果は

is obtained (step (j10)). In the formula, α ₃ is a measurement sensitivity coefficient (unknown) which will be described later. The extraction result based on the measurement results when no external DC magnetic field H _z ^{dc (ex)} is applied, that is, at H _z ^{dc (ex)} = 0, is

である（工程（ｊ１４））。式（５１ａ）と式（５１ｂ）との差をとると

(Step (j14)). Taking the difference between equation (51a) and equation (51b),

が得られる。Ｈ_ｚ ^{ｄｃ（ｅｘ）}が既知であれば、式（５１ｃ）から測定感度係数α_３を求めることができ（工程（ｊ１５））、さらに式（５１ａ）からＨ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}を較正できる（工程（ｊ１６））。
なお、較正用の磁場Ｈ_ｚ ^{ｄｃ（ｅｘ）}が空間的に一様でない場合には、式（１２ａ）は

is obtained. If H _z ^dc(ex) is known, the measurement sensitivity coefficient α ₃ can be obtained from equation (51c) (step (j15)), and furthermore, H _z ^dc(sample) can be calibrated from equation (51a) ( Process (j16)).
Note that if the magnetic field for calibration H _z ^dc(ex) is not uniform spatially, equation (12a) becomes

となり、波数フィルタの前提となる式にない第４項：

The fourth term, which is not in the equation and is the premise of the wave number filter, is:

が測定データに加わることで誤差が生じる。
式（５１）の値がゼロになる面内座標を（ｘ”，ｙ”）とすると（工程（ｊ１））、

is added to the measurement data, causing an error.
If the in-plane coordinates where the value of equation (51) becomes zero are (x'', y'') (step (j1)),

であるから、面内座標（ｘ”，ｙ”）の集合は、測定試料からの垂直磁場Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}が－Ｈ_ｚ ^{ｄｃ（ｅｘ）}である等値線を形成する。実際に測定を行った測定点（格子点）において値がゼロにならず、隣接する２つの測定点において値が異符号である場合には、式（５１）の値がゼロになる面内座標（ｘ”，ｙ”）を補間により求めることができる。式（４４）により得られる磁場像Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ）の較正は、式（４４）により得られる磁場像の面内座標（ｘ’，ｙ’）及び（ｘ”，ｙ”）における値が０及び－Ｈ_ｚ ^{ｄｃ（ｅｘ）}にそれぞれ対応するように、式（４４）により得られる磁場像の強度を補正する（定数倍する）ことにより、行うことができる（工程（ｊ４））。
また、式（４６）又は（４８）により得られる磁場像Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ；（ｋ_ｘ，ｋ_ｙ）≠（０，０））の較正は、式（４６）又は（４８）により得られる磁場像の上記面内座標（ｘ’，ｙ’）及び（ｘ”，ｙ”）における値が０及び－Ｈ_ｚ ^{ｄｃ（ｅｘ）}にそれぞれ対応するように、式（４６）又は（４８）により得られる磁場像の一定値成分および信号強度を補正する（例えば、定数倍して一定値を加える）ことにより、行うことができる（工程（ｊ４））。信号強度（定数倍成分）を別の方法により較正できる場合には、上記の方法で一定値成分のみを較正してもよい。

Therefore, the set of in-plane coordinates (x'', y'') forms an isoline where the vertical magnetic field H _z ^dc(sample) from the measurement sample is −H _z ^dc(ex) . If the value does not become zero at the actual measurement point (lattice point) and the values have different signs at two adjacent measurement points, the in-plane coordinate at which the value of equation (51) becomes zero (x'', y'') can be obtained by interpolation. Calibration of the magnetic field image H _z ^{dc (sample)} (x, y, z) obtained by equation (44) is performed using the in-plane coordinates (x', y') and (x'') of the magnetic field image obtained by equation (44). This can be done by correcting (multiplying by a constant) the intensity of the magnetic field image obtained by equation (44) so that the values at 0 and _−Hz ^dc(ex) respectively correspond to Process (j4)).
Furthermore, the calibration of the magnetic field image H _z ^{dc (sample)} (x, y, z; (k _x , k _y )≠(0,0)) obtained by equation (46) or (48) is performed using equation (46) _Or , the formula ⁽ 46) or (48) by correcting the constant value component and signal intensity of the magnetic field image (for example, multiplying by a constant and adding a constant value) (step (j4)). If the signal strength (constant multiplication component) can be calibrated using another method, only the constant value component may be calibrated using the above method.

In the magnetic field image H _z ^{dc (sample)} (x, y, z) obtained by equation (44), there exists an in-plane coordinate (x', y') where the magnetic field value becomes zero (satisfying equation (49)). If not (the values have the same sign at all measurement points), for example, use an ion implanter to locally demagnetize a part of the sample to form a non-magnetic region in a part of the sample. By implanting ions, preprocessing may be performed such that in-plane coordinates (x', y') where the magnetic field value becomes zero (satisfying equation (49)) are present in the scanning region. In addition, by embedding the sample in a non-magnetic matrix such as resin and polishing the surface to form a boundary between the flat sample and the non-magnetic matrix, we can create a surface where the magnetic field value becomes zero (satisfying equation (49)). Preprocessing may be performed to make the inner coordinates (x', y') exist in the scanning area.

In addition, in the magnetic field image H _z ^{dc (sample)} (x, y, z) obtained by equation (44), in-plane coordinates (x', y') that satisfy equation (49), that is, the magnetic field value becomes zero does not exist (the values have the same sign at all measurement points), the magnetic field values can be calibrated as follows. For each in-plane coordinate (x, y) under the condition that a uniform external DC magnetic field H _z ^{dc (ex)} of known intensity is applied to the probe in a direction parallel to the external AC magnetic field H _z ^ac . If there is an in-plane coordinate (x', y') where the magnetic field value is zero when measuring,

である（工程（ｊ１））。実際に測定を行った測定点（格子点）において値がゼロにならず、隣接する２つの測定点において値が異符号である場合には、式（５３）を満たす面内座標（ｘ’，ｙ’）を補間により求めることができる。すなわち、面内座標（ｘ’，ｙ’）における磁場値は、外部交流磁場Ｈ_ｚ ^ａｃに平行な方向であって、強度のわかった一様な外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ）}を探針に印加した条件で各面内座標について測定を行ったとき、式（４４）により算出される磁場値が当該面内座標（ｘ’，ｙ’）においてゼロとなる外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ）}について、値－Ｈ_ｚ ^{ｄｃ（ｅｘ）}として求めることができる。一の実施形態において、式（４４）により得られる磁場像Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ）の較正は、式（４４）により得られる磁場像の上記面内座標（ｘ’，ｙ’）における値が－Ｈ_ｚ ^{ｄｃ（ｅｘ）}に対応するように、式（４４）により得られる磁場像の強度を補正することにより、行うことができる（工程（ｊ２））。他の実施形態において、さらに、外部交流磁場Ｈ_ｚ ^ａｃに平行な方向であって、強度のわかった一様な外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ２）}であって、上記Ｈ_ｚ ^{ｄｃ（ｅｘ）}とは異なる強度を有する外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ２）}を探針に印加した条件で、各面内座標（ｘ，ｙ）について測定を行ったとき、磁場値がゼロになる面内座標（ｘ”，ｙ”）が存在したならば、

(Step (j1)). If the value is not zero at the actual measurement point (lattice point) and the values at two adjacent measurement points have different signs, then the in-plane coordinates (x', y') can be obtained by interpolation. That is, the magnetic field value at the in-plane coordinates (x', y') is in a direction parallel to the external AC magnetic field H _z ^ac , and the uniform external DC magnetic field H _z ^dc(ex) of known intensity is detected by the probe. When measuring each in-plane coordinate under the condition that the external DC magnetic field H _z ^{dc (ex )} can be determined as the value −H _z ^dc(ex) . In one embodiment, the calibration of the magnetic field image H _z ^dc(sample) (x, y, z) obtained by equation (44) is based on the in-plane coordinates (x', This can be done by correcting the intensity of the magnetic field image obtained by equation (44) so that the value in y') corresponds to -H _z ^dc(ex) (step (j2)). In another embodiment, a uniform external direct current magnetic field H _z dc ^(ex2) _of known intensity is further applied in a direction parallel to the external alternating current magnetic field H z ^ac , the external direct current magnetic field H _z ^{dc(ex2) having a known intensity} . is the in-plane coordinate ⁽ x _, ",y") exists, then

である（工程（ｊ５））。実際に測定を行った測定点（格子点）において値がゼロにならず、隣接する２つの測定点において値が異符号である場合には、式（５４）を満たす面内座標（ｘ”，ｙ”）を補間により求めることができる。すなわち、上記面内座標（ｘ’，ｙ’）とは異なる面内座標（ｘ”，ｙ”）における磁場値は、上記Ｈ_ｚ ^{ｄｃ（ｅｘ）}とは異なる強度を有する外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ２）}を探針に印加した条件で測定を行ったとき、式（４４）により算出される磁場値が当該面内座標（ｘ”，ｙ”）においてゼロとなる外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ２）}について、値－Ｈ_ｚ ^{ｄｃ（ｅｘ２）}として求めることができる。したがって、一の実施形態において、式（４４）により得られる磁場像Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ）の較正は、式（４４）により得られる磁場像の上記面内座標（ｘ’，ｙ’）及び（ｘ”，ｙ”）における値が－Ｈ_ｚ ^{ｄｃ（ｅｘ）}及び－Ｈ_ｚ ^{ｄｃ（ｅｘ２）}にそれぞれ対応するように、式（４４）により得られる磁場像の強度およびゼロ位置を補正することにより、行うことができる（工程（ｊ６））。
また、式（４６）又は（４８）により得られる磁場像Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ；（ｋ_ｘ，ｋ_ｙ）≠（０，０））の較正は、式（４６）又は（４８）により得られる磁場像の上記面内座標（ｘ’，ｙ’）及び（ｘ”，ｙ”）における値が－Ｈ_ｚ ^{ｄｃ（ｅｘ）}及び－Ｈ_ｚ ^{ｄｃ（ｅｘ２）}にそれぞれ対応するように、式（４６）又は（４８）により得られる磁場像の一定値成分および信号強度を補正する（例えば、定数倍して一定値を加える）ことにより、行うことができる（工程（ｊ６））。信号強度（定数倍成分）を別の方法により較正できる場合には、上記の方法で一定値成分のみを較正してもよい。

(Step (j5)). If the value does not become zero at the actual measurement point (lattice point) and the values have different signs at two adjacent measurement points, the in-plane coordinate (x'', y”) can be obtained by interpolation. That is, the magnetic field value at in-plane coordinates (x'', y'') different from the above-mentioned in-plane coordinates (x', y') is an external DC magnetic field H _z ^dc having a different intensity from the above-mentioned H _z ^{dc (ex). (ex2)} is applied to the probe, the external DC magnetic field H _z ^{dc( ex2)} can be determined as the value −H _z ^dc(ex2) . Therefore, in one embodiment, the calibration of the magnetic field image H _z ^dc(sample) (x, y, z) obtained by equation (44) is performed using the in-plane coordinates (x, y, z) of the magnetic field image obtained by equation (44). ', y') and (x'', y'') correspond to _-Hz ^dc(ex) and _-Hz ^dc(ex2) , respectively, and the intensity of the magnetic field image obtained by equation (44). This can be done by correcting the zero position (step (j6)).
Furthermore, the calibration of the magnetic field image H _z ^{dc (sample)} (x, y, z; (k _x , k _y )≠(0,0)) obtained by equation (46) or (48) is performed using equation (46) Or, the values at the above-mentioned in-plane coordinates (x', y') and (x'', y'') of the magnetic field image obtained by (48) correspond to _-Hz ^dc(ex) and _-Hz ^dc(ex2), respectively. (Step (j6) )). If the signal strength (constant multiplication component) can be calibrated using another method, only the constant value component may be calibrated using the above method.

In yet other embodiments, calibration of magnetic field values can be performed as follows.

（式中、αは非ゼロの実定数である。）
を満たす面内座標（ｘ’，ｙ’）の集合は、磁場値がαである等値線を形成する。外部交流磁場Ｈ_ｚ ^ａｃに平行な方向であって、強度のわかった一様な外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ）}を、探針に印加した条件で、各面内座標（ｘ，ｙ）について測定を行う。さらに、外部交流磁場Ｈ_ｚ ^ａｃに平行な方向であって、強度のわかった一様な外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ２）}であって、上記Ｈ_ｚ ^{ｄｃ（ｅｘ）}とは異なる強度を有する外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ２）}を、探針に印加した条件で、各面内座標（ｘ，ｙ）について測定を行う。

(In the formula, α is a non-zero real constant.)
A set of in-plane coordinates (x', y') that satisfy the following form an isovalue line whose magnetic field value is α. For each in-plane coordinate (x, y) under the condition that a uniform external DC magnetic field H _z ^{dc (ex)} of known intensity is applied to the probe in a direction parallel to the external AC magnetic field H _z ^ac . Take measurements. Furthermore, an external ^DC magnetic field H _z ^dc(ex2) having a uniform intensity and a direction parallel to the external AC magnetic field H _z ac and having a different intensity from the above-mentioned H _z ^dc(ex) is applied. Measurement is performed for each in-plane coordinate (x, y) under the condition that a DC magnetic field H _z ^{dc (ex2)} is applied to the probe.

を満たす面内座標（ｘ”，ｙ”）の集合および面内座標（ｘ'''，ｙ'''）の集合が形成する２つの等値線（工程（ｊ７）、（ｊ８））に基づいて、式（４４）により得られる磁場像の信号強度を較正することができる。実際に測定を行った測定点（格子点）において値がαにならず、隣接する２つの測定点において値がα－δ_１及びα＋δ_２（δ_１、δ_２はそれぞれ正の実数である。）である場合には、式（５６）を満たす面内座標（ｘ”，ｙ”）、（ｘ'''、ｙ'''）を補間により求めることができる。すなわち、式（５６）からαを消去すると

In the two isolines (steps (j7), (j8)) formed by the set of in-plane coordinates (x'', y'') and the set of in-plane coordinates (x''', y''') that satisfy Based on this, the signal strength of the magnetic field image obtained by equation (44) can be calibrated. The value does not become α at the measurement point (lattice point) where the measurement was actually performed, and the values at the two adjacent measurement points are α−δ ₁ and α+δ ₂ (δ ₁ and δ ₂ are each positive real numbers). ), in-plane coordinates (x'', y'') and (x''', y''') that satisfy equation (56) can be obtained by interpolation. In other words, if we eliminate α from equation (56), we get

であるから、外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ）}を印加したときに式（４４）により算出される磁場値がαとなる面内座標（ｘ”，ｙ”）と、外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ２）}を印加したときに式（４４）により算出される磁場値がαとなる面内座標（ｘ'''，ｙ'''）とにおける、外部直流磁場を印加していないときの式（４４）により算出される磁場値の差Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}（ｘ”，ｙ”，ｚ）－Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}（ｘ'''，ｙ'''，ｚ）が、外部直流磁場の差Ｈ_ｚ ^{ｄｃ（ｅｘ２）}（ｘ'''，ｙ'''，ｚ）－Ｈ_ｚ ^{ｄｃ（ｅｘ）}（ｘ”，ｙ”，ｚ）に等しくなるように、式（４４）、式（４６）又は（４８）により得られる磁場像の信号強度を較正することができる（工程（ｊ９））。このような較正方法は、走査領域における磁場が全範囲にわたって同符号であるために、式（４４）により算出される磁場値がゼロとなる面内座標が存在せず、かつ、走査領域における磁場が全範囲にわたって非常に強いために、式（４４）により算出される磁場値がゼロとなる面内座標（ｘ’，ｙ’）が存在するような外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ）}を印加できない場合に有用である。一の実施形態において、走査領域内に磁化飽和していることがわかっている位置が存在する場合には、当該位置における磁化飽和値に基づいて、さらに磁場値の絶対値を補正することができる。

Therefore, when the external DC magnetic field H _z ^{dc (ex)} is applied, the in-plane coordinates (x", y") at which the magnetic field value calculated by equation (44) is α, and the external DC magnetic field H _z ^dc The formula when no external DC magnetic field is applied at the in-plane coordinates (x''', y''') where the magnetic field value calculated by equation (44) is α when ^(ex2) is applied. The difference in magnetic field values calculated by (44) H _z ^dc(sample) (x'', y'', z) - H _z ^dc(sample) (x''', y''', z) is _Equation ⁽ 44 ₎ , ^Eq . The signal intensity of the magnetic field image obtained by (46) or (48) can be calibrated (step (j9)). In such a calibration method, since the magnetic field in the scanning region has the same sign over the entire range, there is no in-plane coordinate where the magnetic field value calculated by equation (44) is zero, and the magnetic field in the scanning region is very strong over the entire range, so an external DC magnetic field _Hz ^dc(ex) is applied such that there exists an in-plane coordinate (x', y') where the magnetic field value calculated by equation (44) is zero. This is useful when this is not possible. In one embodiment, if there is a position in the scanning area that is known to be saturated with magnetization, the absolute value of the magnetic field value can be further corrected based on the magnetization saturation value at that position. .

Input the wave number filter (Equations (31a) to (31c) and Equations (40a) to (40c)) as described above.

が不明な定数倍されていても、式（４４）、（４６）、又は（４８）により得られる磁場像の信号強度を較正することができる。当該不明な定数をβとし、磁場の２階微分、磁場の１階微分、及び磁場の測定感度に対応する係数（以下において「測定感度係数」ということがある。）をそれぞれα_１、α_２、及びα_３とすると、波数フィルタと測定感度係数α_１、α_２、α_３との関係は、Ｃ_３がＣ_１と同符号のとき

Even if is multiplied by an unknown constant, the signal strength of the magnetic field image obtained by equation (44), (46), or (48) can be calibrated. The unknown constant is β, and the coefficients corresponding to the second derivative of the magnetic field, the first derivative of the magnetic field, and the measurement sensitivity of the magnetic field (hereinafter sometimes referred to as "measurement sensitivity coefficients") are α ₁ and α ₂ , respectively. , and α ₃ , the relationship between the wave number filter and the measurement sensitivity coefficients α ₁ , α ₂ , α ₃ is as follows when C ₃ has the same sign as C ₁

となり、Ｃ_３がＣ_１と異符号のとき

So, when C ₃ has a different sign from C ₁

となる（式中、ε’は任意に定められる微小実定数であり、その選び方及び好ましい範囲はεと同様である。）。上記説明した磁場値の較正において磁場の強度を補正する操作は、不明な定数βを乗じられた入力

(In the formula, ε' is an arbitrarily determined infinitesimal real constant, and its selection and preferred range are the same as ε.) In the magnetic field value calibration described above, the operation of correcting the magnetic field strength is based on the input multiplied by an unknown constant β.

に対して、測定感度係数α_１、α_２、及び／又はα_３を求める操作に対応する。したがって、波数フィルタの入力（式（５９））がいかなる定数倍を含んでいるかを知る必要はない。

This corresponds to the operation of determining the measurement sensitivity coefficients α ₁ , α ₂ , and/or α ₃ for . Therefore, it is not necessary to know what constant multiple the wave number filter input (Equation (59)) contains.

In this way, the specific calculation in the first wave number filter calculator 631 (FIG. 5) is based on the amplitude H _z ^{ac (coil)} of the alternating magnetic field at the position of the probe 10 and the amplitude of the alternating magnetic field at the position of the probe 10. When the second-order differential of the amplitude with respect to the vibration direction (z direction) of the probe 10 ∂ ² _Hz ^ac(coil) /∂z ² has the same sign, the combination of each wave number (k _x , k _y ), the input (formula (59)) is

を乗じることにより行うことができ、Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}と∂^２Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}／∂ｚ^２とが異符号である場合には、各波数の組み合わせ（ｋ_ｘ，ｋ_ｙ）について、入力（式（５９））に

If H _z ^ac(coil) and ∂ ² H _z ^ac(coil) /∂z ² have opposite signs, then for each wave number combination (k _x , k _y ) , input (Equation (59))

を乗じることにより行うことができる。また、第２の波数フィルタ演算器６３２（図５）における具体的な演算は、Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}と∂^２Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}／∂ｚ^２とが同符号である場合には、各波数の組み合わせ（ｋ_ｘ，ｋ_ｙ）について、入力（式（５９））に

This can be done by multiplying by Further, the specific calculation in the second wave number filter calculation unit 632 (FIG. 5) is as follows when H _z ^ac(coil) and ∂ ² H _z ^ac(coil) /∂z ² have the same sign. For each wave number combination (k _x , k _y ), input (Equation (59))

を乗じることにより行うことができ、Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}と∂^２Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}／∂ｚ^２とが異符号である場合には、各波数の組み合わせ（ｋ_ｘ，ｋ_ｙ）について、入力（式（５９））に

If H _z ^ac(coil) and ∂ ² H _z ^ac(coil) /∂z ² have opposite signs, then for each wave number combination (k _x , k _y ) , input (Equation (59))

を乗じることにより行うことができる。また、第３の波数フィルタ演算器６３３（図５）における具体的な演算は、Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}と∂^２Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}／∂ｚ^２とが同符号である場合には、各波数の組み合わせ（ｋ_ｘ，ｋ_ｙ）について、入力（式（５９））に

This can be done by multiplying by Further, the specific calculation in the third wave number filter calculator 633 (FIG. 5) is as follows when H _z ^ac(coil) and ∂ ² H _z ^ac(coil) /∂z ² have the same sign. For each wave number combination (k _x , k _y ), input (Equation (59))

を乗じることにより行うことができ、Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}と∂^２Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}／∂ｚ^２とが異符号である場合には、各波数の組み合わせ（ｋ_ｘ，ｋ_ｙ）について、入力（式（５９））に

If H _z ^ac(coil) and ∂ ² H _z ^ac(coil) /∂z ² have opposite signs, then for each wave number combination (k _x , k _y ) , input (Equation (59))

を乗じることにより行うことができる。ただし上記の通り、第３の波数フィルタ演算器６３３を用いて入力（式（５９）：フーリエ変換器６２０の出力）から直流磁場の１階微分のフーリエ変換∂Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｋ_ｘ，ｋ_ｙ，ｚ）を抽出することは、探針位置における交流磁場の探針の振動方向についての１階微分∂Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}／∂ｚの値が非ゼロである場合にのみ可能である。なお、∂Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}／∂ｚの値がゼロであっても、第２の波数フィルタ演算器６３２により入力（式（５９））から直流磁場の２階微分のフーリエ変換∂^２Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｋ_ｘ，ｋ_ｙ，ｚ）を抽出し、これを第２／第３の積分フィルタ演算器６５２によりフーリエ空間上で１回積分（∂Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｋ_ｘ，ｋ_ｙ，ｚ）＝－（ｋ_ｘ ^２＋ｋ_ｙ ^２）^－１／２×∂^２Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｋ_ｘ，ｋ_ｙ，ｚ））することにより、直流磁場の１階微分のフーリエ変換∂Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｋ_ｘ，ｋ_ｙ，ｚ）を得ることができ、これを逆フーリエ変換器６４０で二次元逆フーリエ変換することにより、実空間での直流磁場の１階微分∂Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｘ，ｙ，ｚ）を得ることができる。

This can be done by multiplying by However, as mentioned above, the third wave number filter calculator 633 is used to convert the input (Equation (59): output of the Fourier transformer 620) into the Fourier transform of the first differential of the DC magnetic field ∂H _z ^dc(sample) /∂z _{Extracting ( k} ^_ It is only possible to Note that even if the value of ∂H _z ^ac(coil) /∂z is zero, the second wave number filter calculator 632 converts the Fourier transform of the second derivative of the DC magnetic field from the input (Equation (59)) to ∂ ² H _z ^dc(sample) _{/ ∂z} ^{2 (} _k ⁾ /∂z (k _x , k _y , z) = - (k _x ² + k _y ² ) ^-1/2 ×∂ ² H _z ^dc(sample) /∂z ² (k _x , k _y , z)) By doing so, it is possible to obtain the Fourier transform of the first derivative _of the DC magnetic field _{∂H z} ^dc(sample) /∂z(k By converting, the first-order differential of the DC magnetic field in real space ∂H _z ^dc(sample) /∂z(x, y, z) can be obtained.

α ₁ is the measurement sensitivity coefficient of the second derivative of the magnetic field and corresponds to C ₁ . α ₂ is the measurement sensitivity coefficient of the first derivative of the magnetic field and corresponds to C ₂ . α ₃ is the measurement sensitivity coefficient of the magnetic field and corresponds to C ₃ . The measurement sensitivity coefficients α ₁ , α ₂ and α ₃ are proportional to each other via the definition of constants C ₁ , C ₂ and C ₃ (Equation (13)). When an air-core coil is used as the source of the AC magnetic field, once any one of the measurement sensitivity coefficients α ₁ , α ₂ , and α ₃ is determined, the air-core coil equation (15) and the constant C From the definitions of ₁ , C ₂ , and C ₃ (Equation (13)), the remaining two measurement sensitivity coefficients can also be determined. For example, if the measurement sensitivity coefficient α ₃ of the magnetic field is determined, the measurement sensitivity coefficient α ₁ of the second derivative of the magnetic field and the measurement sensitivity coefficient α ₂ of the first derivative of the magnetic field are:

で求めることができる。また例えば、磁場の２階微分の測定感度係数α_１が定まったならば、及び磁場の１階微分の測定感度係数α_２、及び磁場の測定感度係数α_３は

It can be found by For example, if the measurement sensitivity coefficient α ₁ of the second derivative of the magnetic field is determined, the measurement sensitivity coefficient α ₂ of the first derivative of the magnetic field, and the measurement sensitivity coefficient α ₃ of the magnetic field are

で求めることができる。また例えば、磁場の１階微分の測定感度係数α_２が定まったならば、磁場の２階微分の測定感度係数α_１、及び磁場の測定感度係数α_３は

It can be found by For example, if the measurement sensitivity coefficient α ₂ of the first derivative of the magnetic field is determined, the measurement sensitivity coefficient α ₁ of the second derivative of the magnetic field and the measurement sensitivity coefficient α ₃ of the magnetic field are

で求めることができる。

It can be found by

Furthermore, the constants C ₁ , C ₂ , and C ₃ appearing in the wavenumber filter (Equations (31a) to (31c) or Equations (41a) to (41c)) include the magnetic susceptibility χ of the probe (Equation ( 13)) However, in applying the wave number filter, it is not necessary to know the magnetic susceptibility χ of the probe. This is because the coefficients of the wave number filter are determined by the relationship between constants C ₁ , C ₂ , and C ₃ as expressed in equations (31a') to (31c') and equations (40a') to (40c'). This is because it can be expressed as a ratio, and in these ratios, the magnetic susceptibility χ of the probe included in the constants C ₁ , C ₂ , and C ₃ cancel each other out. That is, in the above equations (31a') to (31c') and equations (40a') to (40c'), the coefficients of the wave number filter are

の２つであり、これらは探針の磁化率χに依存しない。特に外部交流磁場の発生源が空芯コイルである場合には、空芯コイルの式（１５）から、これらの２つの係数を算出できる。なお上記式（３１ａ’）～（３１ｃ’）及び式（４０ａ’）～（４０ｃ’）の波数フィルタ部分は、定数Ｃ_１が必ず非ゼロであることを利用して、｜Ｃ_２｜／｜Ｃ_１｜及び｜Ｃ_３｜／｜Ｃ_１｜の２つの比を係数として用いるように、波数フィルタ部分の分母及び分子を｜Ｃ_１｜で除することにより式変形して得られたものであるが、波数フィルタ部分を表す式の形は必ずしもこれに限られるものではない。例えば、波数フィルタの分母および分子の両方に｜Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}｜を乗じることにより、｜Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}｜、｜∂Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}／∂ｚ｜、及び｜∂^２Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}／∂ｚ^２｜の間の２つの比（式（６６）、（６７））に代えて、｜Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}｜、｜∂Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}／∂ｚ｜、及び｜∂^２Ｈ_ｚ ^{ａｃ（ｃｏｉｌ）}／∂ｚ^２｜の３つの値を係数として用いてもよい。また例えば、定数Ｃ_２が非ゼロであれば、｜Ｃ_１｜／｜Ｃ_２｜及び｜Ｃ_３｜／｜Ｃ_２｜の２つの比を係数として用いることも可能である。そのような波数フィルタは次のように表される。

These two do not depend on the magnetic susceptibility χ of the probe. In particular, when the source of the external AC magnetic field is an air-core coil, these two coefficients can be calculated from equation (15) for the air-core coil. Note that the wave number filter portion of the above equations (31a') to (31c') and equations (40a') to (40c') uses the fact that the constant C ₁ is always non-zero to calculate |C ₂ |/| It was obtained by transforming _the formula by dividing the denominator and numerator of the wave number filter part by |C ₁ | so that the two ratios of C 1 | and |C ₃ |/|C ₁ | are used as coefficients. However, the form of the equation representing the wave number filter portion is not necessarily limited to this. For example, by multiplying both the denominator and numerator of a wavenumber filter by |H _z ^{ac(coil) |} , |H _z ^ac(coil) |, |∂H _z ^ac(coil) /∂z|, and |∂ ² Instead of the two ratios between H _z ^ac(coil) /∂z ² | (Equations (66) and (67)), |H _z ^ac(coil) |, |∂H _z ^ac(coil) /∂ Three values of z| and |∂ ² _Hz ^ac(coil) /∂z ² | may be used as coefficients. For example, if the constant C ₂ is non-zero, it is also possible to use two ratios of |C ₁ |/|C ₂ | and |C ₃ |/|C ₂ | as coefficients. Such a wavenumber filter is expressed as follows.

（式中、Ｃ_３はＣ_１と同符号）、

(In the formula, C ₃ has the same sign as C ₁ ),

（式中、Ｃ_３はＣ_１と異符号；ε”は任意に定められる微小実定数であり、その選び方及び好ましい範囲はεと同様である。）
また例えば定数Ｃ_３が非ゼロであれば、｜Ｃ_１｜／｜Ｃ_３｜及び｜Ｃ_２｜／｜Ｃ_３｜の２つの比を係数として用いるように式変形を行うことも可能である。そのような波数フィルタは次のように表される。

(In the formula, _C3 has a different sign from _C1 ; ε'' is an arbitrarily determined infinitesimal real constant, and its selection and preferred range are the same as ε.)
For example, if the constant C ₃ is non-zero, it is also possible to transform the equation so that the two ratios of |C ₁ |/|C ₃ | and |C ₂ |/|C ₃ | are used as coefficients. . Such a wavenumber filter is expressed as follows.

（式中、Ｃ_３はＣ_１と同符号）

(In the formula, C ₃ has the same sign as C ₁ )

（式中、Ｃ_３はＣ_１と異符号；ε’’’は任意に定められる微小実定数であり、その選び方及び好ましい範囲は式（４０ａ）～（４０ｃ）中のεと同様である。）
ただし、汎用性の高さ及び計算の安定性の観点からは、上記式（３１ａ’）～（３１ｃ’）及び式（４０ａ’）～（４０ｃ’）におけるように、｜Ｃ_２｜／｜Ｃ_１｜及び｜Ｃ_３｜／｜Ｃ_１｜の２つの比を、波数フィルタ部分の係数として用いることが好ましい。

(In the formula, C ₃ has a different sign from C ₁ ; ε''' is an arbitrarily determined infinitesimal real constant, and its selection and preferred range are the same as ε in formulas (40a) to (40c). )
However, from the viewpoint of high versatility and stability of calculation, |C ₂ |/|C It is preferable to use two ratios of ₁ | and |C ₃ |/|C ₁ | as coefficients of the wave number filter section.

In still other embodiments, it is also possible to calibrate the magnetic field value as follows (step (j10) to (j13)). Measurement is performed for each in-plane coordinate (x, y) under the condition that an external _DC magnetic field _Hz ^{dc (ex)} of known intensity is applied to ^the probe in a direction parallel to the external AC magnetic field Hz ac. . When information corresponding to the constant value component of the magnetic field, that is, the (k _x , k _y )=(0,0) component is extracted using equation (31c') or (40c'),

が得られる（工程（ｊ１０））。さらに、外部直流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ）}に代えて、Ｈ_ｚ ^{ｄｃ（ｅｘ）}とは強度が同一で逆の極性を有する外部直流磁場－Ｈ_ｚ ^{ｄｃ（ｅｘ）}を印加して同様に測定を行い、同様に磁場の一定値成分すなわち（ｋ_ｘ，ｋ_ｙ）＝（０，０）成分を抽出すると、

is obtained (step (j10)). Furthermore, in place of the external DC magnetic field H _z ^dc(ex) , an external DC magnetic field -H _z ^dc(ex) having the same strength and opposite polarity as that of H _z ^dc(ex) is applied and measurements are made in the same way. Similarly, if we extract the constant value component of the magnetic field, that is, the (k _x , k _y )=(0,0) component, we get

が得られる（工程（ｊ１１））。両測定結果の差（式（６８）－式（６９））は

is obtained (step (j11)). The difference between both measurement results (Equation (68) - Equation (69)) is

に等しい。この値と、外部交流磁場Ｈ_ｚ ^{ｄｃ（ｅｘ）}の値（これは既知である）とから、磁場値の測定感度係数α_３を求めることができる（工程（ｊ１２））。得られた測定感度係数α_３を用いて、式（４４）により得られる磁場像の信号強度を較正できる。さらに、両測定結果の和（式（６８）＋式（６９））は

be equivalent to. From this value and the value of the external alternating magnetic field H _z ^dc(ex) (which is known), the measurement sensitivity coefficient α ₃ of the magnetic field value can be determined (step (j12)). Using the obtained measurement sensitivity coefficient α ₃ , the signal intensity of the magnetic field image obtained by equation (44) can be calibrated. Furthermore, the sum of both measurement results (formula (68) + formula (69)) is

に等しい。この値と、先に決定された測定感度係数α_３とから、試料からの直流磁場の一定値成分Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}（（ｋ_ｘ，ｋ_ｙ）＝（０，０），ｚ）を求めることができる（工程（ｊ１３））。このようにして求められた磁場の一定値成分は、式（４６）又は（４８）により得られる磁場像における磁場の一定値成分として用いることができる。また、外部交流磁場の発生源に空芯コイルを用いている場合には、さらに、得られた測定感度係数α_３と、上記式（６０）又は（６１）と、空芯コイルの式（１５）とから、磁場の２階微分の測定感度係数α_１又は磁場の１階微分の測定感度係数α_２を算出して、式（４６）又は（４８）により得られる磁場像の信号強度を較正することができる。

be equivalent to. From this value and the previously determined measurement sensitivity coefficient α ₃ , the constant value component of the DC magnetic field from the sample H _z ^{dc (sample)} ((k _x , k _y ) = (0, 0), z) is calculated. can be obtained (step (j13)). The constant value component of the magnetic field obtained in this way can be used as the constant value component of the magnetic field in the magnetic field image obtained by equation (46) or (48). In addition, when an air-core coil is used as the source of the external AC magnetic field, the obtained measurement sensitivity coefficient α ₃ , the above equation (60) or (61), and the air-core coil equation (15 ), calculate the measurement sensitivity coefficient α ₁ of the second-order differential of the magnetic field or the measurement sensitivity coefficient α ₂ of the first-order differential of the magnetic field, and calibrate the signal strength of the magnetic field image obtained by equation (46) or (48). can do.

In the DC magnetic field measurement device 1000 (FIG. 4), the AC magnetic field generator 300 generates an AC magnetic field by supplying AC current to the air-core coil 310, so information necessary for wave number filtering, that is, the probe position The alternating current magnetic field H _z ^ac(coil) , its first derivative ∂H _z ^ac(coil) /∂z, and second derivative ∂ ² H _z ^ac(coil) /∂z ² are expressed by the air-core coil equation (15). (It can be directly determined from the Biot-Savart law). On the other hand, in the DC magnetic field measuring device 2000 (FIG. 6), the AC magnetic field generator 2300 generates an AC magnetic field by supplying an AC current to a coil 2320 of an electromagnet including an electromagnetic core 2310. As in the DC magnetic field measuring device 2000, when an electromagnet having a magnetic core and a coil wound around the magnetic core is used instead of an air-core coil as a source of the AC magnetic field, the above equations (31a') to (31c) are used. ') and (40a') to (40c'), it is generally difficult to accurately evaluate the coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ |. When using an electromagnet as the source of the alternating magnetic field, for example, formulas (44) and (46) can be expressed based on the results of observing the same sample (standard sample) using an air-core coil as the source of the alternating magnetic field. Or to the magnetic field image H _z ^dc(sample) (x, y, z) or H _z ^dc(sample) (x, y, z; (x, y)≠(0,0)) obtained by (48) , a magnetic field image H _z ^{dc (sample)} (x, y, z) or Hz dc calculated by equation (44), equation (46), or (48) from the measurement results using an electromagnet as a source of an alternating _magnetic ^{field. (sample)} Either formula (31a') to (31c') or (40a') to (40c') so as to match (x, y, z; (x, y)≠(0,0)) By optimizing (by parameter fitting operator 2800) the coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ | (and optionally a constant multiple of the image) _at |/|C ₁ | and |C ₃ |/|C ₁ | can be determined (step (o)). In another embodiment, a second-order differential image ∂ ² _Hz ^dc(sample) /∂z obtained based on the results of observing the same sample (standard sample) using an air-core coil as a source of an alternating magnetic field. ² (x, y, z) or ∂ ² _Hz ^dc(sample) /∂z ² (x, y, z; (x, y)≠(0,0)), an electromagnet is used as a source of an alternating magnetic field. The second-order differential image ∂ ² _Hz ^dc(sample) /∂z ² (x, y, z) or ∂ ² _Hz ^dc(sample ) /∂z ² (x, y, z) calculated from the measurement results used ; (x, y)≠(0,0)), the coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ |( and optionally a constant multiple of the image), the coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ | may be determined (step (o)). Before the optimization calculation, preprocessing may be performed, such as normalization so that the maximum and minimum values of the image signals are the same between the two images. Determining these two coefficients is equivalent to determining the two ratios between the constants |C ₁ |, |C ₂ |, |C ₃ |, and at the same time, the amplitude of the alternating magnetic field at the position of the probe 10. H _z ^ac(coil) , the first-order differential of the amplitude of the AC magnetic field at the position of the probe 10 with respect to the vibration direction of the probe 10 ∂H _z ^ac(coil) /∂z, and the AC magnetic field at the position of the probe 10 This is equivalent to finding the two ratios of the amplitude of the magnetic field with respect to the vibration direction of the probe 10, ^{∂ 2} _Hz ^ac(coil) /∂z ² . Note that when an electromagnet is used as an AC magnetic field source, the amplitude H _z ^{ac (coil)} of the AC magnetic field at the position of the probe 10 and its second-order differential ∂ ² H _z ^{ac (coil)} / ∂z ² have different signs (that is, C ₁ and _C3 are often of opposite signs). In the DC magnetic field measuring device 2000, when observing the same sample using an air-core coil as the source of the AC magnetic field, by switching the changeover switch 2340 from the electromagnetic coil 2320 side to the air-core coil 310 side, Measurements can be performed by supplying alternating current from alternating current/ direct current source 2330 to air core coil 310. As long as the conditions regarding the electromagnets are the same (that is, the same electromagnet is supplied with the same current and the positional relationship between the electromagnet and the probe is the same), the coefficients |C ₂ |/|C ₁ | and |C ₃ | /|C ₁ | is kept the same. Therefore, the obtained coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ | can also be applied to other measurements, as long as the conditions regarding the electromagnets are the same. Thereafter, in other measurements, applying the same conditions for the electromagnet and the obtained coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ |, by the operation described above. , the magnetic field values can be calibrated.
Generally, the measurement result of the second derivative of the magnetic field has the richest amount of information, so it can be obtained using equation (48) based on the results of observing the same sample using an air-core coil as the source of the alternating magnetic field. The magnetic field image H _z ^{dc (sample)} (x, y, z; (x, y)≠(0,0)) is calculated by equation (48) from the measurement results using an electromagnet as the source of the alternating magnetic field. In order to match the magnetic field image H _z ^{dc (sample)} (x, y, z; (x, y)≠(0,0)), the coefficient |C ₂ |/ By optimizing |C ₁ | and |C ₃ |/|C ₁ | (and optionally a constant multiple of the image), the coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ It is preferable to determine |. In addition, from the viewpoint of being less susceptible to measurement noise, the magnetic field image H _z ^{dc( sample)} (x, y, z) to match the magnetic field image H _z ^dc(sample) (x, y, z) calculated by equation (44) from the measurement results using an electromagnet as the source of the alternating magnetic field. By optimizing the coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ | (and optionally a constant multiple of the image) in equation (31c') or (40c'), Preferably, the coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ | are determined. Thereafter, in other measurements applying the same conditions for the electromagnet, the previously determined coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ | are applied, and the operations described above are performed. , the magnetic field values can be calibrated.
In the optimization calculation, a known optimization method can be adopted. For example, trust region methods such as the Levenberg-Marquardt method and Dogleg method; conjugate gradient methods such as the Hager-Zhang (HZ) method; Narushima - Ternary conjugate gradient methods such as the Yabe-Ford method; quasi-Newton methods such as the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and limited memory BFGS (L-BFGS) method; simulated annealing (SA) method; downhill simplex A well-known nonlinear optimization algorithm such as the above method can be applied.

The principle of operation of the direction conversion filter calculator 660 will be explained. Furthermore, in the present invention, information on a magnetic field in an in-plane direction (for example, the (x, y) direction) perpendicular to the direction (for example, the (x, y) direction) can be obtained from a measurement result in one direction (for example, the vertical (z) direction). As explained above, the magnetic field H(r) generated at the coordinate r by the magnetic charge distribution ρ(r') distributed at the coordinate r' is the z-direction component F of the magnetic force F exerted on the magnetic moment m existing at the coordinate r. Gradient of _z F _z '(r) (Equation (24), reprinted):

を、積分（式（２５）、再掲）

, integral (Equation (25), reprinted)

で与える伝達関数Ｇ_ρ（ｒ）のｘ、ｙに関するフーリエ変換は、式（２６）（再掲）：

The Fourier transform with respect to x and y of the transfer function G _ρ (r) given by is equation (26) (reprinted):

（ｋ_ｘ，ｋ_ｙは波数（空間周波数））
で表される。ｚ方向に外部交流磁場を印加する、上記説明した測定においては、磁気モーメントｍのｘ、ｙ、及びｚ成分であるｍ_ｘ、ｍ_ｙ、ｍ_ｚについて、ｍ_ｘ＝ｍ_ｙ＝０、ｍ_ｚ＝ｍ_０である。ここでｍ_０は磁気モーメントｍの強度（ノルム）であるから、Ｇ_ρ（ｋ_ｘ，ｋ_ｙ，ｚ）は

(k _x , k _y are wave numbers (spatial frequencies))
It is expressed as In the above-described measurement in which an external alternating magnetic field is applied in the z direction, for m x , m y , m _z which are the _x , _y , and z components of the magnetic moment m, m _x = _my = 0, m _z = m ₀ . Here, m ₀ is the strength (norm) of the magnetic moment m, so G _ρ (k _x , k _y , z) is

であった。同一の強度ｍ_０を有する磁気モーメントｍをｘ方向に向けた場合には、ｍ_ｘ＝ｍ_０、ｍ_ｙ＝ｍ_ｚ＝０となるので、Ｇ_ρ（ｋ_ｘ，ｋ_ｙ，ｚ）は

Met. When the magnetic moment m having the same strength m ₀ is directed in the x direction, m _x = m ₀ and m _y = m _z = 0, so G _ρ (k _x , k _y , z) is

となる。したがって、試料からの磁場のｘ成分Ｈ_ｘ ^{ｄｃ（ｓａｍｐｌｅ）}のｚ方向での２階微分∂^２Ｈ_ｘ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２の、ｘ、ｙについてのフーリエ変換は、式（２７）から

becomes. Therefore, the Fourier transform with respect to x and y of the second differential in the z direction of the x component H _x ^{dc (sample)} of the magnetic field from the sample, ∂ ² H _x ^{dc (sample)} / ∂z ² , is given by Equation (27) from

となる。式（７４）により、磁場のｚ成分の２階微分のフーリエ変換∂^２Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｋ_ｘ，ｋ_ｙ，ｚ）から、磁場のｘ成分の２階微分のフーリエ変換∂^２Ｈ_ｘ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｋ_ｘ，ｋ_ｙ，ｚ）を得ることができる。

becomes. From equation (74), from the Fourier transform of the second derivative of the z component of the magnetic field, ^{∂ 2} _Hz ^dc(sample) /∂z ² (k _x , k _y , z), the Fourier transform of the second derivative of the x component of the magnetic field is The transformation ∂ ² H _x ^dc(sample) /∂z ² (k _x , k _y , z) can be obtained.

Similarly, when a magnetic moment m having the same strength m ₀ is directed in the y direction, m _y = m ₀ and m _z = m _z = 0, so G _ρ (k _x , k _y , z )teeth

となる。したがって、試料からの磁場のｙ成分Ｈ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}のｚ方向での２階微分∂^２Ｈ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２の、ｘ、ｙについてのフーリエ変換は、式（２７）から

becomes. Therefore, the Fourier transform with respect to x and y of the second differential in the z direction of the y component H _y ^{dc (sample)} of the magnetic field from the sample, ∂ ² H _y ^{dc (sample)} / ∂z ² , is given by Equation (27) from

となる。式（７６）により、磁場のｚ成分の２階微分のフーリエ変換∂^２Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｋ_ｘ，ｋ_ｙ，ｚ）から、磁場のｙ成分の２階微分のフーリエ変換∂^２Ｈ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｋ_ｘ，ｋ_ｙ，ｚ）を得ることができる。

becomes. From equation (76), from the Fourier transform of the second derivative of the z component of the magnetic field, ^{∂ 2} _Hz ^dc(sample) /∂z ² (k _x , k _y , z), the Fourier transform of the second derivative of the y component of the magnetic field is The transformation ∂ ² H _y ^dc(sample) /∂z ² (k _x , k _y , z) can be obtained.

In this way, the Fourier transform of the second differential in the z direction (the vibration direction of the tip) of the z (external alternating current magnetic field direction) component of the magnetic field from the sample in the in-plane (x, y) direction of the scanning region ∂ ² From H _z ^dc(sample) /∂z ² (k _x , k _y , z), the Fourier transform of the second derivative of the x and y components of the magnetic field in the z direction ∂ ² H _x ^dc(sample) /∂z ² (k _x , k _y , z) and ∂ ² H _y ^dc(sample) /∂z ² (k _x , k _y , z), respectively.

として得ることができ（工程（ｋ２））、これらを逆フーリエ変換することにより、磁場のｘ成分およびｙ成分の２階微分∂^２Ｈ_ｘ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｘ，ｙ，ｚ）及び∂^２Ｈ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｘ，ｙ，ｚ）を、それぞれ

^can _be ^{obtained as} ) and ∂ ² H _y ^dc(sample) /∂z ² (x, y, z), respectively.

として得ることができる（工程（ｌ２））。

(Step (l2)).

Similarly, from the Fourier transform H _z ^dc(sample) (k _{x , k y , z) of the z (external alternating current magnetic field direction) component of the magnetic field from the sample in the in-plane (x} , _y ) direction of the scanning area, Obtain the Fourier transforms H _x ^{dc (sample)} (k _x , k _y , z) and H _y ^{dc (sample)} (k _x , k _y , z) of the x and y components of the magnetic field as follows, respectively. I can do it.
By integrating the Fourier transform of the second derivative of the z-component of the magnetic field, ∂ ² H _z ^dc(sample) /∂z ² (k _x , k _y , z) twice in the z-direction in Fourier space, the z-component of the magnetic field is The Fourier transform of H _z ^dc(sample) can be obtained. i.e.

である。上記同様に、同一強度ｍ_０の磁気モーメントｍがｘ方向を向いた（ｍ_ｘ＝ｍ_０、ｍ_ｙ＝ｍ_ｚ＝０）とき、試料からの磁場のｘ成分の２階微分のフーリエ変換∂^２Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｋ_ｘ，ｋ_ｙ，ｚ）をフーリエ空間でｚ方向に２回積分することにより、試料からの磁場のｘ成分のフーリエ変換Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}（ｋ_ｘ，ｋ_ｙ，ｚ）を得ることができて、

It is. Similarly to the above, when a magnetic moment m with the same strength m ₀ points in the x direction (m _x = m ₀ , m _y = m _z =0), the Fourier transform of the second differential of the x component of the magnetic field from the sample ∂ By integrating ² H _z ^dc(sample) /∂z ² (k _x , k _y , z) twice in the z direction in Fourier space, the Fourier transform of the x component of the magnetic field from the sample H _z ^dc(sample) (k _x , k _y , z) can be obtained,

である。式（７９）及び（８０）から、

It is. From equations (79) and (80),

が得られる。また上記同様に、同一強度ｍ_０の磁気モーメントｍがｙ方向を向いた（ｍ_ｙ＝ｍ_０、ｍ_ｘ＝ｍ_ｚ＝０）とき、試料からの磁場のｙ成分の２階微分のフーリエ変換∂^２Ｈ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｋ_ｘ，ｋ_ｙ，ｚ）をフーリエ空間でｚ方向に２回積分することにより、試料からの磁場のｙ成分のフーリエ変換Ｈ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}（ｋ_ｘ，ｋ_ｙ，ｚ）を得ることができて、

is obtained. Similarly to the above, when a magnetic moment m with the same strength m ₀ is directed in the y direction ( _my = m ₀ , m _x = m _z = 0), the Fourier transform of the second differential of the y component of the magnetic field from the sample is By integrating ∂ ² H _y ^dc(sample) /∂z ² (k _x , k _y , z) twice in the z direction in Fourier space, the Fourier transform H _y ^{dc(sample )} (k _x , k _y , z) can be obtained,

である。式（７９）及び（８２）から、

It is. From equations (79) and (82),

が得られる。このように、試料からの磁場のｚ成分のフーリエ変換Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}（ｋ_ｘ，ｋ_ｙ，ｚ）から、磁場のｘ成分およびｙ成分のフーリエ変換Ｈ_ｘ ^{ｄｃ（ｓａｍｐｌｅ）}（ｋ_ｘ，ｋ_ｙ，ｚ）及びＨ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}（ｋ_ｘ，ｋ_ｙ，ｚ）を、それぞれ

is obtained. In this way, from the Fourier transform H _z ^dc(sample) (k _x , k _y , z) of the z component of the magnetic field from the sample, the Fourier transform H _x ^dc(sample) (k _x , k _y , z) and H _y ^dc(sample) (k _x , k _y , z), respectively.

として得ることができ（工程（ｋ０））、これらを逆フーリエ変換することにより、磁場のｘ成分およびｙ成分Ｈ_ｘ ^{ｄｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ）及びＨ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ）を、それぞれ

(step (k0)), and by inverse Fourier transforming these, the x and y components of the magnetic field H _x ^dc(sample) (x, y, z) and H _y ^dc(sample) (x , y, z) respectively.

として得ることができる（工程（ｌ０））。この磁場方向変換により得られる面内磁場Ｈ_ｘ ^{ｄｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ）及びＨ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ）は、走査領域内の位置によらない一定値成分を含まない磁場像、すなわちＨ_ｘ ^{ｄｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ；（ｋ_ｘ，ｋ_ｙ）≠（０，０））、Ｈ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ；（ｋ_ｘ，ｋ_ｙ）≠（０，０））である。

(Step (l0)). The in-plane magnetic fields H _x ^dc(sample) (x, y, z) and H _y ^dc(sample) (x, y, z) obtained by this magnetic field direction conversion are constant value components that are independent of the position within the scanning area. H _x ^dc(sample) (x, y, z; (k _x , k _y )≠(0,0)), H _y ^dc(sample) (x, y, z; (k _x , k _y )≠(0,0)).

Similarly, the Fourier transform of the first-order differential in the z direction (the vibration direction of the tip) of the z (external alternating current magnetic field direction) component of the magnetic field from the sample is ∂H _z ^dc(sample) /∂z(k _x , k _y , z), the Fourier transform of the first derivative of the x and y components of the magnetic field in the z direction ∂H _x ^dc(sample) /∂z(k _x , k _y , z), ∂H _y ^dc(sample) /∂ z(k _x , k _y , z) can be obtained as follows.
By integrating the Fourier transform of the second derivative of the z-component of the magnetic field, ∂ ² H _z ^dc(sample) /∂z ² (k _x , k _y , z) once in the z-direction in Fourier space, the z-component of the magnetic field is The Fourier transform of the first differential of ∂H _z ^dc(sample) /∂z(k _x , k _y , z) can be obtained. i.e.

である。上記同様に、同一強度ｍ_０の磁気モーメントｍがｘ方向を向いた（ｍ_ｘ＝ｍ_０、ｍ_ｙ＝ｍ_ｚ＝０）とき、試料からの磁場のｘ成分の２階微分のフーリエ変換∂^２Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｋ_ｘ，ｋ_ｙ，ｚ）をフーリエ空間でｚ方向に１回積分することにより、試料からの磁場のｘ成分のフーリエ変換Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}（ｋ_ｘ，ｋ_ｙ，ｚ）を得ることができて、

It is. Similarly to the above, when a magnetic moment m with the same strength m ₀ points in the x direction (m _x = m ₀ , m _y = m _z = 0), the Fourier transform of the second differential of the x component of the magnetic field from the sample is By integrating ² H _z ^dc(sample) /∂z ² (k _x , k _y , z) once in the z direction in Fourier space, the Fourier transform of the x component of the magnetic field from the sample H _z ^dc(sample) (k _x , k _y , z) can be obtained,

である。式（８６）及び（８７）から、

It is. From equations (86) and (87),

が得られる。また上記同様に、同一強度ｍ_０の磁気モーメントｍがｙ方向を向いた（ｍ_ｙ＝ｍ_０、ｍ_ｘ＝ｍ_ｚ＝０）とき、試料からの磁場のｙ成分の２階微分のフーリエ変換∂^２Ｈ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｋ_ｘ，ｋ_ｙ，ｚ）をフーリエ空間でｚ方向に１回積分することにより、試料からの磁場のｙ成分の１階微分のフーリエ変換∂Ｈ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｋ_ｘ，ｋ_ｙ，ｚ）を得ることができて、

is obtained. Similarly to the above, when a magnetic moment m with the same strength m ₀ is directed in the y direction ( _my = m ₀ , m _x = m _z = 0), the Fourier transform of the second differential of the y component of the magnetic field from the sample is By integrating ∂ ² H _y ^dc(sample) /∂z ² (k _x , k _y , z) once in the z direction in Fourier space, we can calculate the Fourier transform of the first differential of the y component of the magnetic field from the sample ∂ H _y ^dc(sample) /∂z(k _x , k _y , z) can be obtained,

である。式（８６）及び（８９）から、

It is. From equations (86) and (89),

が得られる。このように、試料からの磁場のｚ成分の１階微分のフーリエ変換∂Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｋ_ｘ，ｋ_ｙ，ｚ）から、磁場のｘ成分およびｙ成分の１階微分のフーリエ変換∂Ｈ_ｘ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｋ_ｘ，ｋ_ｙ，ｚ）及び∂Ｈ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｋ_ｘ，ｋ_ｙ，ｚ）を、それぞれ

is obtained. In this way, from the Fourier transform of the first-order differential of the z-component of the magnetic field from the sample, ∂H _z ^dc(sample) /∂z(k _x , k _y , z), we can calculate the first-order differential of the x- and y-components of the magnetic field. The Fourier transforms of ∂H _x ^dc(sample) /∂z(k _x , k _y , z) and ∂H _y ^dc(sample) /∂z(k _x , k _y , z) are respectively

として得ることができ（工程（ｋ１））、これらを逆フーリエ変換することにより、磁場のｘ成分およびｙ成分の１階微分∂Ｈ_ｘ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｘ，ｙ，ｚ）及び∂Ｈ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｘ，ｙ，ｚ）を、それぞれ

(step (k1)), and by inverse Fourier transforming these, the first-order differentials of the x and y components of the magnetic field ∂H _x ^dc(sample) /∂z(x, y, z) and ∂H _y ^dc(sample) /∂z(x, y, z), respectively

として得ることができる（工程（ｌ１））。

(Step (l1)).

In this way, the specific calculation in the direction conversion filter calculator 660 is to obtain the x component from the z (vertical direction) component by calculating each combination of wave numbers except (k _x , k _y )=(0,0). For (k _x , k _y ), this can be done by multiplying the input value by -ik _x /(k _x ² +k _y ² ) ^1/2 . Also, obtaining the y component from the z (vertical direction) component means that for each combination of wave numbers (k _x , k _y ) except (k _x , k _y )=(0,0), the input value is - This can be done by multiplying by ik _y /(k _x ² +k _y ² ) ^1/2 .

The operating principle of the distance conversion filter calculator 670 will be explained. Furthermore, in the present invention, magnetic field information at different probe-sample distances (z+Δz) can be obtained from magnetic field information obtained by measurement at one probe-sample distance (z coordinate).
Regarding the z component of the magnetic field H _z ^{dc (sample)} , by replacing z with z+Δz in equation (79),

が得られる。磁場のｘ成分Ｈ_ｘ ^{ｄｃ（ｓａｍｐｌｅ）}についても同様に、式（８０）においてｚをｚ＋Δｚに置き換えることにより、

is obtained. Similarly, regarding the x component of the magnetic field H _x ^{dc (sample)} , by replacing z with z+Δz in equation (80),

が得られる。磁場のｙ成分Ｈ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}についても同様に、式（８２）においてｚをｚ＋Δｚに置き換えることにより、

is obtained. Similarly, for the y component H _y ^{dc (sample)} of the magnetic field, by replacing z with z+Δz in equation (82),

が得られる。このように、一つの探針－試料間距離（ｚ座標）における磁場のフーリエ変換Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}（ｋ_ｘ，ｋ_ｙ，ｚ）、Ｈ_ｘ ^{ｄｃ（ｓａｍｐｌｅ）}（ｋ_ｘ，ｋ_ｙ，ｚ）、及びＨ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}（ｋ_ｘ，ｋ_ｙ，ｚ）から、探針－試料間距離がΔｚ異なる位置における磁場のフーリエ変換Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}（ｋ_ｘ，ｋ_ｙ，ｚ＋Δｚ）、Ｈ_ｘ ^{ｄｃ（ｓａｍｐｌｅ）}（ｋ_ｘ，ｋ_ｙ，ｚ＋Δｚ）、及びＨ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}（ｋ_ｘ，ｋ_ｙ，ｚ＋Δｚ）を、それぞれ

is obtained. In this way, the Fourier transform of the magnetic field at one tip-sample distance (z coordinate) H _z ^dc(sample) (k _x , k _y , z), H _x ^dc(sample) (k _x , k _y , z), and H _y ^dc(sample) (k _x , k _y , z), the Fourier transform of the magnetic field at the position where the tip-sample distance differs by Δz H _z ^dc(sample) (k _x , k _y , z+Δz ), H _x ^dc(sample) (k _x , k _y , z+Δz), and H _y ^dc(sample) (k _x , k _y , z+Δz), respectively.

として得ることができ（工程（ｍ２））、これらを逆フーリエ変換することにより、探針－試料間距離がΔｚ異なる位置における磁場Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ＋Δｚ）、Ｈ_ｘ ^{ｄｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ＋Δｚ）、及びＨ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ＋Δｚ）を、それぞれ

(Step (m2)), and by performing inverse Fourier transform on these, the magnetic field H _z ^{dc (sample)} (x, y, z + Δz), H _x dc at positions where the tip-sample distance differs by ^{Δz (sample)} (x, y, z+Δz) and H _y ^dc(sample) (x, y, z+Δz), respectively.

として得ることができる（工程（ｎ２））。

(Step (n2)).

Conversion of the tip-sample distance can be similarly considered for the first-order differential of the magnetic field. Regarding the first derivative of the z component of the magnetic field, by replacing z with z+Δz in equation (86),

が得られる。磁場のｘ成分の１階微分についても同様に、式（８７）においてｚをｚ＋Δｚに置き換えることにより、

is obtained. Similarly, regarding the first derivative of the x component of the magnetic field, by replacing z with z+Δz in equation (87),

が得られる。磁場のｙ成分の１階微分についても同様に、式（８９）においてｚをｚ＋Δｚに置き換えることにより、

is obtained. Similarly, for the first derivative of the y component of the magnetic field, by replacing z with z+Δz in equation (89),

が得られる。このように、一つの探針－試料間距離（ｚ座標）における磁場のｚ方向における１階微分のフーリエ変換∂Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｋ_ｘ，ｋ_ｙ，ｚ）、∂Ｈ_ｘ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｋ_ｘ，ｋ_ｙ，ｚ）、及び∂Ｈ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｋ_ｘ，ｋ_ｙ，ｚ）から、探針－試料間距離がΔｚ異なる位置における磁場の１階微分のフーリエ変換∂Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｋ_ｘ，ｋ_ｙ，ｚ＋Δｚ）、∂Ｈ_ｘ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｋ_ｘ，ｋ_ｙ，ｚ＋Δｚ）、及び∂Ｈ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｋ_ｘ，ｋ_ｙ，ｚ＋Δｚ）を、それぞれ

is obtained. In this way, the Fourier transform of the first differential in the z direction of the magnetic field at one tip-sample distance (z coordinate) ∂H _z ^dc(sample) /∂z(k _x , k _y , z), ∂H _x ^{dc (sample)} / ∂z (k _x , k _y , z) and ∂H _y ^{dc (sample)} / ∂z (k _x , k _y , z), the position where the tip-sample distance differs by Δz The Fourier transform of the first derivative of the magnetic field at ∂H _z ^dc(sample) /∂z(k _x , k _y , z+Δz), ∂H _x ^dc(sample) /∂z(k _x , k _y , z+Δz), and ∂H _y ^dc(sample) /∂z(k _x , k _y , z+Δz), respectively

として得ることができ（工程（ｍ１））、これらを逆フーリエ変換することにより、探針－試料間距離がΔｚ異なる位置における磁場の１階微分∂Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｘ，ｙ，ｚ＋Δｚ）、∂Ｈ_ｘ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｘ，ｙ，ｚ＋Δｚ）、及び∂Ｈ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ（ｘ，ｙ，ｚ＋Δｚ）を、それぞれ

(Step (m1)), and by performing inverse Fourier transform on these, the first derivative of the magnetic field at positions where the tip-sample distance differs by Δz ∂H _z ^dc(sample) /∂z(x, y, z+Δz), ∂H _x ^dc(sample) /∂z(x, y, z+Δz), and ∂H _y ^dc(sample) /∂z(x, y, z+Δz), respectively.

として得ることができる（工程（ｎ１））。

(Step (n1)).

Conversion of the tip-sample distance can be similarly considered for the second-order differential of the magnetic field. Regarding the second derivative of the z component of the magnetic field, by replacing z with z+Δz in the first equation of equation (27),

が得られる。磁場のｘ成分の２階微分についても同様に、式（７４）においてｚをｚ＋Δｚに置き換えることにより、

is obtained. Similarly, for the second derivative of the x component of the magnetic field, by replacing z with z+Δz in equation (74),

が得られる。磁場のｙ成分の２階微分についても同様に、式（７６）においてｚをｚ＋Δｚに置き換えることにより、

is obtained. Similarly, for the second derivative of the y component of the magnetic field, by replacing z with z+Δz in equation (76),

が得られる。このように、一つの探針－試料間距離（ｚ座標）における磁場のｚ方向における２階微分のフーリエ変換∂^２Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｋ_ｘ，ｋ_ｙ，ｚ）、∂^２Ｈ_ｘ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｋ_ｘ，ｋ_ｙ，ｚ）、及び∂^２Ｈ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｋ_ｘ，ｋ_ｙ，ｚ）から、探針－試料間距離がΔｚ異なる位置における磁場の２階微分のフーリエ変換∂^２Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｋ_ｘ，ｋ_ｙ，ｚ＋Δｚ）、∂^２Ｈ_ｘ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｋ_ｘ，ｋ_ｙ，ｚ＋Δｚ）、及び∂^２Ｈ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｋ_ｘ，ｋ_ｙ，ｚ＋Δｚ）を、それぞれ

is obtained. In this way, the Fourier transform of the second derivative in the z direction of the magnetic field at one tip-sample distance (z coordinate) is ∂ ² Hz _dc ^(sample) /∂z ² (k _x , k _y , z), From ∂ ² H _x ^dc(sample) /∂z ² (k _x , k _y , z) and ∂ ² H _y ^dc(sample) / ∂z ² (k _x , k _y , z), the tip-sample Fourier transform of the second derivative of the magnetic field at positions where the distance between them differs by Δz ^{∂ 2} H _z ^dc(sample) /∂z ² (k _x , k _y , z+Δz), ∂ ² H _x ^dc(sample) /∂z ² ( k _x , k _y , z+Δz) and ∂ ² H _y ^dc(sample) /∂z ² (k _x , k _y , z+Δz), respectively.

として得ることができ（工程（ｍ２））、これらを逆フーリエ変換することにより、探針－試料間距離がΔｚ異なる位置における磁場の２階微分∂^２Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｘ，ｙ，ｚ＋Δｚ）、∂^２Ｈ_ｘ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｘ，ｙ，ｚ＋Δｚ）、及び∂^２Ｈ_ｙ ^{ｄｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｘ，ｙ，ｚ＋Δｚ）を、それぞれ

(Step (m2)), and by performing inverse Fourier transform on these, the second derivative of the magnetic field at positions where the tip-sample distance differs by Δz ∂ ² _Hz ^dc(sample) /∂z ² ( x, y, z+Δz), ∂ ² H _x ^dc(sample) /∂z ² (x, y, z+Δz), and ∂ ² H _y ^dc(sample) /∂z ² (x, y, z+Δz), respectively.

として得ることができる（工程（ｎ２））。

(Step (n2)).

In this way, the specific calculation in the distance conversion filter calculator 670 is (k _x , k _y ) = (0, 0) except for each combination of wave numbers (k _x , k _y ), by multiplying the input value by exp (-(k _x ² + k _y ² ) ^1/2 Δz). I can do it.

<3. AC magnetic field measurement device and AC magnetic field measurement method>
The alternating current magnetic field measurement method of the present invention includes the embodiments of [50] to [74] below.
[50] A method for measuring an alternating current magnetic field, comprising:
(a) exciting a cantilever having a superparamagnetic probe at one end that generates a magnetic moment in the direction of the applied magnetic field;
(b) while performing the step (a), frequency-modulating the excitation vibration of the cantilever by applying a DC magnetic field to the probe from a DC magnetic field generator;
(c) while performing the step (b), detecting the vibration of the probe and demodulating the frequency of the detection signal of the vibration of the probe;
(d) measuring a frequency component of the signal demodulated in step (c) that corresponds to the frequency component to be measured of the alternating magnetic field;
(e) The probe is caused to scan a scanning area set within a plane intersecting the vibration direction of the probe, and the steps (a) to ( d);
(f) performing a two-dimensional Fourier transform on the information corresponding to the measurement result of the step (d) in the scanning region in the in-plane direction of the scanning region;
(g0) From the Fourier transform information obtained in step (f), two-dimensional Fourier transform of the amplitude of the frequency component of the alternating current magnetic field that is parallel to the direct current magnetic field is performed in the in-plane direction of the scanning area. a step of extracting information corresponding to the
(i0) By two-dimensional inverse Fourier transform based on information corresponding to two-dimensional Fourier transform of the amplitude of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field in the in-plane direction of the scanning area, for each in-plane coordinate within the scanning area, obtaining a value corresponding to the amplitude of a component of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field,
The extraction in the step (g0) includes the DC magnetic field at the position of the probe, the first derivative of the DC magnetic field at the position of the probe with respect to the vibration direction of the probe, and the position of the probe. is performed based on the second derivative of the DC magnetic field with respect to the vibration direction of the probe, or two ratios therebetween, and a combination of two wave numbers in the in-plane direction within the scanning region,
AC magnetic field measurement, characterized in that the value of the DC magnetic field at the position of the probe and the second derivative of the DC magnetic field at the position of the probe with respect to the vibration direction of the probe are non-zero. Method.

[51] The alternating current magnetic field measurement method according to [50], further comprising the step of (j) calibrating at least the measurement sensitivity.

[52] The step (j) further includes calibrating a constant value component of the amplitude of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field that is independent of the position within the scanning region. 51], the DC magnetic field measurement method described in [51].

[53] The step (j) is
(j1) further applying to the probe an external alternating current magnetic field whose intensity of the component parallel to the direct current magnetic field is H ^ac(ex) and whose frequency and phase match the frequency component of the alternating current magnetic field to be measured; while performing the steps (a) to (f) and (g0) to (i0), and corresponding to the amplitude of the frequency component of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field obtained in the step (i0). specifying a first in-plane coordinate within the scanning area where the value is zero;
(j2) The frequency component of the alternating current magnetic field such that the amplitude value of the component parallel to the direct current magnetic field of the frequency component of the alternating current magnetic field becomes −H ^ac(ex) in the first in-plane coordinate. calibrating the intensity of the amplitude of the component parallel to the DC magnetic field at each in-plane coordinate within the scanning region.

[54] The step (j) is
(j1) While applying to the probe an external alternating current magnetic field whose amplitude of the component parallel to the direct current magnetic field is ^Hac(ex) and whose frequency and phase match the frequency component to be measured of the alternating current magnetic field, Performing the steps (a) to (f) and (g0) to (i0), a value corresponding to the amplitude of the frequency component of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field obtained in the step (i0) specifying a first in-plane coordinate within the scanning region where the coordinate is zero;
(j3) When the external alternating magnetic field is not applied to the probe, the frequency component of the alternating magnetic field obtained by performing the steps (a) to (f) and (g0) to (i0) identifying a second in-plane coordinate within the scanning region where the value corresponding to the amplitude of the component parallel to the DC magnetic field is zero;
(j4) The value of the amplitude of the frequency component of the AC magnetic field parallel to the DC magnetic field is −H ^ac(ex) at the first in-plane coordinate, and zero at the second in-plane coordinate. [51] calibrating the intensity and constant value component at each in-plane coordinate in the scanning area of the amplitude of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field so that Or the alternating current magnetic field measurement method described in [52].

[55] The step (j) is
(j10) Applying to the probe a first external AC magnetic field whose amplitude of the component parallel to the DC magnetic field is H ^{ac (ex)} and whose frequency and phase match those of the frequency component to be measured of the AC magnetic field. While performing the steps (a) to (e), the amplitude of the frequency component of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field corresponds to a constant value component independent of the in-plane coordinates within the scanning area. a step of extracting a first value;
(j11) Performing the steps (a) to (e) while applying a second external AC magnetic field having the same frequency and intensity as the first external AC magnetic field and an opposite phase to the probe, and extracting a second value corresponding to a constant value component of the amplitude of a component parallel to the DC magnetic field of the frequency component of the AC magnetic field, which is independent of in-plane coordinates within the scanning area;
(j12) Based on the difference between the first value and the second value and the H ^ac(ex) , correspond to the amplitude of the frequency component of the AC magnetic field parallel to the DC magnetic field. a step of determining the measurement sensitivity of the value;
(j13) Based on the sum of the first value and the second value and the measurement sensitivity obtained in the step (j12), calculate the component of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field. The alternating current magnetic field measuring method according to [51] or [52], including the step of determining a constant value component of amplitude that is independent of in-plane coordinates within the scanning area.

[56] The direction of the DC magnetic field is parallel to the vibration direction of the probe,
The method includes:
(k0) Information corresponding to the two-dimensional Fourier transform of the amplitude of the frequency component of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field in the in-plane direction of the scanning area. converting the amplitude of the component in the in-plane direction into information corresponding to a two-dimensional Fourier transform in the in-plane direction of the scanning area;
(l0) obtaining a value corresponding to the amplitude of the in-plane direction component of the frequency component of the alternating current magnetic field by two-dimensional inverse Fourier transform based on the information obtained in the step (k0); In addition, it includes
The alternating current magnetic field measuring method according to any one of [50] to [55], wherein the conversion in the step (k0) is performed based on a combination of two wave numbers in an in-plane direction within the scanning region.

[57] (m0) The amplitude of the component of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field, obtained by measurement at the first probe position in the vibration direction of the probe, in the scanning area. The information corresponding to the two-dimensional Fourier transform in the in-plane direction is expressed as the frequency component of the alternating current magnetic field at a virtual second probe position shifted from the first probe position in the vibration direction of the probe. converting the amplitude of the component parallel to the DC magnetic field into information corresponding to two-dimensional Fourier transform in the in-plane direction of the scanning area;
(n0) Based on the information obtained in the step (m0), the amplitude of the frequency component of the frequency component of the AC magnetic field parallel to the DC magnetic field at the second probe position is determined by two-dimensional inverse Fourier transformation. further comprising the step of obtaining a value corresponding to
The conversion in the step (m0) is based on the distance of the second probe position from the first probe position in the vibration direction of the probe, and two wave numbers in the in-plane direction within the scanning area. The alternating current magnetic field measurement method according to any one of [50] to [56], which is carried out based on a combination of.

[58] (g2) From the Fourier transform information obtained in step (f), the second order of the amplitude of the frequency component of the alternating current magnetic field that is parallel to the direct current magnetic field, with respect to the vibration direction of the probe. further comprising the step of extracting information corresponding to a two-dimensional Fourier transform of the differential in the in-plane direction of the scanning area,
The extraction in step (g2) includes the DC magnetic field at the probe position, the first derivative of the DC magnetic field at the probe position with respect to the vibration direction of the probe, and the DC magnetic field at the probe position. carried out based on the second derivative of the DC magnetic field with respect to the vibration direction of the probe, or two ratios therebetween, and a combination of two wave numbers in the in-plane direction within the scanning region, [50] The alternating current magnetic field measurement method according to any one of ~[57].

[59] (h2-0) The information extracted in the step (g2) is converted into two-dimensional information in the in-plane direction of the scanning area of the amplitude of the frequency component of the alternating current magnetic field that is parallel to the direct current magnetic field. a step of converting into information corresponding to Fourier transform;
(i2-0) Based on the information obtained in the step (h2-0), the DC magnetic field of the frequency component of the AC magnetic field is determined for each in-plane coordinate in the scanning area by two-dimensional inverse Fourier transformation. and obtaining a value corresponding to the amplitude of the component parallel to
The alternating current magnetic field measurement method according to [58], wherein the conversion in the step (h2-0) is performed based on a combination of two wave numbers in an in-plane direction within the scanning region.

[60] (i2-2) Based on the information obtained in step (g2), two-dimensional inverse Fourier transformation is performed to transform the frequency component of the alternating current magnetic field into the direct current for each in-plane coordinate within the scanning area. The alternating current magnetic field measurement method according to [58] or [59], further comprising the step of obtaining a value corresponding to the second-order differential of the amplitude of the component parallel to the magnetic field with respect to the vibration direction of the probe.

[61] The direction of the DC magnetic field is parallel to the vibration direction of the probe,
The method includes:
(k2) Corresponds to the two-dimensional Fourier transform of the second derivative of the amplitude of the frequency component of the AC magnetic field parallel to the DC magnetic field with respect to the vibration direction of the probe in the in-plane direction of the scanning area. The information corresponding to the two-dimensional Fourier transform of the amplitude of the in-plane direction component of the frequency component of the alternating current magnetic field, with respect to the vibration direction of the probe, in the in-plane direction of the scanning area. a process of converting the information into
(l2) Based on the information obtained in step (k2), the amplitude of the in-plane component of the frequency component of the alternating current magnetic field is determined in the vibration direction of the probe by two-dimensional inverse Fourier transformation. further comprising the step of obtaining a value corresponding to the second derivative,
The alternating current magnetic field measuring method according to [60], wherein the conversion in the step (k2) is performed based on a combination of two wave numbers in an in-plane direction within the scanning region.

[62] (m2) The amplitude of the component of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field, obtained by measurement at the first probe position in the vibration direction of the probe, of the probe. Information corresponding to the two-dimensional Fourier transform in the in-plane direction of the scanning area of the second differential with respect to the vibration direction is transferred to a virtual second probe position shifted from the first probe position in the vibration direction of the probe. Two-dimensional Fourier in the in-plane direction of the scanning region of the second derivative of the amplitude of the frequency component of the AC magnetic field parallel to the DC magnetic field with respect to the vibration direction of the probe at the probe position. a step of converting into information corresponding to the conversion;
(n2) Based on the information obtained in the step (m2), the amplitude of the frequency component of the AC magnetic field parallel to the DC magnetic field at the second probe position is determined by two-dimensional inverse Fourier transformation. further comprising the step of obtaining a value corresponding to the second differential with respect to the vibration direction of the probe,
The conversion in the step (m2) includes the distance of the second probe position from the first probe position in the vibration direction of the probe, and two wave numbers in the in-plane direction within the scanning area. The alternating current magnetic field measurement method according to any one of [58] to [61], which is carried out based on a combination of.

[63] (h2-1) The information extracted in step (g2) is calculated by calculating the first-order differential of the amplitude of the frequency component of the alternating current magnetic field that is parallel to the direct current magnetic field with respect to the vibration direction of the probe. further comprising the step of converting into information corresponding to a two-dimensional Fourier transform in the in-plane direction of the scanning area,
The alternating current magnetic field measuring method according to any one of [58] to [62], wherein the conversion in the step (h2-1) is performed based on a combination of two wave numbers in an in-plane direction within the scanning region.

[64] (g1) Based on the Fourier transform information obtained in step (f), the amplitude of the frequency component of the AC magnetic field parallel to the DC magnetic field is determined in the vibration direction of the probe. further comprising the step of extracting information corresponding to a two-dimensional Fourier transform of the first-order differential in the in-plane direction of the scanning area,
The extraction in step (g1) includes the DC magnetic field at the position of the probe, the first derivative of the DC magnetic field at the position of the probe with respect to the vibration direction of the probe, and the position of the probe. is performed based on the second-order differential of the DC magnetic field with respect to the vibration direction of the probe, or two ratios therebetween, and a combination of two wave numbers in the in-plane direction within the scanning region,
The alternating current magnetic field measuring method according to any one of [50] to [62], wherein the value of the first-order differential of the direct current magnetic field at the position of the probe with respect to the vibration direction of the probe is non-zero.

[65] (h1-0) The information extracted in the step (g1) is converted into two-dimensional information in the in-plane direction of the scanning region of the amplitude of the frequency component of the alternating current magnetic field that is parallel to the direct current magnetic field. a step of converting into information corresponding to Fourier transform;
(i1-0) Based on the information obtained in the step (h1-0), the DC magnetic field of the frequency component of the AC magnetic field is determined for each in-plane coordinate in the scanning area by two-dimensional inverse Fourier transformation. and obtaining a value corresponding to the amplitude of the component parallel to
The alternating current magnetic field measuring method according to [64], wherein the conversion in the step (h1-0) is performed based on a combination of two wave numbers in an in-plane direction within the scanning region.

[66] (i1) Two-dimensional Fourier calculation of the first derivative of the amplitude of the frequency component of the AC magnetic field parallel to the DC magnetic field with respect to the vibration direction of the probe in the in-plane direction of the scanning area. The amplitude of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field is determined by the two-dimensional inverse Fourier transform based on the information corresponding to the transformation, for each in-plane coordinate within the scanning area. The method for measuring an alternating current magnetic field according to any one of [63] to [65], further comprising the step of obtaining a value corresponding to a first-order differential with respect to the vibration direction.

[67] The direction of the alternating magnetic field is parallel to the vibration direction of the probe,
The method includes:
(k3) Corresponds to the two-dimensional Fourier transform of the first derivative of the amplitude of the frequency component of the AC magnetic field parallel to the DC magnetic field with respect to the vibration direction of the probe in the in-plane direction of the scanning area The information corresponding to the two-dimensional Fourier transform of the amplitude of the in-plane direction component of the frequency component of the alternating magnetic field with respect to the vibration direction of the probe with respect to the in-plane direction of the scanning area. a process of converting the information into
(l3) Based on the information obtained in step (k3), a two-dimensional inverse Fourier transform is performed to determine the amplitude of the in-plane component of the frequency component of the alternating magnetic field in the vibration direction of the probe. further comprising the step of obtaining a value corresponding to the first derivative,
The alternating current magnetic field measuring method according to any one of [63] to [66], wherein the conversion in the step (k3) is performed based on a combination of two wave numbers in an in-plane direction within the scanning region.

[68] (m1) The amplitude of the component parallel to the DC magnetic field of the frequency component of the AC magnetic field obtained by measurement at the first probe position in the vibration direction of the probe. Information corresponding to the two-dimensional Fourier transform in the in-plane direction of the scanning area of the first-order differential with respect to the vibration direction is transferred to a virtual second probe position shifted from the first probe position in the vibration direction of the probe. Two-dimensional Fourier in the in-plane direction of the scanning region of the first derivative of the amplitude of the frequency component of the AC magnetic field parallel to the DC magnetic field with respect to the vibration direction of the probe at the probe position. a step of converting into information corresponding to the conversion;
(n1) Based on the information obtained in the step (m1), the amplitude of the frequency component of the frequency component of the AC magnetic field parallel to the DC magnetic field at the second probe position is determined by two-dimensional inverse Fourier transformation. further comprising the step of obtaining a value corresponding to a first-order differential with respect to the vibration direction of the probe,
The conversion in the step (m1) is based on the distance of the second probe position from the first probe position in the vibration direction of the probe, and two wave numbers in the in-plane direction within the scanning area. The alternating current magnetic field measurement method according to any one of [63] to [67], which is carried out based on a combination of.

[69] The DC magnetic field generator,
air core coil,
a direct current source that supplies direct current to the air core coil;
The alternating current magnetic field measurement method according to any one of [50] to [68], comprising:

[70] The alternating current magnetic field measuring method according to [68], wherein the probe is placed in a cavity of the air-core coil.

[71] The alternating current magnetic field measuring method according to [69] or [70], wherein the probe is placed on the central axis of the air-core coil.

[72] The DC magnetic field generator,
an electromagnet having an electromagnetic core and a winding;
a direct current source that supplies direct current to the electromagnet;
The alternating current magnetic field measurement method according to any one of [50] to [68], comprising:

[73] (o) The DC magnetic field at the position of the probe, the first-order differential of the DC magnetic field at the position of the probe with respect to the vibration direction of the probe, and the DC magnetic field at the position of the probe. and a second-order differential with respect to the vibration direction of the probe;
The step (o) includes:
The results of measuring the amplitude of the frequency component of the component parallel to the DC magnetic field of the AC magnetic field when the electromagnet is used as the DC magnetic field generator are compared to The alternating current magnetic field measuring method according to [72], including the step of optimizing the two ratios so as to match the measurement results.

[74] (o) The DC magnetic field at the position of the probe, the first derivative of the DC magnetic field at the position of the probe with respect to the vibration direction of the probe, and the DC magnetic field at the position of the probe. and a second-order differential with respect to the vibration direction of the probe;
The step (o) includes:
When the electromagnet is used as the DC magnetic field generator, the measurement result of the second-order differential in the vibration direction of the probe of the amplitude of the frequency component of the AC magnetic field that is parallel to the DC magnetic field is calculated as the DC magnetic field generator. The alternating current magnetic field measurement method according to [72], comprising the step of optimizing the two ratios so as to match the measurement results when an air-core coil is used as the magnetic field generator.

The alternating current magnetic field measuring device of the present invention includes the embodiments of [75] to [95] below.
[75] A device for measuring an alternating magnetic field, comprising:
a cantilever having a superparamagnetic probe at one end that generates a magnetic moment in the direction of an applied magnetic field;
an exciter that excites the cantilever;
a DC magnetic field generator that frequency-modulates the excitation vibration of the cantilever by applying a DC magnetic field to the probe;
a vibration sensor that detects vibrations of the probe;
a scanning mechanism that causes the probe to scan a scanning area set within a plane intersecting the vibration direction of the probe;
a demodulator that frequency demodulates the detection signal of the vibration sensor;
a detector that measures a frequency component included in the demodulated signal from the demodulator that corresponds to a frequency component to be measured of the alternating current magnetic field;
a storage device that stores a measurement value corresponding to a measurement signal of the detector for each in-plane coordinate in the scanning area;
a Fourier transformer that performs a two-dimensional Fourier transform on the measured values for each in-plane coordinate of the scanning area stored in the storage device with respect to the in-plane coordinate;
Information corresponding to a two-dimensional Fourier transform of the amplitude of a component parallel to the DC magnetic field of the frequency component of the AC magnetic field in the in-plane direction of the scanning area, from the Fourier transform information output from the Fourier transformer. a first wave number filter calculator configured to be able to extract the
The scanning area is determined by two-dimensional inverse Fourier transformation based on information corresponding to two-dimensional Fourier transformation of the amplitude of the frequency component of the frequency component of the alternating current magnetic field parallel to the DC magnetic field in the in-plane direction of the scanning area. an inverse Fourier transformer configured to be able to obtain, for each in-plane coordinate within, a value corresponding to the amplitude of a component of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field;
including;
The extraction in the first wave number filter calculator includes the DC magnetic field at the position of the probe, the first derivative of the DC magnetic field at the position of the probe with respect to the vibration direction of the probe, and the probe. Based on the second derivative of the DC magnetic field at the needle position with respect to the vibration direction of the probe, or the two ratios therebetween, and the combination of two wave numbers in the in-plane direction within the scanning area. I,
AC magnetic field measurement, characterized in that the value of the DC magnetic field at the position of the probe and the second derivative of the DC magnetic field at the position of the probe with respect to the vibration direction of the probe are non-zero. Device.

[76] When the probe scans each in-plane coordinate within the scanning area, an external AC magnetic field whose frequency and phase match the frequency component to be measured, and a DC magnetic field from the DC magnetic field generator. The alternating current magnetic field measuring device according to [75], further comprising an external direct current magnetic field generator configured to be able to apply an external alternating current magnetic field having a predetermined amplitude of a component parallel to the probe to the probe. .

[77] From the Fourier transform information output from the Fourier transformer, calculate the second derivative of the amplitude of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field with respect to the vibration direction of the probe. further comprising a second wave number filter calculator configured to be capable of extracting information corresponding to two-dimensional Fourier transform in the in-plane direction of the scanning area,
The extraction in the second wave number filter calculator includes the DC magnetic field at the position of the probe, the first-order differential of the DC magnetic field at the position of the probe with respect to the vibration direction of the probe, and the Performed based on the second derivative of the DC magnetic field at the position with respect to the vibration direction of the probe, or two ratios therebetween, and a combination of two wave numbers in the in-plane direction within the scanning area. The alternating current magnetic field measuring device according to [75] or [76].

[78] The scanning of the second-order differential with respect to the vibration direction of the probe of the amplitude of the frequency component of the alternating current magnetic field that is parallel to the direct current magnetic field, extracted by the second wave number filter calculator. information corresponding to a two-dimensional Fourier transform in the in-plane direction of the scanning region, and converting information corresponding to a two-dimensional Fourier transform in the in-plane direction of the scanning region of the amplitude of a component of the frequency component of the alternating current magnetic field parallel to the DC magnetic field into a two-dimensional Fourier transform in the in-plane direction of the scanning region. further comprising a first integral filter calculator configured to be able to convert into corresponding information;
The alternating current magnetic field measuring device according to [77], wherein the conversion in the first integral filter calculator is performed based on a combination of two wave numbers in an in-plane direction within the scanning region.

[79] The inverse Fourier transformer calculates, with respect to the in-plane direction of the scanning region, the second derivative of the amplitude of the frequency component of the alternating current magnetic field that is parallel to the direct current magnetic field, with respect to the vibration direction of the probe. Based on the information corresponding to the two-dimensional Fourier transform of The alternating current magnetic field measuring device according to [77] or [78], further configured to be able to obtain a value corresponding to a second-order differential with respect to the vibration direction of the probe.

[80] The scanning of the second-order differential with respect to the vibration direction of the probe of the amplitude of the frequency component of the alternating current magnetic field that is parallel to the direct current magnetic field, extracted by the second wave number filter calculator. The information corresponding to the two-dimensional Fourier transform in the in-plane direction of the region is obtained by calculating the first differential of the amplitude of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field with respect to the vibration direction of the probe. further comprising a second integral filter calculator configured to be capable of converting into information corresponding to two-dimensional Fourier transform in the in-plane direction of the scanning area,
The alternating current magnetic field measuring device according to any one of [77] to [79], wherein the conversion in the second integral filter calculator is performed based on a combination of two wave numbers in an in-plane direction within the scanning region. .

[81] From the Fourier transform information output from the Fourier transformer, calculate the first-order differential of the amplitude of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field with respect to the vibration direction of the probe. further comprising a third wave number filter calculator configured to be able to extract information corresponding to two-dimensional Fourier transform in the in-plane direction of the scanning area,
The extraction in the third wave number filter calculator includes the DC magnetic field at the position of the probe, the first-order differential of the DC magnetic field at the position of the probe with respect to the vibration direction of the probe, and the probe. Based on the second derivative of the DC magnetic field at the needle position with respect to the vibration direction of the probe, or the two ratios therebetween, and the combination of two wave numbers in the in-plane direction within the scanning area. I,
The alternating current magnetic field measuring device according to any one of [75] to [80], wherein the value of the first-order differential of the direct current magnetic field at the position of the probe with respect to the vibration direction of the probe is non-zero.

[82] The first derivative of the amplitude of the component of the alternating current magnetic field parallel to the direct current magnetic field, extracted by the third wave number filter calculator, with respect to the vibration direction of the probe, within the plane of the scanning region. Converting information corresponding to a two-dimensional Fourier transform about the direction into information corresponding to a two-dimensional Fourier transform about the in-plane direction of the scanning area of the amplitude of a component of the alternating current magnetic field parallel to the direct current magnetic field. further comprising a third integral filter operator configured to enable
The alternating current magnetic field measuring device according to [81], wherein the conversion in the third integral filter calculator is performed based on a combination of two wave numbers in an in-plane direction within the scanning region.

[83] The inverse Fourier transformer converts the two-dimensional Fourier transformer in the in-plane direction of the scanning region of the first derivative of the amplitude of the component of the alternating current magnetic field parallel to the direct current magnetic field with respect to the vibration direction of the probe. Based on the information corresponding to the transformation, for each in-plane coordinate in the scanning region, the amplitude of the component of the alternating current magnetic field parallel to the direct current magnetic field is calculated with respect to the vibration direction of the probe by two-dimensional inverse Fourier transform based on the information corresponding to the transformation. The alternating current magnetic field measuring device according to any one of [80] to [82], further configured to be able to obtain a value corresponding to a first-order differential.

[84] The DC magnetic field applied to the probe by the DC magnetic field generator is parallel to the vibration direction of the probe,
The alternating current magnetic field measuring device includes:
Information corresponding to the two-dimensional Fourier transform of the amplitude of the frequency component of the frequency component of the AC magnetic field parallel to the DC AC magnetic field in the in-plane direction of the scanning area is converted into two dimensional Fourier transforms in the in-plane direction within the scanning area. Based on the combination of wave numbers, the amplitude of the in-plane direction component of the frequency component of the alternating current magnetic field can be converted into information corresponding to a two-dimensional Fourier transform in the in-plane direction of the scanning area. further including a direction conversion filter operator,
The inverse Fourier transformer performs a two-dimensional inverse Fourier transform based on information corresponding to a two-dimensional Fourier transform in the in-plane direction of the scanning area of the amplitude of the in-plane direction component of the frequency component of the alternating magnetic field. further configured to be capable of obtaining, by transformation, for each in-plane coordinate within the scanning region, a value corresponding to the amplitude of the in-plane direction component of the frequency component of the alternating magnetic field; [75] The alternating current magnetic field measuring device according to any one of [83] to [83].

[85] The direction conversion filter calculator calculates the second differential of the amplitude of the frequency component of the AC magnetic field parallel to the DC magnetic field with respect to the vibration direction of the probe in the in-plane direction of the scanning area. The information corresponding to the two-dimensional Fourier transformation of It is further configured to be capable of converting a second differential with respect to the vibration direction of the needle into information corresponding to a two-dimensional Fourier transform with respect to the in-plane direction of the scanning area,
The inverse Fourier transformer is a two-dimensional Fourier transformer in the in-plane direction of the scanning region of the second derivative of the amplitude of the in-plane direction component of the frequency component of the alternating magnetic field with respect to the vibration direction of the probe. Based on the information corresponding to the transformation, the amplitude of the in-plane direction component of the frequency component of the alternating current magnetic field is changed by two-dimensional inverse Fourier transform for each in-plane coordinate in the scanning region. The alternating current magnetic field measuring device according to [84], further configured to be able to obtain a value corresponding to a second-order differential with respect to a direction.

[86] The direction conversion filter calculator calculates the first differential of the amplitude of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field with respect to the vibration direction of the probe in the in-plane direction of the scanning area. The information corresponding to the two-dimensional Fourier transformation of It is further configured to be capable of converting a first-order differential with respect to the vibration direction of the needle into information corresponding to a two-dimensional Fourier transform with respect to the in-plane direction of the scanning area,
The inverse Fourier transformer is a two-dimensional Fourier transformer in the in-plane direction of the scanning area of the first-order differential of the amplitude of the in-plane direction component of the frequency component of the alternating magnetic field with respect to the vibration direction of the probe. Based on the information corresponding to the transformation, the amplitude of the in-plane direction component of the frequency component of the alternating magnetic field is changed by two-dimensional inverse Fourier transform for each in-plane coordinate in the scanning area. The alternating current magnetic field measuring device according to [84] or [85], further configured to be able to obtain a value corresponding to a first-order differential with respect to a direction.

[87] The in-plane direction of the scanning region of the amplitude of the frequency component of the frequency component of the alternating current magnetic field that is parallel to the direct current magnetic field, obtained by measurement at the first probe position in the vibration direction of the probe. information corresponding to the two-dimensional Fourier transform of the frequency component of the alternating current magnetic field at a virtual second probe position shifted from the first probe position in the vibration direction of the probe. further comprising a distance conversion filter calculator configured to be able to convert the amplitude of the component parallel to the magnetic field into information corresponding to two-dimensional Fourier transform in the in-plane direction of the scanning area,
The conversion in the distance conversion filter calculator calculates two values: the distance of the second probe position from the first probe position in the vibration direction of the probe, and the distance in the in-plane direction within the scanning area. The alternating current magnetic field measuring device according to any one of [75] to [86], which is carried out based on a combination of wave numbers.

[88] The distance conversion filter calculator calculates the amplitude of a component of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field, obtained by measurement at the first probe position in the vibration direction of the probe. , information corresponding to the two-dimensional Fourier transform of the second differential with respect to the vibration direction of the probe in the in-plane direction of the scanning area is calculated as the frequency component of the alternating current magnetic field at the second probe position. It is further possible to convert into information corresponding to a two-dimensional Fourier transform in the in-plane direction of the scanning area of the second derivative of the amplitude of the component parallel to the DC magnetic field with respect to the vibration direction of the probe. It is composed of
The conversion of information corresponding to the two-dimensional Fourier transform of the second order differential in the distance conversion filter calculation unit is based on the distance of the second probe position from the first probe position in the vibration direction of the probe. and a combination of two wave numbers in the in-plane direction within the scanning area, the alternating current magnetic field measuring device according to [87].

[89] The distance conversion filter calculator calculates the amplitude of a component of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field, obtained by measurement at the first probe position in the vibration direction of the probe. The information corresponding to the two-dimensional Fourier transform of the first differential with respect to the vibration direction of the probe in the in-plane direction of the scanning area is expressed as the frequency component of the alternating current magnetic field at the second probe position. The first differential of the amplitude of the component parallel to the DC magnetic field with respect to the vibration direction of the probe can be converted into information corresponding to a two-dimensional Fourier transform in the in-plane direction of the scanning area. has been
The conversion of information corresponding to the two-dimensional Fourier transform of the first-order differential in the distance conversion filter calculator is based on the distance of the second probe position from the first probe position in the vibration direction of the probe. and a combination of two wave numbers in the in-plane direction within the scanning area.
[87] or the alternating current magnetic field measuring device according to [88].

[90] The DC magnetic field generator,
air core coil,
a direct current source that supplies direct current to the air core coil;
The alternating current magnetic field measuring device according to any one of [75] to [89], comprising:

[91] The alternating current magnetic field measuring method according to [90], wherein the probe is placed in a cavity of the air-core coil.

[92] The alternating current magnetic field measuring device according to [90] or [91], wherein the probe is arranged on the central axis of the air-core coil.

[93] The DC magnetic field generator,
an electromagnet comprising an electromagnetic core and a coil wound around the electromagnetic core;
a direct current source that supplies direct current to the electromagnet;
The alternating current magnetic field measuring device according to any one of [75] to [92], comprising:

[94] When the electromagnet is used as the DC magnetic field generator, the measurement result of the amplitude of the component parallel to the DC magnetic field of the frequency component of the AC magnetic field is calculated using an air-core coil as the DC magnetic field generator. The DC magnetic field at the probe position, the first derivative of the DC magnetic field at the probe position with respect to the vibration direction of the probe, and the probe position a parameter fitting operation configured to be able to determine the two ratios by optimizing two ratios between the second order differential of the DC magnetic field with respect to the vibration direction of the probe; The alternating current magnetic field measuring device according to [93], further comprising a device.

[95] When the electromagnet is used as the DC magnetic field generator, the measurement result of the second-order differential in the vibration direction of the probe of the amplitude of the frequency component of the AC magnetic field that is parallel to the DC magnetic field. , the DC magnetic field at the position of the probe and the vibration direction of the probe of the DC magnetic field at the position of the probe so as to match the measurement results when an air-core coil is used as the DC magnetic field generator. determining the two ratios by optimizing two ratios between a first derivative with respect to the direction of vibration of the probe and a second derivative of the DC magnetic field at the position of the probe with respect to the vibration direction of the probe; The alternating current magnetic field measuring device according to [93], further comprising a parameter fitting calculator configured to be able to perform the following operations.

The alternating current magnetic field measuring device of the present invention will be explained along with each step of the alternating current magnetic field measuring method. FIG. 7 is a diagram schematically explaining an alternating current magnetic field measuring device 3000 according to one embodiment of the present invention. In FIG. 7, elements that have already appeared in FIGS. 1 to 6 are denoted by the same reference numerals as those in FIGS. 1 to 5, and their explanations may be omitted. The AC magnetic field measuring device 3000 is a device for observing an AC magnetic field generated from the sample 20'. The AC magnetic field measuring device 3000 includes a cantilever 100, an exciter 200, a DC magnetic field generator 3300, a vibration sensor 400, a demodulator 430, a detector 3440, a scanning mechanism 500, a signal processing device 3600, and an external AC magnetic field generator 3700. We are prepared. Among these, the probe 10, the cantilever 100, the vibration sensor 400, the demodulator 430, and the scanning mechanism 500 have the same configuration as in the DC magnetic field measurement method 1000 (FIG. 4). The AC magnetic field measuring device 3000 includes a DC magnetic field generator 3300 in place of the AC magnetic field generator 300, an external AC magnetic field generator 3700 in place of the external DC magnetic field generator 700, and a detector 3440 in place of the detector 440. Equipped with.

(Sample 20')
The sample 20' that is the measurement target of the AC magnetic field measuring device 3000 is a sample that generates an AC magnetic field. A specific example of the sample 20' is an AC electromagnet.

(Exciter 200)
The probe 10 is provided near one end (free end) of the cantilever 100, and the other end (fixed end) of the cantilever 100 is fixed. The exciter 200 excites the cantilever 100 (step (a)).

(DC magnetic field generator 3300)
The DC magnetic field generator 3300 is a device that applies a DC magnetic field to the probe 10. The DC magnetic field applied to the probe 10 by the DC magnetic field generator 3300 preferably has an intensity that does not saturate the magnetization of the probe 10. In the AC magnetic field measuring device 3000 of FIG. 7, the DC magnetic field generator 3300 includes an air-core coil 310 and a DC current source 3320 that supplies DC current to the air-core coil 310. By supplying a DC current from the DC current source 3320 to the air-core coil 310, a DC magnetic field parallel to the vibration direction of the probe 10 (z-axis direction: direction perpendicular to the sample surface) is applied to the probe 10. (Step (b)).

The strength of the DC magnetic field applied to the probe 10 by the DC magnetic field generator 3300 is such that the magnetization of the probe 10 is not saturated and the probe 10 is not attracted to the sample 20', and the desired magnetic field measurement sensitivity is achieved. It can be adjusted as appropriate within the obtainable range.

The installation positions of the elements constituting the DC magnetic field generator 3300 are determined based on the intensity of the DC magnetic field from the DC magnetic field generator 3300 and the value of the second-order differential in the vibration direction of the probe 10 (z-axis direction in FIG. 7). There is no particular limitation as long as it is non-zero. For example, in the alternating current magnetic field measuring device 3000 in FIG. 7, the probe 10 is preferably disposed in a hollow portion of the air-core coil 310, and preferably on the central axis of the air-core coil 310. In one preferred embodiment, the probe 10 is disposed on the central axis of the air-core coil 310 and at the center of the thickness of the air-core coil 310. At this position, the magnetic field generated from the air-core coil 310 is at its maximum, so by arranging the probe 10 at this position, it is possible to further increase the measurement sensitivity.

(Vibration sensor 400, demodulator 430, detector 440)
Due to the magnetic interaction between the magnetic field vector formed by superimposing the AC magnetic field from the sample 20' and the DC magnetic field from the DC magnetic field generator 3300 and the magnetic moment of the probe 10, the probe 10 has a periodic strength. is subjected to a magnetic force that fluctuates. The gradient of the magnetic force whose strength periodically varies causes the effective spring constant of the cantilever 100 to vary periodically, thereby causing the frequency of vibration of the probe 10 to vary periodically. Vibration sensor 400, demodulator 430, and detector 440 can extract information corresponding to the amplitude of the magnetic force gradient at the position of probe 10 from this frequency-modulated vibration of probe 10. Vibration sensor 400 has the same configuration as vibration sensor 400 in DC magnetic field measuring device 1000 (FIG. 4). The demodulator 430 frequency demodulates the detection signal of the vibration sensor 400 (step (c)) to obtain a signal corresponding to the alternating current component of the magnetic force acting on the probe 10. The signal frequency demodulated by demodulator 430 is input to detector 3440.

(Detector 3440)
The detector 3440 measures the intensity (amplitude) of the frequency component corresponding to the frequency component to be measured of the alternating current magnetic field generated from the sample 20', which is included in the demodulated signal input from the demodulator 430 (step (d)). As will be described later, the measurement signal of the detector 3440 corresponds to the amplitude of the gradient in the vibration direction of the probe 10 of the component of the magnetic force acting on the probe 10 in the vibration direction of the probe 10 . Such a detector 3440 includes, for example, a narrowband bandpass filter capable of extracting a specific frequency component (i.e., a frequency component corresponding to the frequency component to be measured of the alternating magnetic field from the sample 20') and amplitude demodulation. It is also possible to configure it in combination with a device, or, for example, it can also be configured using a spectrum analyzer that measures the intensity of the sideband spectrum corresponding to the frequency of the frequency component to be measured of the alternating current magnetic field. In the AC magnetic field measurement apparatus 3000 of FIG. 7, the sample 20' is an AC electromagnet, and the detector 3440 uses the voltage signal or current signal of an AC current source (not shown) of the sample 20' as a reference signal to generate an input signal. Among them, a frequency component having a frequency corresponding to the alternating current magnetic field is detected and its intensity (amplitude) is measured. Such a detector 3440 can be configured with a lock-in amplifier or a synchronous detector.

The scanning mechanism 500 scans a scanning area (for example, a scanning area set on the surface of the sample 20') set in a plane (x, y directions) intersecting the vibration direction (z direction) of the probe 10. The needle 10 scans, and the measurement results output from the detector 3440 are stored in the memory 610 of the signal processing device 600 for each in-plane coordinate (x, y) set within the scanning area (step (e) ). In-plane coordinates (measurement points) (x, y) for performing measurements within the scanning area are preferably arranged in a grid pattern (that is, so as to constitute Cartesian coordinates). The number of measurement points in the scanning area can be set to an integer power of 2 in each of the x direction and the y direction, for example, so that the two-dimensional Fourier transform described later is easy.

(External AC magnetic field generator 3700)
The external AC magnetic field generator 3700 generates an external AC magnetic field whose frequency and phase match the AC magnetic field of the sample 20' and the frequency component to be measured when the probe 10 scans each in-plane coordinate (x, y) in the scanning area. It is configured to be able to apply to the probe 10 an external AC magnetic field in which the amplitude of the component parallel to the DC magnetic field from the DC magnetic field generator 3300 has a predetermined value. In the alternating current magnetic field measuring device 3000 of FIG. 7, the external alternating current magnetic field generator 3700 supplies a predetermined alternating current to the electromagnet including an electromagnetic core 710 and a coil 720 wound around the electromagnetic core 710, and to the electromagnetic coil 720. and an alternating current source 3730 configured to be able to do so. The external AC magnetic field generator 3700 is used when calibrating the measured value of magnetic field information using the AC magnetic field measuring device 3000. Details of the calibration method will be described later.

(Signal processing device 3600)
FIG. 8 is a diagram illustrating the configuration of the signal processing device 3600 and the flow of data processing in the signal processing device 3600. In FIG. 8, elements that are the same as those already shown in FIGS. 1 to 7 are denoted by the same reference numerals as in FIGS. 1 to 7, and explanations thereof may be omitted in whole or in part. The signal processing device 3600 includes a memory 610, a Fourier transformer 620, a first wavenumber filter calculator 3631, a second wavenumber filter calculator 3632, a third wavenumber filter calculator 3633, and an inverse Fourier transformer. 640, a first integral filter calculator 651, a second/third integral filter calculator 652, a direction conversion filter calculator 660, and a distance conversion filter calculator 670. The signal processing device 3600 includes a first wave number filter computing unit 3631, a second wave number filter computing unit 3633, and a second wave number filter computing unit 631, a second wave number filter computing unit 632, and a third wave number filter computing unit 3633. This differs from the signal processing device 600 (FIG. 5) in the DC magnetic field measuring device 1000 in that it includes a filter computing device 3632 and a third wave number filter computing device 3633, respectively.

The memory 610 stores measurement values corresponding to the measurement signals of the detector 3440 for each in-plane coordinate (x, y) within the scanning area. The Fourier transformer 620 performs a two-dimensional Fourier transform on the measured values for each in-plane coordinate (x, y) of the scanning area stored in the storage device 610, and converts the result into a two-dimensional Fourier transform for the in-plane coordinate (x, y). Output (step (f)).

The first wave number filter calculator 3631 calculates, from the Fourier transform information output from the Fourier transformer 620, the component (here, It is possible to extract information corresponding to the two-dimensional Fourier transform H _z ^ac(sample) (k _x , k _y , z) of the amplitude of the z component) in the in-plane direction of the scanning area (step (g0)) It is composed of The extraction calculation in the first wave number filter calculator 3631 is performed by extracting the DC magnetic field H ^dc at the position of the probe 10 and the DC magnetic field H dc at the position of the probe 10 with respect to the vibration direction of the probe 10 (here, the z direction). 2 between the order differential ∂H ^dc /∂z and the second order differential ∂ ² H ^dc /∂z ² of the DC magnetic field at the position of the probe 10 in the vibration direction of the probe 10 (here, the z direction). and a combination (k _x , k _y ) of two wave numbers in the in-plane (x, y) direction within the scanning area. Further details will be discussed below.

The second wave number filter calculator 3632 calculates, from the Fourier transform information output from the Fourier transformer 620, the component (here, Two-dimensional Fourier transform of the second-order differential of the amplitude of the z component) with respect to the vibration direction of the probe 10 (here, the z direction) in the in-plane direction of the scanning region ∂ ² _Hz ^ac(sample) /∂z ² It is configured to be able to extract information corresponding to (k _x , k _y , z) (step (g2)). The extraction calculation in the second wave number filter calculator 3632 is performed by extracting the DC magnetic field H ^dc at the position of the probe 10 and 1 of the DC magnetic field at the position of the probe 10 in the vibration direction of the probe 10 (here, the z direction). 2 between the order differential ∂H ^dc /∂z and the second order differential ∂ ² H ^dc /∂z ² of the DC magnetic field at the position of the probe 10 in the vibration direction of the probe 10 (here, the z direction). and a combination (k _x , k _y ) of two wave numbers in the in-plane (x, y) direction within the scanning area. Further details will be discussed below.

The third wave number filter calculator 3633 calculates the amplitude of the component parallel to the DC magnetic field from the DC magnetic field generator 3300 of the frequency component of the AC magnetic field to be measured, based on the Fourier transform information output from the Fourier transformer 620. , the two-dimensional Fourier transform of the first-order differential with respect to the vibration direction of the probe 10 (here, the z direction) in the in-plane (x, y) direction of the scanning region ∂H _z ^ac(sample) /∂z(k _x , k _y , z) (step (g3)). The extraction calculation in the third wave number filter calculator 3633 is performed by extracting the DC magnetic field H ^dc at the position of the probe 10 and the DC magnetic field H dc at the position of the probe 10 with respect to the vibration direction of the probe 10 (here, the z direction). 2 between the order differential ∂H ^dc /∂z and the second order differential ∂ ² H ^dc /∂z ² of the DC magnetic field at the position of the probe 10 in the vibration direction of the probe 10 (here, the z direction). and a combination (k _x , k _y ) of two wave numbers in the in-plane (x, y) direction within the scanning area. Further details will be discussed below. However, the third wave number filter calculator 3633 functions only when the first-order differential ^{∂H dc} /∂z of the DC magnetic field at the position of the probe 10 with respect to the vibration direction of the probe 10 (here, the z direction) Only if the value is non-zero.

The inverse Fourier transformer 640 generates information about the two-dimensional Fourier transform in the in-plane ( _x , _y ) direction of the scanning region (i.e., the value F(k _x , k _y )), the value (f(x, y)) in real space corresponding to the input is obtained for each in-plane (x, y) coordinate in the scanning area by two-dimensional inverse Fourier transformation (step (i0), (i2-0), (i2-2), (i1-0), (i1), (l0), (l2), (l1), (n0), (n2), (n1)) It is configured to be possible. For example, the scanning area of the amplitude _Hz ^ac(sample) (x, y, z) of the component parallel to the DC magnetic field from the DC magnetic field generator 3300 (here, the z component) of the frequency component of the AC magnetic field to be measured. When information corresponding to the two-dimensional Fourier transform H _z ^ac(sample) (k _x , k _y , z) in the in-plane (x, y) direction is input to the inverse Fourier transformer 640, the inverse Fourier transformer 640 is a two-dimensional inverse Fourier transform of the input information, and for each in-plane coordinate (x, y) in the scanning region, the value H _z ^ac corresponding to the component parallel to the DC magnetic field of the frequency component of the AC magnetic field. ^(sample) (x, y, z) is obtained (step (i0)).

The first integral filter calculator 651 performs an operation of integrating the input two-dimensional Fourier transform twice in the vibration direction of the probe 10 (here, the z direction) in Fourier space. Regarding the vibration direction of the probe 10 (here, the z-direction) of the component (here, the z-component) parallel to the DC magnetic field of the frequency component to be measured of the AC magnetic field extracted by the second wave number filter calculator 3632 The information corresponding to the two-dimensional Fourier transform ∂ ² _Hz ^ac(sample) /∂z ² (k _x , k _y , z) in the in-plane (x, y) direction of the scanning area of the second derivative of is expressed as When inputted to the first integral filter calculator 651, the inputted information is calculated in the plane of the scanning area (x, y) is converted into information corresponding to the two-dimensional Fourier transform H _z ^ac(sample) (k _x , k _y , z) and output (step (h2-0)). The above conversion in the first integral filter calculator 651 is performed based on a combination of two wave numbers (k _x , k _y ) in the in-plane (x, y) direction within the scanning area. Such an operation is to multiply the input value by 1/(k _x ² + k _y ² ) for each combination of wave numbers (k _x , k _y ) except for (k _x , _ky ) = (0, 0). This can be done by:

The second/third integral filter calculator 652 performs an operation (step (h2-1 ), (h1-0)). For example, the second derivative of the amplitude of the component parallel to the DC magnetic field (here, the z component) of the frequency component to be measured of the AC magnetic field, with respect to the vibration direction of the probe 10 (here, the z direction), in the scanning region. The information corresponding to the two-dimensional Fourier transform ∂ ² H _z ^ac(sample) /∂z ² (k _x , k _y , z) in the in-plane (x, y) direction is subjected to the second/third integral filter operation. When the input information is input to the device 652, the input information is the amplitude of the component (here, the z component) parallel to the DC magnetic field of the frequency component of the AC magnetic field, with respect to the vibration direction of the probe 10 (here, the z direction). The first derivative is converted into information corresponding to the two-dimensional Fourier transform ∂H _z ^ac(sample) /∂z(k _x , k _y , z) in the in-plane (x, y) direction of the scanning area and output. (Step (h2-1)). For example, the scanning area of the first derivative of the amplitude of the component parallel to the DC magnetic field (the z component here) of the frequency component to be measured of the AC magnetic field with respect to the vibration direction of the probe 10 (here the z direction) The information corresponding to the two-dimensional Fourier transform ∂H _z ^ac(sample) /∂z(k _x , k _y , z) in the in-plane (x, y) direction of 652, the input information is the two-dimensional Fourier transform of the frequency component of the AC magnetic field parallel to the DC magnetic field (in this case, the z component) in the in-plane (x, y) direction of the scanning area. It is converted into information corresponding to H _z ^ac(sample) (k _x , k _y , z) and output (step (h1-0)). Specifically, the above conversion in the second/third integral filter calculator 652 is performed based on a combination of two wave numbers (k _x , k _y ) in the in-plane (x, y) direction within the scanning region. For each combination of wavenumbers (k _x , k _y ) except (k _x , k _y )=(0,0), such an operation adds −1/(k _x ² +k _{y )} to the input value. ² ) This can be done by multiplying by ^1/2 .

The direction conversion filter calculator 660 uses magnetic field information (which may be the amplitude of the alternating magnetic field itself, or the vibration direction of the probe 10 of the amplitude of the alternating magnetic field) of a component (here, the z component) parallel to the vibration direction of the probe 10. In the plane of the scanning region ( An operation is performed to convert information corresponding to two-dimensional Fourier transform in the x, y) direction into magnetic field information of a component (here, the z component) in the in-plane (x, y) direction of the scanning area (step (k0) , (k2), (k1)). For example, the two-dimensional Fourier transform H _z ^{ac(sample )} _{( k} The information corresponding to the two-dimensional Fourier transform H _x ^ac(sample) (k _x , k _y , z) and H _y ^{ac (sample)} (k _x , k _y , z) in the in-plane (x, y) direction is is output (step (k0)). For example, the second derivative of the amplitude of the component (z component) parallel to the DC magnetic field of the frequency component to be measured of the AC magnetic field with respect to the vibration direction of the probe 10 in the plane of the scanning region (x, y) When information corresponding to the two-dimensional Fourier transform ∂ ² _Hz ^ac(sample) /∂z ² (k _x , k _y , z) regarding the direction is input to the direction conversion filter calculator 660, the frequency component of the alternating current magnetic field is Two-dimensional Fourier transform of the amplitude of the component in the in-plane (x, y) direction with respect to the vibration direction (z direction) of the probe 10 in the in-plane (x, y) direction of the scanning region ∂ Information corresponding to ² H _x ^ac(sample) /∂z ² (k _x , k _y , z) and ∂ ² H _y ^{ac (sample)} /∂z ² (k _x , k _y , z) is output. (Step (k2)). For example, the first derivative of the amplitude of the component (z component) parallel to the DC magnetic field of the frequency component to be measured of the AC magnetic field with respect to the vibration direction (z direction) of the probe 10 in the plane of the scanning region ( When information corresponding to the two-dimensional Fourier transform ∂H _z ^ac(sample) /∂z(k _x , k _y , z) in the x, y) direction is input to the direction conversion filter calculator 660, Two-dimensional Fourier in the in-plane (x, y) direction of the scanning region of the first derivative of the amplitude of the in-plane (x, y) direction component of the frequency component with respect to the vibration direction (z direction) of the probe 10 Information corresponding to the transformation ∂H _x ^ac(sample) /∂z(k _x , k _y , z), ∂H _y ^ac(sample) /∂z(k _x , k _y , z) is output (step (k1)). Each of the above conversions in the direction conversion filter calculator 660 is performed based on a combination (k _x , k _y ) of two wave numbers in the in-plane (x, y) direction within the scanning region. Specifically, the conversion from the z (vertical direction) component to the x component is performed by adding -ik _x / (k _x ² + k _y ² ) ¹ to the input value for each wavenumber combination (k _x , k _y ). ^/2 (i is an imaginary unit), and the conversion from the z (vertical direction) component to the y component can be performed by multiplying each wave number combination by (k _x , k _y ) = (0, 0). For (k _x , k _y ), this can be done by multiplying the input value by -ik _y /(k _x ² +k _y ² ) ^1/2 . Note that when the input magnetic field information is information on a perpendicular magnetic field component (z component), the direction conversion filter calculator 660 is configured such that when the input magnetic field information is information on a vertical magnetic field component (z component), that is, when the direction of application of the DC magnetic field from the DC magnetic field generator 3700 is direction (z direction, ie vertical direction).

The distance conversion filter calculator 670 uses magnetic field information (of the amplitude itself of the alternating magnetic field) obtained by measurement at the first probe position (z=z') in the vibration direction of the probe 10 (here, the z direction). The information may be information about the first order differential of the amplitude of the alternating magnetic field in the direction of vibration of the probe 10 (z direction), or the information of the first order differential of the amplitude of the alternating magnetic field in the direction of vibration of the probe 10 (z direction). It may also be information on the second-order differential of ), the information corresponding to the two-dimensional Fourier transform in the in-plane (x, y) direction of the scanning area can be transferred from the first tip position to a virtual second tip position shifted in the tip vibration direction. An operation of converting into magnetic field information at the probe position (z=z'+Δz) is performed (steps (m0), (m2), (m1)).
For example, the amplitude of the component parallel to the DC magnetic field (here, the z component) of the frequency component to be measured of the AC magnetic field at the probe position z = z', in the in-plane (x, y) direction of the scanning area. When information corresponding to the dimensional Fourier transform H _z ^ac(sample) (k _x , k _y , z') and Δz are input to the distance conversion filter calculator 670, the alternating magnetic field at the probe position z=z'+Δz is Two-dimensional Fourier transform H _z ^ac(sample) (k _x , k _y , z '+Δz) is output (step (m0)). Furthermore, for example, the two-dimensional Fourier transform _H When information corresponding to ^ac(sample) (k _x , k _y , z') and H _y ^{ac (sample)} (k _x , k _y , z') and Δz are input to the distance conversion filter calculator 670, Two-dimensional Fourier transform H _x ^ac( information corresponding to ^sample) (k _x , k _y , z'+Δz) and H _y ^{ac (sample)} (k _x , k _y , z'+Δz) is output. For example, the second derivative of the amplitude of the component (z component) parallel to the DC magnetic field of the frequency component of the AC magnetic field at the probe position z=z' with respect to the vibration direction (z direction) of the probe 10, The information corresponding to the two-dimensional Fourier transform ∂ ² _Hz ^ac(sample) /∂z ² (k _x , k _y , z') in the in-plane (x, y) direction of the scanning area and Δz are distance-transformed. When input to the filter calculator 670, the amplitude of the component parallel to the DC magnetic field (z component) of the frequency component of the AC magnetic field at the probe position z = z' + Δz, regarding the vibration direction (z direction) of the probe 10. Information corresponding to the two-dimensional Fourier transform ∂ ² _Hz ^ac(sample) /∂z ² (k _x , k _y , z'+Δz) in the in-plane (x, y) direction of the scanning area of the second derivative of is output (step (m2)). For example, the scanning area of the second derivative of the amplitude of the in-plane components (x, y components) of the frequency component of the alternating current magnetic field at the probe position z=z' with respect to the vibration direction (z direction) of the probe 10 Two-dimensional Fourier transform in the in-plane (x, y) direction of ^{∂ 2} H _x ^ac(sample) /∂z ² (k _x , k _y , z'), ∂ ² H _y ^ac(sample) /∂z ² When information corresponding to (k _x , k _y , z') and Δz are input to the distance conversion filter calculator 670, the in-plane component (x , y component) with respect to the vibration direction (z direction) of the probe 10, two-dimensional Fourier transform in the in-plane (x, y) direction of the scanning region ∂ ² H _x ^ac(sample) /∂z ² (k _x , k _y , z'+Δz) and information corresponding to ∂ ² H _y ^ac(sample) /∂z ² (k _x , k _y , z'+Δz) are output. Further, for example, the first-order differential of the amplitude of the component (z component) of the frequency component of the AC magnetic field parallel to the DC magnetic field at the probe position z=z' with respect to the vibration direction (z direction) of the probe 10, The information corresponding to the two-dimensional Fourier transform ∂H _z ^ac(sample) /∂z(k _x , k _y , z') in the in-plane (x, y) direction of the scanning area and Δz are subjected to a distance conversion filter operation. 1 in the vibration direction (z direction) of the probe 10 of the amplitude of the component parallel to the DC magnetic field (z component) of the frequency component of the AC magnetic field at the probe position z = z' + Δz. Information corresponding to the two-dimensional Fourier transform ∂H _z ^ac(sample) /∂z(k _x , k _y , z'+Δz) of the order differential in the in-plane (x, y) direction of the scanning area is output. (Step (m1)). Further, for example, the scanning area of the first derivative of the amplitude of the in-plane components (x, y components) of the frequency component of the alternating current magnetic field at the probe position z=z' with respect to the vibration direction (z direction) of the probe 10 Two-dimensional Fourier transform in the in-plane (x, y) direction ∂H _x ^ac(sample) /∂z(k _x , k _y , z'), ∂H _y ^ac(sample) /∂z(k _x , When the information corresponding to k _y , z') and Δz are input to the distance conversion filter calculator 670, the in-plane components (x, y components) of the frequency component of the AC magnetic field at the probe position z=z'+Δz The two-dimensional Fourier transform of the first-order differential of the amplitude with respect to the vibration direction (z direction) of the probe 10 in the in-plane (x, y) direction of the scanning region ∂H _x ^ac(sample) /∂z(k _x , k _y , z'+Δz) and ∂H _y ^ac(sample) /∂z(k _x , k _y , z'+Δz) are output.
Each of the above conversions in the distance conversion filter calculator 670 is performed based on a combination (k _x , k _y ) of two wave numbers in the in-plane (x, y) direction within the scanning region. _Specifically , _such conversion of _the tip position is performed by adding _exp ( This can be done by multiplying by -(k _x ² + k _y ² ) ^1/2 Δz).

FIG. 9 is a diagram schematically illustrating an AC magnetic field measuring device 4000 according to another embodiment. In FIG. 9, elements that have already appeared in FIGS. 1 to 8 are given the same reference numerals as those in FIGS. 1 to 8, and their explanations may be omitted. The AC magnetic field measuring device 4000 has a DC magnetic field generator 4300 instead of the DC magnetic field generator 3300, and is configured so that the DC magnetic field generator 4300 can also function as an external AC magnetic field generator, as shown in FIG. This is different from the AC magnetic field measuring device 3000 of . That is, the AC magnetic field measuring device 4000 includes a DC/AC current source 4330 instead of the DC current source 3320 and the AC current source 3730. The DC/AC current source 2330 is a current source that, in addition to supplying a DC current, can also supply a current in which an AC current is superimposed on a DC current, if necessary. The DC magnetic field generator 4300 includes an electromagnet including an electromagnetic core 4320 and a coil 4310 wound around the electromagnetic core 4320, and a DC/AC generator that supplies DC current and, if necessary, AC current to the coil 4310 of the electromagnet. A current source 4330 is provided. The DC magnetic field generator 4300 further includes a changeover switch 4340, which allows the user to switch between supplying the current from the DC/AC current source 4330 to the electromagnetic coil 4320 or to the air core coil 310. can. The AC magnetic field measuring device 4000 further includes a parameter fitting calculator 4800. In one embodiment, the parameter fitting calculator 4800 calculates the following when the electromagnet is used as the DC magnetic field generator 4300 (that is, when DC current from the DC/AC current source 4330 is supplied to the coil 4320 of the electromagnet): The measurement result of the amplitude of the component parallel to the DC magnetic field of the frequency component to be measured of the AC magnetic field is calculated when the air-core coil 310 is used as the DC magnetic field generator (that is, when the DC current from the DC/AC current source 4330 is The DC magnetic field H ^dc at the position of the probe 10 and the direction of vibration of the probe 10 (z direction) of the DC magnetic field at the position of the probe 10 are adjusted so as to match the measurement results of (when supplied to the air core coil 310) ^The two ratios between the first-order differential ^{∂H dc} / ^∂z of By optimizing, it may be possible to determine the ratio between the two. In another embodiment, the parameter fitting calculator 4800 uses the electromagnet described above as the DC magnetic field generator 4300 (that is, when the DC current from the DC/AC current source 4330 is supplied to the coil 4320 of the electromagnet) The measurement result of the second-order differential in the vibration direction (z direction) of the probe 10 of the amplitude of the frequency component of the frequency component of the AC magnetic field parallel to the DC magnetic field is measured using the air-core coil 310 as a DC magnetic field generator. The DC magnetic field H dc at the position of the probe 10 and the position of the probe 10 are adjusted so as to match the measurement results when the DC/AC current source 4330 supplies ^DC current to the air-core coil 310. The first-order differential ∂H ^dc /∂z of the DC magnetic field at the position of the probe 10 with respect to the vibration direction (z direction) and the second-order differential ∂H dc /∂z of the DC magnetic field at the position of the probe 10 with respect to the vibration direction of the probe 10. It may be possible to determine the two ratios by optimizing the two ratios between ² H ^dc /∂z ² . The effects of the AC magnetic field measuring device and method of the present invention can also be obtained by the AC magnetic field measuring device 4000 having such a configuration.

In the above description of the present invention, the AC magnetic field measurement apparatuses 3000 and 4000 and the AC magnetic field measurement method are taken as examples in which the processing by the direction conversion filter calculation unit 660 is applied before the processing by the distance conversion filter calculation unit 670. However, the present invention is not limited to this form. For example, it is also possible to provide an AC magnetic field measurement device and an AC magnetic field measurement method in which the processing by the distance conversion filter calculation unit 670 is first applied, and then the processing by the direction conversion filter calculation unit 660 is applied.

(Measurement principle: measurement of alternating current magnetic field)
The operating principle of the alternating current magnetic field measuring device of the present invention and the measurement principle of the alternating current magnetic field measuring method of the present invention will be explained. The measurement, calibration, and conversion principles described above for measuring samples that generate only DC magnetic fields can also be applied when measuring samples that generate only AC magnetic fields.
In the xyz coordinate system, the direction of vibration of the probe is the z direction. A DC magnetic field H ^dc is applied to the probe from a DC magnetic field generator (for example, an air-core coil, etc.). Similarly, the magnetic field H at the probe position is expressed by equation (5):

（Ｈ^ｄｃ：直流磁場発生器からの直流磁場、Ｈ^ａｃ：試料からの交流磁場の振幅）
で表される。式（５）自体に変更はないが、直流磁場試料を測定する場合とは、Ｈ^ｄｃ及びＨ^ａｃの定義が異なっている。ωは試料からの交流磁場の角周波数である。超常磁性探針に誘起される磁気モーメントｍは、同様に式（６）：

(H ^dc : DC magnetic field from the DC magnetic field generator, H ^ac : amplitude of the AC magnetic field from the sample)
It is expressed as Although the formula (5) itself remains unchanged, the definitions of H ^dc and H ^ac are different from those in the case of measuring a DC magnetic field sample. ω is the angular frequency of the alternating magnetic field from the sample. Similarly, the magnetic moment m induced in the superparamagnetic tip is expressed by equation (6):

（χ：超常磁性探針の磁化率）
で表される。磁場Ｈ中に存在する磁気モーメントｍの位置エネルギーＵは、同様に式（７）：

(χ: Magnetic susceptibility of superparamagnetic tip)
It is expressed as Similarly, the potential energy U of the magnetic moment m existing in the magnetic field H is expressed by equation (7):

で表される。探針に作用する磁気力Ｆのｚ方向成分Ｆ_ｚの勾配Ｆ_ｚ’は、同様に式（８）：

It is expressed as Similarly, the gradient _Fz ' of the z-direction component _Fz of the magnetic force F acting on the probe is expressed by equation (8):

で表されるから、その角周波数ωで振動する成分（ωｔ成分）Ｆ_ｚ’（ωｔ）は、同様に式（９）：

Therefore, the component (ωt component) F _z '(ωt) that vibrates at the angular frequency ω is similarly expressed by equation (9):

で表される。試料からの交流磁場Ｈ^ａｃをＨ^{ａｃ（ｓａｍｐｌｅ）}と書き直す。探針位置の直流磁場がｚ軸方向であるとき（例えば空芯コイルの平面内の中心からの直流磁場は、空芯コイルの軸方向である。空芯コイルの平面内の中心に探針が配置され、空芯コイルの軸方向がｚ軸方向であるならば、探針位置の直流磁場もｚ軸方向となる。）、探針位置の磁場Ｈは、ｚ軸方向の単位ベクトルｋ_ｚおよび直流磁場Ｈ^ｄｃのｚ成分の強度Ｈ_ｚ ^ｄｃを用いて

It is expressed as The alternating current magnetic field H ^ac from the sample is rewritten as H ^{ac (sample)} . When the DC magnetic field at the probe position is in the z-axis direction (for example, the DC magnetic field from the center in the plane of the air-core coil is in the axial direction of the air-core coil. (If the axial direction of the air-core coil is in the z-axis direction, the DC magnetic field at the probe position will also be in the z-axis direction.), The magnetic field H at the probe position is expressed by the unit vector k _z in the z-axis direction and Using the strength of the z component of the direct current magnetic field H ^dc H _z ^dc

で表され、超常磁性探針に誘起される磁気モーメントｍは

The magnetic moment m induced in the superparamagnetic tip is expressed as

となるから、磁気力勾配のωｔ成分において、試料からの交流磁場Ｈ^{ａｃ（ｓａｍｐｌｅ）}のうちｚ成分Ｈ_ｚ ^{ａｃ（ｓａｍｐｌｅ）}だけが関与して、測定可能量Ｆ_ｚ’（ωｔ）は

Therefore, in the ωt component of the magnetic force gradient, only the z component H _z ^{ac (sample)} of the AC magnetic field H ^{ac (sample)} from the sample is involved, and the measurable quantity F _z '(ωt) is

となる。直流磁場源として空芯コイルを用い、空芯コイル中心の軸方向（ｚ方向）の直流交流磁場Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}を超常磁性探針に印加する場合を考える。コイル定数Ｃ_１、Ｃ_２、及びＣ_３として、

becomes. Consider a case where an air-core coil is used as a DC magnetic field source and a DC/AC magnetic field H _z ^{dc (coil)} in the axial direction (z direction) centered on the air-core coil is applied to a superparamagnetic probe. As coil constants C ₁ , C ₂ , and C ₃ ,

とおく。定数Ｃ_１、Ｃ_２、Ｃ_３に含まれるＨ_ｚ ^{ｄｃ（ｃｏｉｌ）}並びにその１階微分∂Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}／∂ｚおよび２階微分∂^２Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}／∂ｚ^２は、空芯コイルの式（１５）から解析的に又は数値的に求めることができる。それらの符号は空芯コイルを交流磁場源として用いる場合と同様である。探針を空芯コイルの面内（ｘｙ）方向の中心かつ軸方向のｚ＞０の位置に配置するとき、式（１２’）は

far. The constants C ₁ , C ₂ , and C ₃ include H _z ^dc(coil) , its first derivative ∂H _z ^dc(coil) /∂z, and its second derivative ∂ ² H _z ^dc(coil) /∂z ² . , can be determined analytically or numerically from the air-core coil equation (15). These codes are the same as when an air-core coil is used as an alternating current magnetic field source. When the probe is placed at the center of the air-core coil in the in-plane (xy) direction and at the position where z>0 in the axial direction, equation (12') is

となる。振幅を比較することにより

becomes. By comparing the amplitude

が得られる。式（１７’）において左辺が測定可能量である。空芯コイルの中心軸上においてＣ_１の符号は不変であるので、ここではＣ_１＞０を仮定している。式中、σ（Ｃ_３）の定義は式（１８）の通りである。探針の振動方向（ｚ軸方向）に交差する面内（ｘｙ面内方向）に定められた走査領域を探針で走査しながら測定を行う、すなわち、走査領域内の各（ｘ，ｙ）座標について測定を行うことにより、測定可能量

is obtained. In equation (17'), the left side is the measurable quantity. Since the sign of C ₁ does not change on the central axis of the air-core coil, it is assumed here that C ₁ >0. In the formula, σ(C ₃ ) is defined as in formula (18). Measurement is performed while the probe scans a scanning area defined in a plane (xy plane direction) that intersects the vibration direction (z-axis direction) of the probe, that is, each (x, y) within the scanning area Measurable quantities by making measurements on coordinates

（すなわち式（１７’）の左辺）の走査領域内（ｘｙ面内）における分布：

(i.e., the left side of equation (17')) within the scanning area (in the xy plane):

が得られる。その面内方向（ｘ及びｙ）についてのフーリエ変換（二次元フーリエ変換）は、式（１７’）及びフーリエ変換の線型性から、

is obtained. The Fourier transform (two-dimensional Fourier transform) in the in-plane direction (x and y) is given by equation (17') and the linearity of the Fourier transform.

を満たす。式中、ｋ_ｘ及びｋ_ｙは面内方向における波数である。式中、

satisfy. In the formula, k _x and k _y are wave numbers in the in-plane direction. During the ceremony,

はそれぞれ、

are each

の面内方向（ｘ及びｙ）についてのフーリエ変換である。再び、Ｓａｉｔｏの式（２６）から、式（２１’）において

is a Fourier transform in the in-plane direction (x and y) of . Again, from Saito's equation (26), in equation (21')

である。式中、ρ（ｋ_ｘ，ｋ_ｙ，ｚ_０）は、ｚ＝ｚ_０における（仮想的な）磁荷分布のｘ及びｙについてのフーリエ変換である。上記同様にｍ_ｚ／（２μ_０）＝１で規格化すると、式（２１’）から

It is. In the formula, ρ(k _x , k _y , z ₀ ) is the Fourier transform of the (virtual) magnetic charge distribution at z=z ₀ with respect to x and y. If normalized by m _z /(2μ ₀ )=1 in the same way as above, from equation (21'),

であるから、Ｃ_１、Ｃ_２、及びＣ_３について、それぞれ上記同様に

Therefore, for C ₁ , C ₂ and C ₃ , the same as above

を得る。すなわち、測定可能量の面内方向についてのフーリエ変換（式（２１’）左辺、式（３０ａ’）～（３０ｃ’）右辺第２項）から、コイル定数Ｃ_１、Ｃ_２、Ｃ_３、及び面内方向の波数ｋ_ｘ、ｋ_ｙに基づいて、探針位置における試料からの交流磁場の振幅のｚ成分Ｈ_ｚ ^{ａｃ（ｓａｍｐｌｅ）}並びにその１階微分（勾配）∂Ｈ_ｚ ^{ａｃ（ｓａｍｐｌｅ}／∂ｚ及び２階微分∂^２Ｈ_ｚ ^{ａｃ（ｓａｍｐｌｅ}／∂ｚ^２の、それぞれの面内方向（ｘ及びｙ）についてのフーリエ変換（左辺）を分離抽出することができる（波数フィルタ）。分離抽出された各左辺をｋ_ｘ、ｋ_ｙについて二次元逆フーリエ変換することにより、探針位置における試料からの交流磁場の振幅のｚ成分Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ）並びにその１階微分（勾配）∂Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ}／∂ｚ（ｘ，ｙ，ｚ）及び２階微分∂^２Ｈ_ｚ ^{ｄｃ（ｓａｍｐｌｅ}／∂ｚ^２（ｘ，ｙ，ｚ）を復元することができる。
Ｃ_３がＣ_１と同符号（Ｃ_３＞０）である場合には、σ（Ｃ_３）＝＋１であるので、式（３０ａ’）～（３０ｃ’）は

get. That is, from the Fourier transform in the in-plane direction of the measurable quantity (the left side of equation (21'), the second term on the right side of equations (30a') to (30c')), the coil constants C ₁ , C ₂ , C ₃ , and _Based on ^the in- _{plane wave} ^numbers _k The Fourier transform (left side) for each in-plane direction (x and y) of _z and second-order differential ∂ ² Hz ^{ac (sample} /∂z ² ) can be separated and extracted (wave number filter). By performing a two _- ^dimensional inverse Fourier transform on each left side _of the equation with respect to _k The differential (gradient) ∂H _z ^dc(sample /∂z(x,y,z)) and the second derivative ∂ ² H _z ^dc(sample /∂z ² (x,y,z)) can be recovered.
When C ₃ has the same sign as C ₁ (C ₃ >0), σ(C ₃ )=+1, so equations (30a') to (30c') are

となる。Ｃ_３がＣ_１と異符号（Ｃ_３＜０）である場合には、σ（Ｃ_３）＝－１であるので、式（３０ａ’）～（３０ｃ’）は

becomes. When C ₃ has a different sign from C ₁ (C ₃ <0), σ(C ₃ )=-1, so equations (30a') to (30c') are

となる。波数フィルタ部分は直流磁場測定の場合と同一であるので、その処理も直流磁場測定の場合と同様に考えることができる。直流磁場測定の場合と同様に、波数フィルタ（式（１０８ａ）～（１０８ｃ）及び式（１０９ａ）～（１０９ｃ））の入力

becomes. Since the wave number filter part is the same as in the case of DC magnetic field measurement, its processing can be considered in the same way as in the case of DC magnetic field measurement. As in the case of DC magnetic field measurement, input the wave number filter (Equations (108a) to (108c) and Equations (109a) to (109c))

は不明な定数（β）倍されていてもよい。上記同様に磁場の２階微分、磁場の１階微分、及び磁場の測定感度に対応する係数（測定感度係数）をα_１、α_２、α_３とすると、Ｃ_３がＣ_１と同符号のとき

may be multiplied by an unknown constant (β). Similarly to the above, if the coefficients corresponding to the second derivative of the magnetic field, the first derivative of the magnetic field, and the measurement sensitivity of the magnetic field (measurement sensitivity coefficients) are α ₁ , α ₂ , α ₃ , C ₃ has the same sign as C ₁ time

となり、Ｃ_３がＣ_１と異符号のとき

So, when C ₃ has a different sign from C ₁

となる（式中、ε’は任意に定められる微小実定数であり、その選び方及び好ましい範囲は直流磁場測定について説明したε’（式（４０ａ）～（４０ｃ））と同様である。）。直流磁場測定の場合と同様に、磁場像の較正において磁場の強度を補正する操作は、不明な定数βを乗じられた入力

(In the formula, ε' is an arbitrarily determined infinitesimal real constant, and its selection and preferred range are the same as ε' (Equations (40a) to (40c)) described for DC magnetic field measurement.) As in the case of DC magnetic field measurements, the operation of correcting the magnetic field strength in calibrating the magnetic field image is based on the input multiplied by an unknown constant β.

に対して、測定感度係数α_１、α_２、及び／又はα_３を求める操作に対応する。したがって、波数フィルタの入力（式（５９’））がいかなる定数倍を含んでいるかを知る必要はない。

This corresponds to the operation of determining the measurement sensitivity coefficients α ₁ , α ₂ , and/or α ₃ for . Therefore, it is not necessary to know what constant multiple the input to the wave number filter (Equation (59')) contains.

In this way, the specific calculation in the first wave number filter calculator 3631 (FIG. 8) is based on the detection of the DC magnetic field _Hz ^{dc (coil)} at the position of the probe 10 and the DC magnetic field at the position of the probe 10. If the second-order differential ∂ ² _Hz ^dc(coil) /∂z ² with respect to the vibration direction (z direction) of the needle 10 has the same sign, the input for each wave number combination (k _x , k _y ) (Formula (59'))

を乗じることにより行うことができ、Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}と∂^２Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}／∂ｚ^２とが異符号である場合には、各波数の組み合わせ（ｋ_ｘ，ｋ_ｙ）について、入力（式（５９’））に

If H _z ^{dc (coil)} and ∂ ² H _z ^{dc (coil)} / ∂z ² have opposite signs, then for each wave number combination (k _x , k _y ) , input (equation (59'))

を乗じることにより行うことができる。また、第２の波数フィルタ演算器３６３２（図８）における具体的な演算は、Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}と∂^２Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}／∂ｚ^２とが同符号である場合には、各波数の組み合わせ（ｋ_ｘ，ｋ_ｙ）について、入力（式（５９’））に

This can be done by multiplying by Further, the specific calculation in the second wave number filter calculation unit 3632 (FIG. 8) is as follows when H _z ^dc(coil) and ∂ ² H _z ^dc(coil) /∂z ² have the same sign. For each wavenumber combination (k _x , k _y ), input (Equation (59'))

を乗じることにより行うことができ、Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}と∂^２Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}／∂ｚ^２とが異符号である場合には、各波数の組み合わせ（ｋ_ｘ，ｋ_ｙ）について、入力（式（５９’））に

If H _z ^{dc (coil)} and ∂ ² H _z ^{dc (coil)} / ∂z ² have opposite signs, then for each wave number combination (k _x , k _y ) , input (equation (59'))

を乗じることにより行うことができる。また、第３の波数フィルタ演算器３６３３（図８）における具体的な演算は、Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}と∂^２Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}／∂ｚ^２とが同符号である場合には、各波数の組み合わせ（ｋ_ｘ，ｋ_ｙ）について、入力（式（５９’））に

This can be done by multiplying by Further, the specific calculation in the third wave number filter calculator 3633 (FIG. 8) is as follows when H _z ^dc(coil) and ∂ ² H _z ^dc(coil) /∂z ² have the same sign. For each wave number combination (k _x , k _y ), input (Equation (59'))

を乗じることにより行うことができ、Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}と∂^２Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}／∂ｚ^２とが異符号である場合には、各波数の組み合わせ（ｋ_ｘ，ｋ_ｙ）について、入力（式（５９’））に

If H _z ^dc(coil) and ∂ ² H _z ^dc(coil) /∂z ² have opposite signs, then for each wavenumber combination (k _x , k _y ) , input (equation (59'))

を乗じることにより行うことができる。ただし上記の通り、第３の波数フィルタ演算器３６３３を用いて入力（式（５９’）：フーリエ変換器６２０の出力）から交流磁場の振幅の１階微分のフーリエ変換∂Ｈ_ｚ ^{ａｃ（ｓａｍｐｌｅ）}／∂ｚ（ｋ_ｘ，ｋ_ｙ，ｚ）を抽出することは、探針位置における直流磁場の探針の振動方向についての１階微分∂Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}／∂ｚの値が非ゼロである場合にのみ可能である。なお、∂Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}／∂ｚの値がゼロであっても、第２の波数フィルタ演算器３６３２により入力（式（５９’））から交流磁場の２階微分のフーリエ変換∂^２Ｈ_ｚ ^{ａｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｋ_ｘ，ｋ_ｙ，ｚ）を抽出し、これを第２／第３の積分フィルタ演算器６５２によりフーリエ空間上で１回積分（∂Ｈ_ｚ ^{ａｃ（ｓａｍｐｌｅ）}／∂ｚ（ｋ_ｘ，ｋ_ｙ，ｚ）＝－（ｋ_ｘ ^２＋ｋ_ｙ ^２）^－１／２×∂^２Ｈ_ｚ ^{ａｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｋ_ｘ，ｋ_ｙ，ｚ））することにより、交流磁場の振幅の１階微分のフーリエ変換∂Ｈ_ｚ ^{ａｃ（ｓａｍｐｌｅ）}／∂ｚ（ｋ_ｘ，ｋ_ｙ，ｚ）を得ることができ、これを逆フーリエ変換器６４０で二次元逆フーリエ変換することにより、実空間での交流磁場の振幅の１階微分∂Ｈ_ｚ ^{ａｃ（ｓａｍｐｌｅ）}／∂ｚ（ｘ，ｙ，ｚ）を得ることができる。
波数フィルタの部分において、係数｜Ｃ_２｜／｜Ｃ_１｜及び｜Ｃ_３｜／｜Ｃ_１｜は

This can be done by multiplying by However, as mentioned above, the third wave number filter calculator 3633 is used to convert the input (Equation (59'): output of the Fourier transformer 620) into the Fourier transform of the first differential of the amplitude of the AC magnetic field ∂H _z ^{ac (sample)} _Extracting / _{∂z (} ^k This is possible only if . Note that even if the value of ∂H _z ^dc(coil) /∂z is zero, the second wave number filter calculator 3632 converts the Fourier transform of the second-order differential of the alternating magnetic field ^∂ 2 from the input (formula (59')). H _z ^{ac (sample)} _{/ ∂z} ^{2 (} _k ^sample) /∂z(k _x , k _y , z) = -(k _x ² + k _y ² ) ^-1/2 ×∂ ² H _z ^ac(sample) /∂z ² (k _x , k _y , z) ), the Fourier transform of the first differential of the amplitude of the alternating magnetic field ∂H _z ^ac(sample) /∂z(k _x , k _y , z) can be obtained, and this is double By performing dimensional inverse Fourier transform, the first-order differential ∂H _z ^ac(sample) /∂z(x, y, z) of the amplitude of the alternating magnetic field in real space can be obtained.
In the wavenumber filter part, the coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ | are

であり、これらは探針の磁化率χに依存しない。特に外部直流磁場の発生源が空芯コイルである場合には、空芯コイルの式（１５）から、これらの２つの係数を算出できる。なお上記式（１０８ａ’）～（１０８ｃ’）及び式（１０９ａ’）～（１０９ｃ’）の波数フィルタ部分は、定数Ｃ_１が必ず非ゼロであることを利用して、｜Ｃ_２｜／｜Ｃ_１｜及び｜Ｃ_３｜／｜Ｃ_１｜の２つの比を係数として用いるように、波数フィルタ部分の分母及び分子を｜Ｃ_１｜で除することにより式変形して得られたものであるが、波数フィルタ部分を表す式の形は必ずしもこれに限られるものではない。例えば、波数フィルタの分母および分子の両方に｜Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}｜を乗じることにより、｜Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}｜、｜∂Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}／∂ｚ｜、及び｜∂^２Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}／∂ｚ^２｜の間の２つの比（式（６６’）、（６７’））に代えて、｜Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}｜、｜∂Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}／∂ｚ｜、及び｜∂^２Ｈ_ｚ ^{ｄｃ（ｃｏｉｌ）}／∂ｚ^２｜の３つの値を係数として用いてもよい。また、直流磁場測定の場合と同様に、例えば定数Ｃ_２が非ゼロであれば、｜Ｃ_１｜／｜Ｃ_２｜及び｜Ｃ_３｜／｜Ｃ_２｜の２つの比を係数として用いることも可能である。そのような波数フィルタは次のように表される。

and these do not depend on the magnetic susceptibility χ of the tip. In particular, when the source of the external DC magnetic field is an air-core coil, these two coefficients can be calculated from equation (15) for the air-core coil. Note that the wave number filter portion of the above equations (108a') to (108c') and equations (109a') to (109c') utilizes the fact that the constant C ₁ is always non-zero to calculate |C ₂ |/| It was obtained by transforming _the formula by dividing the denominator and numerator of the wave number filter part by |C ₁ | so that the two ratios of C 1 | and |C ₃ |/|C ₁ | are used as coefficients. However, the form of the equation representing the wave number filter portion is not necessarily limited to this. For example, by multiplying both the denominator and numerator of a wavenumber filter by |H _z ^dc(coil) |, |H _z ^dc(coil) |, |∂H _z ^dc(coil) /∂z|, and |∂ ² Instead of the two ratios between H _z ^dc(coil) /∂z ² | (Equations (66') and (67')), |H _z ^dc(coil) |, |∂H _z ^dc(coil) /∂z| and |∂ ² H _z ^dc(coil) /∂z ² | may be used as coefficients. Also, as in the case of DC magnetic field measurement, for example, if the constant C ₂ is non-zero, the two ratios of |C ₁ |/|C ₂ | and |C ₃ |/|C ₂ | can be used as coefficients. is also possible. Such a wavenumber filter is expressed as follows.

（式中、Ｃ_３はＣ_１と同符号）、

(In the formula, C ₃ has the same sign as C ₁ ),

（式中、Ｃ_３はＣ_１と異符号；ε”は任意に定められる微小実定数であり、その選び方及び好ましい範囲はε’と同様である。）
また例えば定数Ｃ_３が非ゼロであれば、｜Ｃ_１｜／｜Ｃ_３｜及び｜Ｃ_２｜／｜Ｃ_３｜の２つの比を係数として用いるように式変形を行うことも可能である。そのような波数フィルタは次のように表される。

(In the formula, _C3 has a different sign from _C1 ; ε'' is an arbitrarily determined infinitesimal real constant, and its selection and preferred range are the same as ε'.)
For example, if the constant C ₃ is non-zero, it is also possible to transform the equation so that the two ratios of |C ₁ |/|C ₃ | and |C ₂ |/|C ₃ | are used as coefficients. . Such a wavenumber filter is expressed as follows.

（式中、Ｃ_３はＣ_１と同符号）

(In the formula, C ₃ has the same sign as C ₁ )

（式中、Ｃ_３はＣ_１と異符号；ε’’’は任意に定められる微小実定数であり、その選び方及び好ましい範囲はε’と同様である。）
ただし、汎用性の高さ及び計算の安定性の観点からは、上記式（１０８ａ’）～（１０８ｃ’）及び式（１０９ａ’）～（１０９ｃ’）におけるように、｜Ｃ_２｜／｜Ｃ_１｜及び｜Ｃ_３｜／｜Ｃ_１｜の２つの比を、波数フィルタ部分の係数として用いることが好ましい。

(In the formula, C ₃ has a different sign from C ₁ ; ε''' is an arbitrarily determined infinitesimal real constant, and its selection method and preferred range are the same as ε'.)
However, from the viewpoint of high versatility and stability of calculation, |C ₂ |/|C It is preferable to use two ratios of ₁ | and |C ₃ |/|C ₁ | as coefficients of the wave number filter section.

As in the case of DC magnetic field measurements, α ₁ is the measurement sensitivity coefficient of the second derivative of the magnetic field and corresponds to C ₁ . α ₂ is the measurement sensitivity coefficient of the first derivative of the magnetic field and corresponds to C ₂ . α ₃ is the measurement sensitivity coefficient of the magnetic field and corresponds to C ₃ . The measurement sensitivity coefficients α ₁ , α ₂ and α ₃ are proportional to each other via the definition of constants C ₁ , C ₂ and C ₃ (Equation (13′)). The operation of calibrating the signal strength corresponds to determining one of the measurement sensitivity coefficients. When an air-core coil is used as the source of the AC magnetic field, once any one of the measurement sensitivity coefficients α ₁ , α ₂ , and α ₃ is determined, the equation (15) and constant C of the air-core coil can be calculated. From the definitions of ₁ , C ₂ , and C ₃ (Equation (13)), the remaining two measurement sensitivity coefficients can also be determined. For example, if the measurement sensitivity coefficient α ₃ of the magnetic field is determined, the measurement sensitivity coefficient α ₁ of the second derivative of the magnetic field and the measurement sensitivity coefficient α ₂ of the first derivative of the magnetic field are:

で求めることができる。また例えば、磁場の２階微分の測定感度係数α_１が定まったならば、及び磁場の１階微分の測定感度係数α_２、及び磁場の測定感度係数α_３は

It can be found by For example, if the measurement sensitivity coefficient α ₁ of the second derivative of the magnetic field is determined, the measurement sensitivity coefficient α ₂ of the first derivative of the magnetic field, and the measurement sensitivity coefficient α ₃ of the magnetic field are

で求めることができる。また例えば、磁場の１階微分の測定感度係数α_２が定まったならば、磁場の２階微分の測定感度係数α_１、及び磁場の測定感度係数α_３は

It can be found by For example, if the measurement sensitivity coefficient α ₂ of the first derivative of the magnetic field is determined, the measurement sensitivity coefficient α ₁ of the second derivative of the magnetic field and the measurement sensitivity coefficient α ₃ of the magnetic field are

で求めることができる。

It can be found by

Calculating the AC magnetic field in real space from the extraction results of the wave number filter is similar to the case of DC magnetic field measurement.
(a) Integrating the second-order differential extraction result (Equation (108a) or (109a)) with respect to the z-direction (vibration direction of the probe) of the amplitude of the alternating current magnetic field using a wavenumber filter twice in the z-direction in Fourier space (step (h2-0)) to obtain information on the Fourier transform of the amplitude of the alternating magnetic field, and then perform a two-dimensional inverse Fourier transform on this for k _x and k _y (step (i2-0)) ,
(b) Integrate the first-order differential extraction result (Equation (108b) or (109b)) in the z-axis direction (probe vibration direction) of the amplitude of the alternating magnetic field by the wave number filter once in the z-direction in Fourier space. After obtaining information on the Fourier transform of the magnetic field by performing the operation (step (h1-0)), this is subjected to two-dimensional inverse Fourier transform for k _x and k _y (step (i1-0)), or ,
(c) performing two-dimensional inverse Fourier transform on the extraction result of the amplitude of the alternating current magnetic field (formula (108c) or (109c)) by the wave number filter with respect to k _x and k _y (step (i0));
This can be done by However, when an air-core coil is used as the source of the external DC magnetic field H ^dc , (a) or (c) is preferable from the viewpoint of increasing signal strength. Further, among the components extracted by the wave number filter, the second-order differential has the richest amount of information, so (a) is preferable from the viewpoint of making use of the amount of information included in the second-order differential. However, the magnetic field obtained by integrating the second-order differential twice in Fourier space does not include the component (k _x , k _y ) = (0, 0) (a constant value component that does not depend on in-plane coordinates), so The component of (k _x , k _y )≠(0,0) is obtained by (a), and the measurement sensitivity and the calibration of the constant value component of (k _x , k _y )=(0,0) are obtained by (c). It is particularly preferable to carry out by.

The above case (c) is expressed as follows.

上記（ｃ）の場合においては、面内座標（ｘ，ｙ）に依存しない一定値成分（すなわち（ｋ_ｘ，ｋ_ｙ）＝（０，０）の成分）の情報も波数フィルタの抽出結果に含まれているので、逆フーリエ変換により一定値成分を含む交流磁場振幅像を直接得ることができる。ここで、交流磁場について「一定値成分」とは、振幅が走査領域内で均一である成分を意味する。

In case (c) above, information on constant value components that do not depend on in-plane coordinates (x, y) (i.e., components of (k _x , k _y ) = (0, 0)) is also included in the extraction results of the wave number filter. Therefore, an alternating current magnetic field amplitude image including constant value components can be directly obtained by inverse Fourier transform. Here, the "constant value component" of the alternating current magnetic field means a component whose amplitude is uniform within the scanning region.

In the case of (a) above, the operation (step (h2-0 )) can be done using the following relationship.

このスペクトルを二次元逆フーリエ変換することにより、交流磁場の振幅の一定値成分を含まない交流磁場振幅像を得ることができる（工程（ｉ２－０））。これを式に表すと次の通りである。

By subjecting this spectrum to two-dimensional inverse Fourier transform, an AC magnetic field amplitude image that does not include a constant value component of the amplitude of the AC magnetic field can be obtained (step (i2-0)). This can be expressed as follows.

In the case of (b) above, the operation (step (h1 -0)) can be done using the following relationship.

上記（ａ）の場合と同様に、このスペクトルを二次元逆フーリエ変換することにより、交流磁場の振幅の一定値成分を含まない交流磁場振幅像を得ることができる（工程（ｉ１－０））。これを式に表すと次の通りである。

As in the case of (a) above, by performing two-dimensional inverse Fourier transform on this spectrum, it is possible to obtain an AC magnetic field amplitude image that does not include a constant value component of the amplitude of the AC magnetic field (step (i1-0)). . This can be expressed as follows.

The magnetic field image H _z ^ac(sample) (x, y, z) obtained by the above equation (44') and the magnetic field image H _z ^ac(sample) (x , y, z; (k _x , k _y ) ≠ (0, 0)) is that the constant value component of the magnetic field ((k _x , k _y ) = (0, 0) component) is The latter is not included, whereas the latter is not.

Calibration of the magnetic field value when measuring an alternating current magnetic field (step (j)) can also be considered in the same way as when measuring a direct current magnetic field. For example, the above formulas (108a') to (108c') and formulas (109a') to (109c') (or formulas (108a'') to (108c'') and formulas (109a'') to (109c'' ), or based on equations (108a''') to (108c''') and equations (109a''') to (109c''')), it is possible to calibrate the magnetic field value as follows. (Steps (j10) to (j13)). _Each in _- plane ^{coordinate (} x, y). Here, the external AC magnetic field H _z ^ac(ex) has the same frequency as the AC magnetic field H _z ^ac(sample) . The external AC magnetic field H _z ^{ac (ex)} is spatially uniform, which means that the amplitude of H _z ^{ac (ex)} at the position of all pixels (each in-plane coordinate (x, y)) within the scanning area is This means that the phases can be considered equal. If this condition is satisfied, the gradient of the magnetic field, ∂H _z ^ac(ex) /∂z(x, y, z), ∂ ² H _z ^ac(ex) /∂z ² (x, y, z) is not necessarily zero. It doesn't have to be nearby. Such an external alternating magnetic field can be generated, for example, by supplying an alternating current to the electromagnetic coil 3720 of the external alternating magnetic field generator 3700. For example, measuring each in-plane coordinate (x, y) under the condition that a spatially uniform external alternating current magnetic field H _z ^{ac (ex)} is applied to the probe is performed using the electromagnet of the external alternating current magnetic field generator 3700. This can be done by scanning the scanning area with the probe 10 while keeping the alternating current supplied to the coil 3720 and the positional relationship between the electromagnet of the external alternating magnetic field generator 3700 and the probe 10 the same. Such scanning can be performed, for example, by fixing the positional relationship between the electromagnet of the external AC magnetic field generator 3700 and the probe 10 and moving only the sample in the in-plane direction. For example, when an air-core coil is used as a DC magnetic field source, a spatially uniform external AC magnetic field H _z ^ac(ex) is superimposed on the DC current and supplies AC current to the air-core coil. It is also possible to generate it by
When measuring the alternating current magnetic field H ^ac(sample) cos(ωt), ^a spatially uniform external alternating current having the same frequency as the alternating current magnetic field H ac( _sample ⁾ cos(ωt) is used together with the direct current magnetic field H z dc. When applying a magnetic field H _z ^ac(ex) cos(ωt+φ) (however, H _z ^ac(ex) has the same sign as H _z ^ac(sample) ), equation (12') becomes

となる。Ｅｕｌｅｒの式に基づき、交流磁場Ｈ^{ａｃ（ｓａｍｐｌｅ）}ｃｏｓ（ωｔ）はＨ^{ａｃ（ｓａｍｐｌｅ）}ｅｘｐ（ｉωｔ）の実部であり、外部交流磁場Ｈ_ｚ ^{ａｃ（ｅｘ）}ｃｏｓ（ωｔ＋φ）はＨ_ｚ ^{ａｃ（ｅｘ）}ｅｘｐ（ωｔ＋φ）の実部であるから、式（１２’ａ）は

becomes. Based on Euler's equation, the AC magnetic field H ^ac(sample) cos(ωt) is the real part of H ^ac(sample) exp(iωt), and the external AC magnetic field H _z ^ac(ex) cos(ωt+φ) is H _z ^{ac (ex)} is the real part of exp(ωt+φ), so equation (12'a) is

の実部となる。Ｈ_ｚ ^{ａｃ（ｅｘ）}が空間的に一様な場合、

is the real part of If H _z ^ac(ex) is spatially uniform,

（好ましくは例えば、それぞれ右辺が左辺の１／１０未満であり得る。）であるから、さらに

(Preferably, for example, each right side may be less than 1/10 of the left side.)

となる。式（１０８ｃ”）又は（１０９ｃ”）により、磁場の均一成分すなわち（ｋ_ｘ，ｋ_ｙ）＝（０，０）成分に対応する情報を抽出すると、

becomes. When information corresponding to the uniform component of the magnetic field, that is, the (k _x , k _y )=(0,0) component is extracted using equation (108c") or (109c"),

が得られ、これは交流磁場Ｈ^{ａｃ（ｓａｍｐｌｅ）}と外部交流磁場Ｈ_ｚ ^{ａｃ（ｅｘ）}との位相差φの関数である。式（１１０）の実部の絶対値はφ＝０のとき（すなわち外部交流磁場Ｈ_ｚ ^{ａｃ（ｅｘ）}の位相が交流磁場Ｈ^{ａｃ（ｓａｍｐｌｅ）}と同位相に調整された条件で測定が行われたとき）最大となり、このとき

is obtained, which is a function of the phase difference φ between the alternating magnetic field H ^ac(sample) and the external alternating magnetic field H _z ^ac(ex) . The absolute value of the real part of equation (110) is when φ = 0 (that is, the measurement is performed under the condition that the phase of the external AC magnetic field H _ac ^(ex) is adjusted to the same phase as the AC magnetic field H ^{ac (sample)} ). ) is maximum, and at this time

を与える。また式（１１０）の実部の絶対値はφ＝πのとき（すなわち外部交流磁場Ｈ_ｚ ^{ａｃ（ｅｘ）}が交流磁場Ｈ^{ａｃ（ｓａｍｐｌｅ）}と逆位相に調整された条件で測定が行われたとき）最小となり、このとき

give. Furthermore, the absolute value of the real part of equation (110) is measured when φ = π (i.e., the measurement was performed under the condition that the external AC magnetic field H _ac ^(ex) was adjusted to have the opposite phase to the AC magnetic field H ^{ac (sample)} ). ) becomes the minimum, and at this time

を与える。両者の差（式（１１０ａ）－式（１１０ｂ））を取ることにより

give. By taking the difference between the two (Equation (110a) - Equation (110b))

が得られる。この値と、外部交流磁場Ｈ_ｚ ^{ａｃ（ｅｘ）}の均一成分の強度Ｈ_ｚ ^{ａｃ（ｅｘ）}（ｋ_ｘ＝０，ｋ_ｙ＝０，ｚ）（これは既知である）とから、磁場値の測定感度係数α_３を求めることができる（工程（ｊ１２））。得られた測定感度係数α_３を用いて、式（４４’）により得られる磁場像の信号強度を較正できる。さらに、両者の和（式（１１０ａ）＋式（１１０ｂ））は

is obtained. From this value and the strength of the uniform component of the external alternating magnetic field _{H z} ^{ac (ex )} (k _x =0, k _y =0, z) (which is known), the magnetic field value can be calculated. A measurement sensitivity coefficient α ₃ can be determined (step (j12)). Using the obtained measurement sensitivity coefficient α ₃ , the signal intensity of the magnetic field image obtained by equation (44′) can be calibrated. Furthermore, the sum of both (formula (110a) + formula (110b)) is

に等しい。この値と、先に決定された測定感度係数α_３とから、試料からの交流磁場の均一成分Ｈ_ｚ ^{ａｃ（ｓａｍｐｌｅ）}（（ｋ_ｘ，ｋ_ｙ）＝（０，０），ｚ）を求めることができる（工程（ｊ１３））。このようにして求められた磁場の均一成分Ｈ_ｚ ^{ａｃ（ｓａｍｐｌｅ）}（（ｋ_ｘ，ｋ_ｙ）＝（０，０），ｚ）は、式（４６’）又は（４８’）により得られる磁場像における磁場の均一成分として用いることができる。また、外部交流磁場の発生源に空芯コイルを用いている場合には、さらに、得られた測定感度係数α_３と、上記式（６０’）又は（６１’）と、空芯コイルの式（１５）とから、磁場の２階微分の測定感度係数α_１又は磁場の１階微分の測定感度係数α_２を算出して、式（４６’）又は（４８’）により得られる磁場像の信号強度を較正することができる。
なお、較正用の磁場Ｈ_ｚ ^{ａｃ（ｅｘ）}が空間的に一様でない場合には、式（１２’ｂ）は

be equivalent to. From this value and the previously determined measurement sensitivity coefficient α ₃ , find the uniform component of the AC magnetic field from the sample H _z ^{ac (sample)} ((k _x , k _y ) = (0, 0), z) (Step (j13)). The homogeneous component of the magnetic field H _z ^ac(sample) ((k _x , k _y )=(0,0), z) obtained in this way is the magnetic field obtained by equation (46') or (48'). It can be used as a uniform component of the magnetic field in the image. In addition, when an air-core coil is used as the source of the external alternating magnetic field, the obtained measurement sensitivity coefficient α ₃ , the above equation (60') or (61'), and the air-core coil equation (15), calculate the measurement sensitivity coefficient α ₁ of the second-order differential of the magnetic field or the measurement sensitivity coefficient α ₂ of the first-order differential of the magnetic field, and calculate the magnetic field image obtained by equation (46') or (48'). Signal strength can be calibrated.
Note that if the magnetic field for calibration H _z ^ac(ex) is not uniform spatially, equation (12'b) becomes

となって、波数フィルタの前提となる式にない第４項：

Therefore, the fourth term that is not in the equation, which is the premise of the wave number filter:

が測定データに加わることで誤差が生じる。
上記式（１１０）において、φ＝０である状態は、式（１１０）の実部の絶対値が最大値をとっている状態として見出すことができる。また、φ＝πである状態は、式（１１０）の実部の絶対値が最小値をとっている状態として見出すことができる。
このように、試料において交流磁場が発生している場所については、大きさのみならず位相に関する情報も得ることができる。

is added to the measurement data, causing an error.
In the above equation (110), the state where φ=0 can be found as a state in which the absolute value of the real part of equation (110) takes the maximum value. Further, the state where φ=π can be found as a state where the absolute value of the real part of equation (110) takes the minimum value.
In this way, information regarding not only the magnitude but also the phase can be obtained regarding the location where the alternating magnetic field is generated in the sample.

Note that if there is a place in the sample where no alternating magnetic field is generated, the magnitude of the alternating magnetic field H _z ^{ac (sample)} from the sample can be calibrated without considering the phase state. In other words, if the measurement results in the in-plane area where no alternating magnetic field is generated in the scanning area are subjected to two-dimensional Fourier transform and the magnetic field components are extracted using a wave number filter, then from equation (110),

となるので、波数フィルタにより抽出された値Ψと、外部交流磁場Ｈ_ｚ ^{ａｃ（ｅｘ）}の強度（これは既知である）とから、ただちに磁場値の測定感度係数α_３を求めることができる。

Therefore, the measurement sensitivity coefficient α ₃ of the magnetic field value can be immediately obtained from the value Ψ extracted by the wave number filter and the intensity of the external alternating magnetic field H _z ^ac(ex) (which is known).

Furthermore, analysis of the phase of the alternating magnetic field at the in-plane coordinates (x, y) where the alternating magnetic field is generated can be performed, for example, by the following method.
A frequency demodulated signal from demodulator 430 is input to a lock-in amplifier (detector 3440). The input signal includes a component that vibrates at an angular frequency ω. A sine wave vibrating at an angular frequency ω (herein referred to as Acos(ωt)) is further input to the lock-in amplifier as a reference signal. Assuming that the amplitude of the component of angular frequency ω included in the input signal of the lock-in amplifier is R, and the phase delay of this component (with respect to the reference signal) is φ ₀ ,
The output X signal of the lock-in amplifier (lock-in X signal) is X=R cos (φ ₀ ),
The output Y signal of the lock-in amplifier (lock-in Y signal) is Y=Rsin(φ ₀ )
becomes. From the relationship Rexp(iφ ₀ )=X+iY, the following relational expression can be obtained from the measured lock-in X signal and lock-in Y signal.

上記の関係式から、
位相をΔφ変化させたロックインＸ信号Ｒｃｏｓ（φ_０＋Δφ）＝Ｘ’、及び
位相をΔφ変化させたロックインＹ信号Ｒｓｉｎ（φ_０＋Δφ）＝Ｙ’
は次のように計算できる。

From the above relational expression,
Lock-in X signal R cos (φ ₀ + Δφ) = X' whose phase is changed by Δφ, and lock-in Y signal R sin (φ ₀ + Δφ) = Y' whose phase is changed by Δφ
can be calculated as follows.

Δφを連続的に変化させて、一周期の範囲内でＸ’又はＹ’を計算し、Ｘ’又はＹ’がゼロになるΔφを求めることにより、位相遅れφ_０を求めることができる。例えば、Ｘ’＝０、Ｙ’が正ならばφ_０＝π／２－Δφ［ｒａｄ］；Ｘ’＝０、Ｙ’が負ならばφ_０＝３π／２－Δφ［ｒａｄ］；Ｙ’＝０、Ｘ’が正ならばφ_０＝－Δφ；Ｙ’＝０、Ｘ’が負ならばφ_０＝π－Δφ［ｒａｄ］、として、位相遅れφ_０を求めることができる。さらに、得られた位相遅れφ_０と、参照信号の位相とから、交流磁場の位相を求めることができる。上記の手順を複数の面内座標（ｘ，ｙ）について繰り返し行うことにより、交流磁場が発生している領域における交流磁場の位相分布を求めることも可能である。

The phase delay φ ₀ can be determined by continuously changing Δφ, calculating X' or Y' within one period, and determining Δφ at which X' or Y' becomes zero. For example, if X'=0 and Y' is positive, φ ₀ =π/2-Δφ[rad]; if X'=0 and Y' is negative, φ ₀ =3π/2-Δφ[rad]; Y' = 0, if X' is positive, φ ₀ = -Δφ; Y' = 0, if X' is negative, φ ₀ = π-Δφ [rad], and the phase delay φ ₀ can be determined. Furthermore, the phase of the alternating current magnetic field can be determined from the obtained phase delay φ ₀ and the phase of the reference signal. By repeating the above procedure for a plurality of in-plane coordinates (x, y), it is also possible to obtain the phase distribution of the alternating magnetic field in the region where the alternating magnetic field is generated.

In the AC magnetic field measurement device 3000 (FIG. 7), the DC magnetic field generator 3300 generates a DC magnetic field by supplying DC current to the air-core coil 310, so information necessary for wave number filtering, that is, the probe position The DC magnetic field H _z ^dc(coil) , its first derivative ∂H _z ^dc(coil) /∂z, and second derivative ∂ ² H _z ^dc(coil) /∂z ² are expressed by the air-core coil equation (15). (It can be directly determined from the Biot-Savart law). On the other hand, in the AC magnetic field measuring device 4000 (FIG. 9), the DC magnetic field generator 4300 generates a DC magnetic field by supplying DC current to the coil 4320 of the electromagnet including the electromagnetic core 4310. As in the AC magnetic field measurement device 4000, when an electromagnet having a magnetic core and a coil wound around the magnetic core is used instead of an air-core coil as the source of the DC magnetic field, the above formulas (108a') to (108c) are used. ') and (109a') to (109c'), it is generally difficult to accurately evaluate the coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ |. When using an electromagnet as a source of a DC magnetic field, for example, formula (44') and formula (46 ') or (48') The magnetic field image H _z ^ac(sample) (x, y, z) or H _z ^ac(sample) (x, y, z; (x, y)≠(0,0 )), the magnetic field image H _z ^ac(sample) (x, y, ^Formulas (108a') to (109c') and (109a') to ₍ 109c') in any of the coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ | (and optionally a constant multiple of the image). Accordingly, the coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ | can be obtained (step (o)). In another embodiment, a second-order differential image ∂ ² _Hz ^ac(sample) /∂z obtained based on the results of observing the same sample (standard sample) using an air-core coil as a source of a DC magnetic field. ² (x, y, z) or ∂ ² _Hz ^ac(sample) /∂z ² (x, y, z; (x, y)≠(0,0)), an electromagnet is used as a source of a DC magnetic field. The second-order differential image ∂ ² _Hz ^ac(sample) /∂z ² (x, y, z) or ∂ ² _Hz ^ac(sample ) /∂z ² (x, y, z) calculated from the measurement results used. ; (x,y)≠(0,0)), the coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ |( and optionally a constant multiple of the image), the coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ | may be determined (step (o)). Before the optimization calculation, preprocessing may be performed, such as normalization so that the maximum and minimum values of the image signals are the same between the two images. Determining these two coefficients is equivalent to determining the two ratios between the constants |C ₁ |, |C ₂ |, |C ₃ |, and at the same time, the DC magnetic field H _z at the position of the probe 10 ^dc(coil) and the first-order differential of the DC magnetic field at the position of the probe 10 with respect to the vibration direction of the probe 10 ∂H _z ^dc(coil) /∂z and the probe of the DC magnetic field at the position of the probe 10 This is equivalent to finding the two ratios between the second-order differential ∂ ² _Hz ^dc(coil) /∂z ² with respect to the vibration direction of the needle 10. Note that when an electromagnet is used as a DC magnetic field source, the DC magnetic field H _z ^{dc (coil)} at the position of the probe 10 and its second-order differential ∂ ² H _z ^{dc (coil)} / ∂z ² have different signs (that is, C ₁ and C ₃ is often the opposite sign). In the AC magnetic field measuring device 4000, when observing the same sample using an air-core coil as the source of the DC magnetic field, by switching the changeover switch 4340 from the electromagnetic coil 4320 side to the air-core coil 310 side, Measurement can be performed by supplying direct current to the air core coil 310 from the direct current/alternating current source 4330. As long as the conditions regarding the electromagnets are the same (i.e., the same electromagnet is supplied with a current of the same amplitude, and the positional relationship between the electromagnet and the probe is the same), the coefficients |C ₂ | / |C ₁ | and |C ₃ |/|C ₁ | is kept the same. Therefore, the obtained coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ | can also be applied to other measurements, as long as the conditions regarding the electromagnets are the same. Thereafter, in other measurements, applying the same conditions for the electromagnet and the obtained coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ |, by the operation described above. , the magnetic field values can be calibrated.
Generally, the measurement result of the second derivative of the magnetic field has the richest amount of information, so it can be obtained using equation (48') based on the results of observing the same sample using an air-core coil as the source of the DC magnetic field. The obtained magnetic field image H _z ^{ac (sample)} (x, y, z; (x, y)≠(0,0)) is calculated by equation (48') from the measurement results using an electromagnet as the source of the DC magnetic field. In order to match the calculated magnetic field image H _z ^ac(sample) (x, y, z; (x, y)≠(0,0)), the coefficient |C ₂ By optimizing the |/|C ₁ | and |C ₃ |/|C ₁ | (and optionally a constant multiple of the image), the coefficients |C ₂ |/|C ₁ | and |C ₃ |/| Preferably, C ₁ | is determined. In addition, from the viewpoint of being less susceptible to measurement noise, the magnetic field image H _z ac obtained by equation (44') based on the results of observing the same sample using an air-core coil as the source of the DC magnetic ^field . ^(sample) (x, y, z) is the magnetic field image H _z ^{ac (sample)} (x, y, z) calculated by equation (44') from the measurement results using an electromagnet as the source of the DC magnetic field. optimizing the coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ | (and optionally a constant multiple of the image) in equation (108c') or (109c') to match. It is preferable to determine the coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ | by. Thereafter, in other measurements applying the same conditions for the electromagnet, the previously determined coefficients |C ₂ |/|C ₁ | and |C ₃ |/|C ₁ | are applied, and the operations described above are performed. , the magnetic field values can be calibrated.
In the optimization calculation, a known optimization method can be employed as in the case of DC magnetic field measurement.

Conversion of the magnetic field direction by the direction conversion filter calculator 660, that is, from the measurement results in one direction (for example, the vertical (z) direction), information on the magnetic field in the in-plane direction (for example, the (x, y) direction) perpendicular to the direction Obtaining it can be considered in the same way as in the case of DC magnetic field measurement. Fourier transform of the second derivative in the z direction (vibration direction of the tip) of the amplitude of the z (external DC magnetic field direction) component of the AC magnetic field from the sample in the in-plane (x, y) direction of the scanning region ∂ ² H From _z ^ac(sample) /∂z ² (k _x , k _y , z), the Fourier transform of the second derivative of the x-component amplitude and y-component amplitude in the z direction of the alternating magnetic field ∂ ² H _x ^ac(sample) /∂z ² (k _x , k _y , z) and ∂ ² H _y ^ac(sample) /∂z ² (k _x , k _y , z), respectively.

として得ることができ（工程（ｋ２））、これらを逆フーリエ変換することにより、交流磁場のｘ成分の振幅およびｙ成分の振幅の２階微分∂^２Ｈ_ｘ ^{ａｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｘ，ｙ，ｚ）及び∂^２Ｈ_ｙ ^{ａｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｘ，ｙ，ｚ）を、それぞれ

(step (k2)), and by performing inverse Fourier transform on these, the second derivative of the amplitude of the x component and the amplitude of the y component of the alternating magnetic field can be obtained as ∂ ² H _x ^ac(sample) /∂z ² ( x, y, z) and ∂ ² H _y ^ac(sample) /∂z ² (x, y, z), respectively.

として得ることができる（工程（ｌ２））。

(Step (l2)).

Similarly, from the Fourier transform of the amplitude of the z (external DC magnetic field direction) component of the AC magnetic field from the sample H _z ^ac(sample) (k _x , k _y , z), we can calculate the x and y components of the amplitude of the AC magnetic field. The Fourier transforms of amplitude H _x ^ac(sample) (k _x , k _y , z) and H _y ^{ac (sample)} (k _x , k _y , z) are respectively

として得ることができ（工程（ｋ０））、これらを逆フーリエ変換することにより、交流磁場のｘ成分の振幅Ｈ_ｘ ^{ａｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ）及びｙ成分の振幅Ｈ_ｙ ^{ａｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ）を、それぞれ

(step (k0)), and by inverse Fourier transforming these, the amplitude of the x component of the alternating current magnetic field H _x ^ac(sample) (x, y, z) and the amplitude of the y component H _y ^{ac( sample)} (x, y, z), respectively

として得ることができる（工程（ｌ０））。この磁場方向変換により得られる面内磁場像Ｈ_ｘ ^{ａｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ）及びＨ_ｙ ^{ａｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ）は、走査領域内の位置によらない一定値成分を含まない磁場像、すなわちＨ_ｘ ^{ａｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ；（ｋ_ｘ，ｋ_ｙ）≠（０，０））及びＨ_ｙ ^{ａｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ；（ｋ_ｘ，ｋ_ｙ）≠（０，０））である。

(Step (l0)). The in-plane magnetic field images H _x ^ac(sample) (x, y, z) and H _y ^ac(sample) (x, y, z) obtained by this magnetic field direction conversion have constant values regardless of the position within the scanning area. Magnetic field images that do not contain components, that is, H _x ^ac(sample) (x, y, z; (k _x , k _y )≠(0,0)) and H _y ^ac(sample) (x, y, z; k _x , k _y )≠(0,0)).

Similarly, the Fourier transform of the first-order differential in the z direction (vibration direction of the tip) of the z (external DC magnetic field direction) component of the AC magnetic field from the sample is ∂H _z ^ac(sample) /∂z(k _x , k _{y .} ^_ _{_ _ _} ^_ ∂z(k _x , k _y , z), respectively

として得ることができ（工程（ｋ１））、これらを逆フーリエ変換することにより、交流磁場のｘ成分およびｙ成分の振幅の１階微分∂Ｈ_ｘ ^{ａｃ（ｓａｍｐｌｅ）}／∂ｚ（ｘ，ｙ，ｚ）及び∂Ｈ_ｙ ^{ａｃ（ｓａｍｐｌｅ）}／∂ｚ（ｘ，ｙ，ｚ）を、それぞれ

(step (k1)), and by inverse Fourier transforming these, the first-order differential of the amplitude of the x and y components of the alternating magnetic field ∂H _x ^ac(sample) /∂z(x, y, z) and ∂H _y ^ac(sample) /∂z(x, y, z), respectively.

として得ることができる（工程（ｌ１））。

(Step (l1)).

In this way, the specific calculation in the direction conversion filter calculator 660 of the signal processing device 3600 is the same as in the case of DC magnetic field measurement. That is, obtaining the x component from the z (vertical direction) component means that for each combination of wavenumbers (k _x , k _y ) except (k _x , k _y )=(0,0), the input value is - This can be done by multiplying by ik _x /(k _x ² + k _y ² ) ^1/2 . Also, obtaining the y component from the z (vertical direction) component means that for each combination of wave numbers (k _x , k _y ) except (k _x , k _y )=(0,0), the input value is - This can be done by multiplying by ik _y /(k _x ² +k _y ² ) ^1/2 .

Conversion of the tip-sample distance by the distance conversion filter calculator 670, that is, from the magnetic field information obtained by measurement at one tip-sample distance (z coordinate), a different tip-sample distance (z + Δz ) can be considered in the same way as in the case of DC magnetic field measurement. Fourier transform of the amplitude of the alternating magnetic field at one tip-sample distance (z coordinate) H _z ^ac(sample) (k _x , k _y , z), H _x ^{ac (sample)} (k _x , k _y , z _{) and} H _y ^{ac (} _sample ⁾ _{( k} , z+Δz), H _x ^ac(sample) (k _x , k _y , z+Δz), and H _y ^ac(sample) (k _x , k _y , z+Δz), respectively.

として得ることができ（工程（ｍ２））、これらを逆フーリエ変換することにより、探針－試料間距離がΔｚ異なる位置における交流磁場の振幅Ｈ_ｚ ^{ａｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ＋Δｚ）、Ｈ_ｘ ^{ａｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ＋Δｚ）、及びＨ_ｙ ^{ａｃ（ｓａｍｐｌｅ）}（ｘ，ｙ，ｚ＋Δｚ）を、それぞれ

(Step (m2)), and by performing inverse Fourier transform on these, the amplitude of the alternating magnetic field H _z ^ac(sample) (x, y, z + Δz) at the position where the tip-sample distance differs by Δz, H _x ^ac(sample) (x, y, z+Δz) and H _y ^ac(sample) (x, y, z+Δz), respectively

として得ることができる（工程（ｎ２））。

(Step (n2)).

Similarly, regarding the first-order differential of the amplitude of the alternating magnetic field, the Fourier transform of the first-order differential in the z direction (the vibration direction of the tip) of the amplitude of the alternating magnetic field at one tip-sample distance (z coordinate) is calculated as ∂H _z ^ac(sample) /∂z(k _x , k _y , z), ∂H _x ^ac(sample) /∂z(k _x , k _y , z), and ∂H _y ^ac(sample) /∂z(k _x , k _y , z), Fourier transform of the first differential of the amplitude of the alternating magnetic field at a position where the tip-sample distance differs by Δz ∂H _z ^ac(sample) /∂z(k _x , k _y , z+Δz) , ∂H _x ^ac(sample) /∂z(k _x , k _y , z+Δz), and ∂H _y ^ac(sample) /∂z(k _x , k _y , z+Δz), respectively.

として得ることができ（工程（ｍ１））、これらを逆フーリエ変換することにより、探針－試料間距離がΔｚ異なる位置における交流磁場の振幅の１階微分∂Ｈ_ｚ ^{ａｃ（ｓａｍｐｌｅ）}／∂ｚ（ｘ，ｙ，ｚ＋Δｚ）、∂Ｈ_ｘ ^{ａｃ（ｓａｍｐｌｅ）}／∂ｚ（ｘ，ｙ，ｚ＋Δｚ）、及び∂Ｈ_ｙ ^{ａｃ（ｓａｍｐｌｅ）}／∂ｚ（ｘ，ｙ，ｚ＋Δｚ）を、それぞれ

(Step (m1)), and by performing inverse Fourier transform on these, the first derivative of the amplitude of the alternating current magnetic field at positions where the tip-sample distance differs by Δz ∂H _z ^ac(sample) /∂z (x, y, z+Δz), ∂H _x ^ac(sample) /∂z(x, y, z+Δz), and ∂H _y ^ac(sample) /∂z(x, y, z+Δz), respectively.

として得ることができる（工程（ｎ１））。

(Step (n1)).

Similarly, regarding the second derivative of the amplitude of the alternating magnetic field, the Fourier transform of the second derivative in the z direction (vibration direction of the tip) of the amplitude of the alternating magnetic field at one tip-sample distance (z coordinate) is calculated by ∂ ² H _z ^ac(sample) /∂z ² (k _x , k _y , z), ∂ ² H _x ^{ac (sample)} /∂z ² (k _x , k _y , z), and ∂ ² H _y ^{ac (sample)} /∂z ² (k _x , k _y , z), the Fourier transform of the second derivative of the amplitude of the alternating magnetic field at positions where the tip-sample distance differs by Δz ^{∂ 2} H _z ^ac(sample) /∂z ² ( _{k _} ^_ _{_} ^{_ _} _{_ _} ^_ _{_} ^{_ _} _{_ _} ,z+Δz), respectively

として得ることができ（工程（ｍ２））、これらを逆フーリエ変換することにより、探針－試料間距離がΔｚ異なる位置における交流磁場の振幅の２階微分∂^２Ｈ_ｚ ^{ａｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｘ，ｙ，ｚ＋Δｚ）、∂^２Ｈ_ｘ ^{ａｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｘ，ｙ，ｚ＋Δｚ）、及び∂^２Ｈ_ｙ ^{ａｃ（ｓａｍｐｌｅ）}／∂ｚ^２（ｘ，ｙ，ｚ＋Δｚ）を、それぞれ

(Step (m2)), and by inverse Fourier transforming these, the second derivative of the amplitude of the alternating magnetic field at positions where the tip-sample distance differs by Δz ² H _z ^ac(sample) /∂ z ² (x, y, z+Δz), ∂ ² H _x ^ac(sample) /∂z ² (x, y, z+Δz), and ∂ ² H _y ^ac(sample) /∂z ² (x, y, z+Δz) , respectively

として得ることができる（工程（ｎ２））。

(Step (n2)).

In this way, the specific calculation in the distance conversion filter calculator 670 of the signal processing device 3600 is the same as in the case of DC magnetic field measurement. That is, for the first probe position z=z' and the virtual second _probe position z=z'+Δz, _each combination of wave numbers (k _x , k _y ), the input value is multiplied by exp(−(k _x ² +k _y ² ) ^1/2 Δz).

The present invention will be explained in more detail below using Examples, but the present invention is not limited to the Examples.

<Example 1>
The DC magnetic field H generated from the permanent magnet 20 (NdFeB magnet) is measured by the DC magnetic field measuring method of the present invention using the DC magnetic field measuring device 1000 (FIG. 4) of the present invention in which the AC magnetic field generator 300 includes an air-core coil 310. ^dc(sample) was measured. A plan view (photograph) of the air-core coil 310 used is shown in FIG. The air-core coil 310 is a flat two-layer air-core coil made of polyurethane copper wire with a diameter of 1.0 mm, and has a total of 14 turns. The magnetic field generated from such an air-core coil and its gradient can be calculated based on the Biot-Savart law.

The superparamagnetic probe 10 was placed on the central axis of the air-core coil 310. The superparamagnetic probe 10 was fabricated by sputtering a 100 nm thick superparamagnetic coating (Co-GdO _x ) on the surface of a non-magnetic (Si) probe for atomic force microscopy (AFM). be.

The cantilever 100 having the superparamagnetic probe 10 at one end was excited in the atmosphere using an exciter 200 including a piezo element (step (a)). By supplying an alternating current with a frequency of 367 Hz from the alternating current source 320 to the air-core coil 310, an alternating current magnetic field H _z ^{ac (coil)} in the vibration direction of the probe is applied to the probe 10 from the air-core coil 310. By. The excitation vibration of the cantilever 100 was frequency modulated (step (b)).

The values of the amplitude H _z ^{ac (coil)} of the alternating current magnetic field at the position of the probe 10 and the second-order differential ∂ ² H _z ^{ac (coil)} /∂z ² of the amplitude with respect to the vibration direction of the probe are as follows. , is non-zero.

The vibration of the probe 10 was detected using the vibration sensor 400, and the frequency of the detection signal of the vibration of the probe 10 was demodulated using the FM demodulator 430 including a PLL circuit (step (c)). The detector 440 equipped with a lock-in amplifier performs lock-in detection on the frequency demodulated signal using the signal from the AC current source 320 as a reference signal, thereby detecting the AC magnetic field H contained in the frequency demodulated signal. The intensity of the frequency component of _z ^{ac (coil)} was measured (step (d)). A scanning area (a square area of 5 μm in height x 5 μm in width) set above the surface of the permanent magnet sample 20 in a plane intersecting the vibration direction of the probe 10 is scanned by the probe 10 using the scanning mechanism 500. By scanning, the above steps (a) to (d) were performed for each in-plane coordinate (x, y) set within the scanning area (step (e)). Each in-plane coordinate (x, y) was arranged in a grid of 256 vertical points x 256 horizontal points in a square scanning area in order to facilitate two-dimensional Fourier transformation processing. Scanning was performed by fixing the in-plane position of the probe and moving the XYZ three-axis stage on which the sample 20 was placed in the in-plane (X, Y) directions. The measurement results of step (d) at each in-plane coordinate were stored in the memory 610 included in the signal processing device 600 in association with the in-plane coordinate (x, y) at which the measurement result was obtained. The information stored in the memory 610 and corresponding to the measurement results in step (d) in the scanning region was subjected to two-dimensional Fourier transform in the in-plane direction of the scanning region by the Fourier transformer 620 (step (f)).

From the Fourier transform information obtained in step (f), the first wave number filter calculator 631 calculates a component of the DC magnetic field H ^{dc (sample)} parallel to the AC magnetic field H _z ^{ac (coil)} H _z ^{dc (sample)} Information corresponding to the two-dimensional Fourier transform H _z ^dc(sample) (k _x , k _y , z) in the in-plane direction of the scanning region was extracted (step (g0)). Based on the information corresponding to H _z ^dc(sample) (k _x , k _y , z), the inverse Fourier transformer 640 performs two-dimensional inverse Fourier transform, and each in-plane coordinate (x, y) in the scanning area is , a value corresponding to the component H _z ^dc(sample) (x, y, z) of the DC magnetic field parallel to the AC magnetic field was obtained (step (i0)).

The measurement sensitivity and zero point of the obtained magnetic field image were calibrated using an external DC magnetic field generator 700 (step (j)). First, a DC magnetic field obtained by performing the above steps (a) to (f) and (g0) to (i0) without applying an external DC magnetic field to the probe 10 from the external DC magnetic field generator 700. A second plane in the scanning region where the value corresponding to the component H _z ^{dc (sample)} (x', y', z) parallel to the alternating magnetic field H _z ^{ac (coil) of} H ^{dc (sample)} is zero. A group (isovalue line) of internal coordinates (x', y') was identified (step (j3)). FIG. 11(A) is a H _z ^dc(sample) (x, y, z) image when no external DC magnetic field is applied, and FIG. 11(B) is an image of H _z ^dc(sample) =0Oe. It is a diagram showing isovalue lines.

Next, the above ^step ( Perform steps a) to (f) and (g0) to (i0), and convert the component of the DC magnetic field parallel to the AC magnetic field H _z ^dc(sample) (x”, y”, z) obtained in step (i0) to A group (isovalue lines) of the first in-plane coordinates (x", y") within the scanning region whose corresponding value is zero was identified (step (j1)). FIG. 11(C) is a H _z ^dc(sample) (x, y, z) image when an external DC magnetic field of H ^dc(ex) =-600 Oe is applied, and FIG. 11(D) is an H z dc(sample) (x, y, _z ) image. It is a figure showing the isopleth line of ^{dc (sample)} =600Oe. Furthermore, FIG. 11(E) is a H _z ^dc(sample) (x, y, z) image when an external DC magnetic field of H ^dc(ex) =-1 kOe is applied, and FIG. 11(F) is It is a figure showing the isopleth line of _Hzdc ^(sample) =1kOe.

The value of the component H z ^{dc (sample)} of the DC magnetic field H ^{dc (sample)} parallel to the AC magnetic field _{H z} ^{ac (coil)} is −H ^{dc (ex )} , and the component H ^{z dc (sample)} parallel to the alternating current magnetic field H _z ^{ac (coil)} of the DC magnetic field H dc (sample) is zero at the second in-plane coordinates (x", _y ") ^{. )} , the intensity and constant value component at each in-plane coordinate (x, y) within the scanning region were calibrated (step (j4)). FIG. 11(G) is an H _z ^dc(sample) (x, y, z) image after calibration. In FIG. 11(G), the unit of the vertical axis is [Oe]. This calibration determined the measurement sensitivity coefficients α ₁ , α ₂ , and α ₃ as well as the constant value component of the magnetic field.

Further, from the Fourier transform information obtained in step (f) based on the measurement without applying an external DC magnetic field, the second wave number filter calculator 632 calculates the component H _z of the DC magnetic field parallel to the AC magnetic field. Second-order differential of ^dc(sample) with respect to the vibration direction of the probe 10 ∂ ² _Hz ^dc(sample) /∂z Two-dimensional Fourier transform of ² with respect to the in-plane direction of the scanning region ∂ ² _Hz ^dc(sample) /∂z ² (k _x , k _y , z; (k _x , k _y )≠(0,0)) was extracted (step (g2)). The information extracted in step (g2) is subjected to two-dimensional Fourier transform of the component H _z ^{dc (sample)} of the DC magnetic field parallel to the AC magnetic field in the in-plane direction of the scanning region by the first integral filter calculator 651. It was converted into information corresponding to H _z ^dc(sample) (k _x , k _y , z; (k _x , k _y )≠(0,0)) (step (h2-0)). Based on the information obtained in step (h2-0), a two-dimensional inverse Fourier transform is performed by the inverse Fourier transformer 640, and for each in-plane coordinate (x, y) within the scanning area, the direct current magnetic field is converted into an alternating current magnetic field. A value corresponding to the parallel component H _z ^dc(sample) (x, y, z) was obtained (step (i2-0)). Also, based on the information obtained in step (g2), a two-dimensional inverse Fourier transform is performed by the Fourier transformer 640, and for each in-plane coordinate (x, y) in the scanning area, parallel to the alternating current magnetic field of the direct current magnetic field. The value corresponding to the second differential ∂ ² _Hz ^{dc(sample) /} ∂z ² (x, y, z) of the component H _z dc(sample) with respect to the vibration direction of the probe 10 was obtained (step ( i2-2)). FIG. 12(A) is a second-order differential ∂ ² H _z ^dc(sample) /∂z ² (x, y, z) image of the DC magnetic field obtained in step (i2-2). FIG. 12(B) is a DC magnetic field H _z ^dc(sample) (x, y, z) image obtained in step (i2-0). These ∂ ² H _z ^dc(sample) /∂z ² (x, y, z) images and Hz _dc ^(sample) (x, y, z) images are calculated based on the calibration results of step (j) above. , could be further calibrated.

1 Core member 2 Cantilever 3 Magnetic coating 41 Chamber 42 Rotation holding table 43 Rotation drive shaft 44 Ferromagnetic element target 45 Non-magnetic element target 10 Probe (superparamagnetic probe)
20, 20' Sample 100 Cantilever 200 Exciter 300, 2300 AC magnetic field generator 3300, 4300 DC magnetic field generator 2340 Selector switch 310 Air-core coil 320, 3730 AC current source 2330 AC/DC current source 4330 DC/AC current source 400 Vibration sensor 410 Light source 420 Optical displacement sensor 430 Demodulator (FM demodulator)
440, 3440 Detector (lock-in amplifier, etc.)
500 Scanning mechanism 600, 3600 Signal processing device 610 Storage device (memory)
620 Fourier transformer 631, 3631 First wave number filter calculator 632, 3632 Second wave number filter calculator 633, 3633 Third wave number filter calculator 640 Inverse Fourier transformer 651 First integral filter calculator 652 Second /Third integral filter calculator 660 Direction conversion filter calculator 670 Distance conversion filter calculator 700 External DC magnetic field generator 3700 External AC magnetic field generator 710, 2310 Electromagnetic core (of the electromagnet) 720, 2320 Coil (of the electromagnet) 730 , 3320 DC current source 2800, 4800 Parameter fitting calculator 1000, 2000 DC magnetic field measuring device 3000, 4000 AC magnetic field measuring device

Claims (4)

A method for measuring a direct current magnetic field, the method comprising:
(a) exciting a cantilever having a superparamagnetic probe at one end that generates a magnetic moment in the direction of the applied magnetic field;
(b) While performing step (a), an alternating current magnetic field is applied to the probe from an alternating current magnetic field generator to periodically vary the magnetization of the probe, thereby modulating the frequency of the excitation vibration of the cantilever. process and
(c) while performing the step (b), detecting the vibration of the probe and demodulating the frequency of the detection signal of the vibration of the probe;
(d) measuring the frequency component of the alternating magnetic field of the signal demodulated in step (c);
(e) The probe is caused to scan a scanning area set within a plane intersecting the vibration direction of the probe, and the steps (a) to ( d);
(f) performing a two-dimensional Fourier transform on the information corresponding to the measurement result of the step (d) in the scanning region in the in-plane direction of the scanning region;
(g0) From the Fourier transform information obtained in the step (f), extract information corresponding to the two-dimensional Fourier transform of the component of the DC magnetic field parallel to the AC magnetic field in the in-plane direction of the scanning area. The process of
(i0) Based on the information corresponding to the two-dimensional Fourier transform of the component of the direct current magnetic field parallel to the alternating current magnetic field in the in-plane direction of the scanning region, each of the components within the scanning region is For in-plane coordinates, obtaining a value corresponding to a component parallel to the alternating current magnetic field of the direct current magnetic field;
including;
The extraction in the step (g0) includes the amplitude of the alternating magnetic field at the position of the probe, the first-order differential of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe, and the a second derivative of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe, or a combination of two ratios therebetween and two wave numbers in the in-plane direction within the scanning region; carried out based on
A method for measuring a DC magnetic field, characterized in that the amplitude of the AC magnetic field at the position of the probe and the value of the second derivative of the amplitude with respect to the vibration direction of the probe are non-zero. A device for measuring a direct current magnetic field,
a cantilever having a superparamagnetic probe at one end that generates a magnetic moment in the direction of an applied magnetic field;
an exciter that excites the cantilever;
an alternating current magnetic field generator that frequency-modulates the excitation vibration of the cantilever by applying an alternating magnetic field to the probe and periodically varying the magnetization of the probe;
a vibration sensor that detects vibrations of the probe;
a scanning mechanism that causes the probe to scan a scanning area set within a plane intersecting the vibration direction of the probe;
a demodulator that frequency demodulates the detection signal of the vibration sensor;
a detector that measures a frequency component of the alternating magnetic field included in the demodulated signal from the demodulator;
a storage device that stores a measurement value corresponding to a measurement signal of the detector for each in-plane coordinate in the scanning area;
a Fourier transformer that performs a two-dimensional Fourier transform on the measured values for each in-plane coordinate of the scanning area stored in the storage device with respect to the in-plane coordinate;
From the Fourier transform information output from the Fourier transformer, it is possible to extract information corresponding to a two-dimensional Fourier transform of a component of the DC magnetic field parallel to the AC magnetic field in an in-plane direction of the scanning area. a first wave number filter computing unit configured to;
Each in-plane coordinate within the scanning area is determined by two-dimensional inverse Fourier transformation based on information corresponding to the two-dimensional Fourier transformation of the component of the DC magnetic field parallel to the alternating current magnetic field in the in-plane direction of the scanning area. an inverse Fourier transformer configured to be able to obtain a value corresponding to a component of the DC magnetic field parallel to the AC magnetic field;
including;
The extraction in the first wave number filter calculator includes the amplitude of the alternating magnetic field at the position of the probe, the first-order differential of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe; and the second derivative of the amplitude of the alternating magnetic field at the position of the probe with respect to the vibration direction of the probe, or two ratios therebetween, and two wave numbers in the in-plane direction within the scanning region. It is done based on a combination of
A DC magnetic field measuring device, wherein the amplitude of the AC magnetic field at the position of the probe and the value of the second derivative of the amplitude with respect to the vibration direction of the probe are non-zero. A method for measuring an alternating magnetic field, the method comprising:
(a) exciting a cantilever having a superparamagnetic probe at one end that generates a magnetic moment in the direction of the applied magnetic field;
(b) while performing the step (a), frequency-modulating the excitation vibration of the cantilever by applying a DC magnetic field to the probe from a DC magnetic field generator;
(c) while performing the step (b), detecting the vibration of the probe and demodulating the frequency of the detection signal of the vibration of the probe;
(d) measuring a frequency component of the signal demodulated in step (c) that corresponds to the frequency component to be measured of the alternating magnetic field;
(e) The probe is caused to scan a scanning area set within a plane intersecting the vibration direction of the probe, and the steps (a) to ( d);
(f) performing a two-dimensional Fourier transform on the information corresponding to the measurement result of the step (d) in the scanning region in the in-plane direction of the scanning region;
(g0) From the Fourier transform information obtained in step (f), two-dimensional Fourier transform of the amplitude of the frequency component of the alternating current magnetic field that is parallel to the direct current magnetic field is performed in the in-plane direction of the scanning area. a step of extracting information corresponding to the
(i0) By two-dimensional inverse Fourier transform based on information corresponding to two-dimensional Fourier transform of the amplitude of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field in the in-plane direction of the scanning area, For each in-plane coordinate within the scanning area, obtaining a value corresponding to the amplitude of a component of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field;
including;
The extraction in the step (g0) includes the DC magnetic field at the position of the probe, the first derivative of the DC magnetic field at the position of the probe with respect to the vibration direction of the probe, and the position of the probe. is performed based on the second derivative of the DC magnetic field with respect to the vibration direction of the probe, or two ratios therebetween, and a combination of two wave numbers in the in-plane direction within the scanning region,
AC magnetic field measurement, characterized in that the value of the DC magnetic field at the position of the probe and the second derivative of the DC magnetic field at the position of the probe with respect to the vibration direction of the probe are non-zero. Method. A device for measuring an alternating magnetic field,
a cantilever having a superparamagnetic probe at one end that generates a magnetic moment in the direction of an applied magnetic field;
an exciter that excites the cantilever;
a DC magnetic field generator that frequency-modulates the excitation vibration of the cantilever by applying a DC magnetic field to the probe;
a vibration sensor that detects vibrations of the probe;
a scanning mechanism that causes the probe to scan a scanning area set within a plane intersecting the vibration direction of the probe;
a demodulator that frequency demodulates the detection signal of the vibration sensor;
a detector that measures a frequency component included in the demodulated signal from the demodulator that corresponds to a frequency component to be measured of the alternating current magnetic field;
a storage device that stores a measurement value corresponding to a measurement signal of the detector for each in-plane coordinate in the scanning area;
a Fourier transformer that performs a two-dimensional Fourier transform on the measured values for each in-plane coordinate of the scanning area stored in the storage device with respect to the in-plane coordinate;
Information corresponding to a two-dimensional Fourier transform of the amplitude of a component parallel to the DC magnetic field of the frequency component of the AC magnetic field in the in-plane direction of the scanning area, from the Fourier transform information output from the Fourier transformer. a first wave number filter calculator configured to be able to extract the
The scanning area is determined by two-dimensional inverse Fourier transformation based on information corresponding to two-dimensional Fourier transformation of the amplitude of the frequency component of the frequency component of the alternating current magnetic field parallel to the DC magnetic field in the in-plane direction of the scanning area. an inverse Fourier transformer configured to be able to obtain, for each in-plane coordinate within, a value corresponding to the amplitude of a component of the frequency component of the alternating current magnetic field parallel to the direct current magnetic field;
including;
The extraction in the first wave number filter calculator includes the DC magnetic field at the position of the probe, the first derivative of the DC magnetic field at the position of the probe with respect to the vibration direction of the probe, and the probe. Based on the second derivative of the DC magnetic field at the needle position with respect to the vibration direction of the probe, or the two ratios therebetween, and the combination of two wave numbers in the in-plane direction within the scanning area. I,
AC magnetic field measurement, characterized in that the value of the DC magnetic field at the position of the probe and the second derivative of the DC magnetic field at the position of the probe with respect to the vibration direction of the probe are non-zero. Device.