CN117148239A - Method for measuring equivalent magnetic moment of magnetic particles and standard sample - Google Patents
Method for measuring equivalent magnetic moment of magnetic particles and standard sample Download PDFInfo
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- CN117148239A CN117148239A CN202311414220.4A CN202311414220A CN117148239A CN 117148239 A CN117148239 A CN 117148239A CN 202311414220 A CN202311414220 A CN 202311414220A CN 117148239 A CN117148239 A CN 117148239A
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- 239000006249 magnetic particle Substances 0.000 title claims abstract description 128
- 238000000034 method Methods 0.000 title claims abstract description 26
- 239000000523 sample Substances 0.000 claims abstract description 154
- 239000010409 thin film Substances 0.000 claims abstract description 26
- 230000008859 change Effects 0.000 claims abstract description 23
- 238000005259 measurement Methods 0.000 claims abstract description 17
- 230000003993 interaction Effects 0.000 claims abstract description 5
- 239000010408 film Substances 0.000 claims description 19
- 230000005415 magnetization Effects 0.000 claims description 12
- 239000013590 bulk material Substances 0.000 claims description 8
- 230000035699 permeability Effects 0.000 claims description 3
- 229910001172 neodymium magnet Inorganic materials 0.000 description 8
- 238000012545 processing Methods 0.000 description 7
- 238000012417 linear regression Methods 0.000 description 6
- 239000000463 material Substances 0.000 description 6
- 229910005335 FePt Inorganic materials 0.000 description 4
- 239000000696 magnetic material Substances 0.000 description 4
- 238000005459 micromachining Methods 0.000 description 4
- 230000003287 optical effect Effects 0.000 description 3
- 241000238366 Cephalopoda Species 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 239000002245 particle Substances 0.000 description 2
- 230000000737 periodic effect Effects 0.000 description 2
- 230000003044 adaptive effect Effects 0.000 description 1
- 238000004458 analytical method Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000006555 catalytic reaction Methods 0.000 description 1
- 238000013500 data storage Methods 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 238000001514 detection method Methods 0.000 description 1
- 238000006073 displacement reaction Methods 0.000 description 1
- 239000003814 drug Substances 0.000 description 1
- 230000007613 environmental effect Effects 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 238000003754 machining Methods 0.000 description 1
- 239000011553 magnetic fluid Substances 0.000 description 1
- 238000000691 measurement method Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000013421 nuclear magnetic resonance imaging Methods 0.000 description 1
- 230000035945 sensitivity Effects 0.000 description 1
- 239000000126 substance Substances 0.000 description 1
Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/12—Measuring magnetic properties of articles or specimens of solids or fluids
- G01R33/1276—Measuring magnetic properties of articles or specimens of solids or fluids of magnetic particles, e.g. imaging of magnetic nanoparticles
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R35/00—Testing or calibrating of apparatus covered by the other groups of this subclass
- G01R35/005—Calibrating; Standards or reference devices, e.g. voltage or resistance standards, "golden" references
- G01R35/007—Standards or reference devices, e.g. voltage or resistance standards, "golden references"
Abstract
The application discloses a method for measuring equivalent magnetic moment of magnetic particles and a standard sample, and relates to the field of precision weak force measurement; the method comprises the following steps: measuring the change amount of the resonance frequency of the probe where the magnetic particles are located caused by the magnetic interaction between the magnetic particles and the standard sample; the standard sample comprises an array of magnetic thin film blocks; the probe comprises a cantilever beam and magnetic particles, wherein the cantilever beam is used as a weak force sensor, and when the cantilever beam is acted by magnetic force between the magnetic particles and a standard sample, the resonance frequency of the probe is changed; and fitting based on a functional relation between the change of the resonance frequency of the probe and the equivalent magnetic moment of the magnetic particle to obtain the equivalent magnetic moment of the magnetic particle. The application solves the problem that the current magnetic measuring instrument can not calibrate the magnetic moment of the magnetic particles with the micron order or below, and provides a new method for measuring the magnetic moment.
Description
Technical Field
The application belongs to the field of precision weak force measurement, and particularly relates to a method for measuring equivalent magnetic moment of magnetic particles and a standard sample.
Background
Micro-nano magnetic particles widely applied in the modern scientific and technical fields of biological medicine, magnetic fluid, catalysis, nuclear magnetic resonance imaging, data storage, precise measurement, environmental protection and the like have been developed rapidly in recent years due to a series of unique and superior physical and chemical properties. However, the geometry of such magnetic particles is generally in the order of micrometers and less, which results in their very small magnetic moment and makes it very difficult to accurately measure the magnetic moment of individual magnetic particles.
However, the magnetic moment of a magnetic material is a very important indicator for measuring its performance, although there are many magnetic measuring instruments in the market at present, such as: vibrating sample magnetometers (Vibrating Sample Magnetometer, VSM), magneto-optical Kerr microscopes, atomic magnetometers, superconducting quantum interferometers (Superconducting Quantum Interference Device, SQUIDs), and the like, but the detection sensitivity of the commercial magnetic measuring instrument-superconducting quantum interferometers (SQUIDs) with the highest measurement accuracy can only be achieved at presentWhereas for magnetic particles with a single geometry below the micrometer scale, the magnetic moment is usually +.>In the following, the magnetic moment of the magnetic particles of micrometer magnitude and below cannot be detected by the magnetic measuring instrument on the market.
Disclosure of Invention
Aiming at the bottleneck of the existing magnetic measurement level, the application provides a magnetic particle equivalent magnetic moment measurement method and a standard sample, and aims to solve the problem that the prior art cannot detect the magnetic moment of magnetic particles with the micrometer magnitude or below.
In a first aspect, the present application provides a method for measuring the equivalent magnetic moment of a magnetic particle, comprising:
measuring the change amount of the resonance frequency of the probe where the magnetic particles are located caused by the magnetic interaction between the magnetic particles and the standard sample; the standard sample comprises an array of magnetic thin film blocks; the probe comprises a cantilever beam and magnetic particles, wherein the cantilever beam is used as a weak force sensor, and when the cantilever beam is acted by magnetic force between the magnetic particles and a standard sample, the resonance frequency of the probe is changed;
determining the relationship between the magnetic force between the magnetic particles and the standard sample and the magnetization intensity of the standard sample, the equivalent magnetic moment of the magnetic particles, the distance between the magnetic particles and the standard sample and the relative position vector; and then fitting based on the relation between the change amount of the resonance frequency of the probe and the magnetic force to obtain the equivalent magnetic moment of the magnetic particles.
It can be understood that a suitable magnetic material can be selected for standard sample preparation according to the magnetic properties of the magnetic particles to be detected, the optimal design of the pattern structure of the standard sample is performed according to the geometric dimensions of the magnetic particles to be detected, and then the standard sample is prepared in a micromachining mode so as to generate magnetic force between the standard sample and the magnetic particles, thereby changing the resonance frequency of the probe and measuring the magnetic moment of the magnetic particles.
It should be noted that the weak force sensor refers to that the cantilever beam will deform after receiving external weak force, and the change of external disturbance force and/or disturbance force gradient received by the cantilever beam can be given by measuring the displacement change of the cantilever beam and/or the change of the resonance frequency of the cantilever beam.
In one possible implementation, the magnetic force between the magnetic particles and the standard sampleThe method comprises the following steps:
wherein,is the equivalent magnetic moment of the magnetic particle, +.>For the magnetization of the standard sample, +.>Is the volume element of the standard sample, < >>Distance between magnetic particles and standard sample, +.>Is the unit vector of the relative position of the magnetic particles and the standard sample,>for the distance of the magnetic particles from the standard sample, +.>Is the permeability in vacuum.
In one possible implementation, the probe resonance frequency is changed by an amountThe method comprises the following steps:
wherein,for the intrinsic resonance frequency of the probe, < >>Is the elastic coefficient of the probe.
In one possible implementation, the magnetic thin film bulk material in the standard sample has perpendicular magnetic anisotropy.
It will be appreciated that magnetic thin film materials have in-plane magnetic anisotropy in addition to perpendicular magnetic anisotropy, i.e., magnetic anisotropy that appears in a certain plane or interface of the magnetic thin film bulk.
In one possible implementation, the remanence ratio of the magnetic thin film block material in the standard sample is greater than a preset ratio.
In general, the remanence ratio may be greater than 80% -90%, even at 100%.
In one possible implementation, the maximum side length of each magnetic thin film block in the standard sample is not greater than the diameter of the magnetic particles, and/or the distance between two adjacent magnetic thin film blocks is not less than a preset proportion of the diameter of the magnetic particles.
It should be noted that, in theory, the distance between two adjacent magnetic thin film blocks should be not smaller than the diameter of the magnetic particles; however, because the standard sample of the application adopts a micro-machining mode, the machining error is not negligible, and in practical application, the distance between the adjacent magnetic film blocks may be slightly smaller than the diameter of the magnetic particles, which is equivalent to the diameter of the magnetic film blocks, i.e. the distance between the magnetic film blocks is smaller than the diameter of the magnetic particles within a preset range. Therefore, the distance between two adjacent magnetic thin film blocks is defined to be not smaller than the preset ratio of the diameters of the magnetic particles in the present application to take into account the processing errors.
In one possible implementation, the magnetic force is generated by:
the magnetic particles are controlled to move at a certain height from the surface of the standard sample along the horizontal transverse direction and/or the horizontal longitudinal direction so as to generate the change of the magnetic force between the magnetic particles and the standard sample.
In one possible implementation, the diameter of the magnetic particles is on the order of micrometers and below.
According to the application, the size of the standard sample is designed according to the geometric size of the magnetic particles, and the proper standard sample material is selected, so that the magnetic force modulated by the space period can be generated between the standard sample and the magnetic particles.
In a second aspect, the present application provides a standard sample for equivalent magnetic moment measurement of magnetic particles, the standard sample comprising an array of magnetic thin film blocks;
the standard sample is used for generating magnetic force with the magnetic particles in a space periodic variation mode, so that the resonance frequency of a probe where the magnetic particles are located is changed, and after the relation between the magnetic force between the magnetic particles and the standard sample and the magnetization intensity of the standard sample, the equivalent magnetic moment of the magnetic particles, the distance between the magnetic particles and the standard sample and the relative position vector is determined, the equivalent magnetic moment of the magnetic particles is obtained through fitting based on the relation between the change of the resonance frequency of the probe and the magnetic force.
In one possible implementation, the magnetic thin film bulk material in the standard sample has perpendicular magnetic anisotropy, and/or the remanence ratio of the magnetic thin film bulk material in the standard sample is greater than a predetermined ratio.
In general, through the above technical solutions conceived by the present application, the following beneficial effects can be obtained:
the application provides a magnetic particle equivalent magnetic moment measuring method and a standard sample, wherein the standard sample is designed based on parameters of magnetic particles, so that magnetic force is generated between the magnetic particles and the standard sample, a cantilever beam is used as a weak force sensing device to measure the change of a probe resonance frequency caused by the magnetic force between the magnetic particles adhered to the tail end of the cantilever beam and the standard sample, and a multiple linear regression method is adopted to fit and obtain the equivalent magnetic moment vector of the magnetic particles based on experimental measurement data, so that a method is provided for measuring the magnetic moment of the magnetic particles.
Drawings
FIG. 1 is a flow chart of a method for measuring equivalent magnetic moment of a magnetic particle according to an embodiment of the present application;
FIG. 2 is a schematic diagram of an experimental principle of equivalent magnetic moment measurement of magnetic particles according to an embodiment of the present application;
FIG. 3 shows the change in the resonance frequency of the probe obtained by experimental measurement in accordance with the embodiment of the present applicationAlong with the change of the horizontal position x of the standard sample;
FIG. 4 shows a variation of the resonant frequency according to an embodiment of the present applicationAnd (5) fitting a result graph.
Detailed Description
For convenience of understanding, the following explains and describes english abbreviations and related technical terms related to the embodiments of the application.
Embodiments of the present application will be described below with reference to the accompanying drawings in the embodiments of the present application.
FIG. 1 is a flow chart of a method for measuring equivalent magnetic moment of a magnetic particle according to an embodiment of the present application; as shown in fig. 1, the method comprises the following steps:
s101, measuring the change amount of the resonance frequency of a probe where the magnetic particles are located caused by magnetic interaction between the magnetic particles and a standard sample; the standard sample comprises an array of magnetic thin film blocks; the probe comprises a cantilever beam and magnetic particles, wherein the cantilever beam is used as a weak force sensor, and when the cantilever beam is acted by magnetic force between the magnetic particles and a standard sample, the resonance frequency of the probe is changed;
s102, fitting based on a functional relation between the change amount of the resonance frequency of the probe and the equivalent magnetic moment of the magnetic particle to obtain the equivalent magnetic moment of the magnetic particle.
Specifically, the magnetic particles to be detected can be adhered to the cantilever beam of the probe under a high-power optical microscope.
Specifically, a magnetic film material with saturation magnetization and coercivity adaptive is selected according to the magnetic performance of the magnetic particles to be detected; according to the particle size of the magnetic particles to be detected, designing the magnetic film into a pattern structure with equivalent size, and optimally designing the interval between adjacent structures; standard samples were prepared using micromachining.
Specifically, the change of the resonance frequency of the probe between the prepared probe and the standard sample due to magnetic force is required to be larger than the measurement precision of a scanning probe microscope, otherwise, the scanning probe microscope cannot measure the magnetic signal.
Specifically, the magnetic thin film bulk material in the standard sample has perpendicular magnetic anisotropy.
It should be noted that, referring to fig. 2, the cantilever beam is placed on the xy plane, the laser beam of the scanning probe microscope is irradiated on the cantilever beam along the z axis direction, and the deformation of the cantilever beam in the z direction caused by the magnetic force is measured.
Further, in order to prevent the magnetic field generated by the magnetic particles from being large and changing the magnetization direction of the magnetic film block, the processing and analysis of later data are inconvenient, so that the magnetic film block is prepared by selecting a material with perpendicular magnetic anisotropy and magnetized to the z-axis direction.
It will be appreciated that if the cantilever beam is placed in the yz plane/xz plane, the magnetization direction of the magnetic particles is along the x-axis/y-axis, and the material of the magnetic thin film block is selected to have in-plane magnetic anisotropy, which is not specifically expanded by the present application.
Specifically, the remanence ratio of the magnetic film block material in the standard sample is larger than a preset ratio.
Specifically, the maximum side length of each magnetic film block in the standard sample is not greater than the diameter of the magnetic particles, and/or the distance between two adjacent magnetic film blocks is not less than the preset proportion of the diameter of the magnetic particles.
Specifically, the magnetic force is generated by:
the magnetic particles are controlled to move at a certain height from the surface of the standard sample along the horizontal transverse direction and/or the horizontal longitudinal direction so as to generate the change of the magnetic force between the magnetic particles and the standard sample.
In particular, the diameter of the magnetic particles is in the order of micrometers and below.
It should be noted that when the size of the standard sample and the magnetic particles are at one level, and the standard sample satisfies the perpendicular magnetic anisotropy and the remanence ratio is sufficiently large, a corresponding magnetic force can be generated so that the magnetic moment of the magnetic particles can be measured.
In a specific embodiment, ndFeB magnetic particles are selected as the object to be measured, and the standard sample is a FePt magnetic material. In order to obtain a periodic signal, the geometry and spacing of the standard sample magnet is optimized according to the geometry of the magnetic particles. As shown in the experimental schematic diagram 2, the diameter of the NdFeB magnetic particles isThe resonance frequency of the probe after bonding under an optical microscope was 122.02 kHz and the elastic modulus was 8.38N/m. After the standard sample preparation is completed, the size of the film block is +.>The magnetization direction is along the z-axis direction, the film block array is in +.>The direction interval is,/>The direction interval is +.>The residual magnetization was measured using a Vibrating Sample Magnetometer (VSM) and found to be 750 kA/m. When at experimental distance->When the experiment is carried out, the multiple linear regression method is adopted to fit experimental measurement data, and a gradient descent algorithm is used to minimize the fitting residual error, and finally the equivalent magnetic moment vector of the NdFeB magnetic particles is obtainedAnd its location。
It will be appreciated that in the above embodiment, taking into consideration the processing error of the magnetic thin film blocks, it is theoretically necessary to control the pitch of the adjacent magnetic thin film blocks to be not smaller than the diameter of the magnetic particles when processing the magnetic thin film blocks, but the pitch between the magnetic thin film blocks that may be actually processed is slightly smaller than the diameter of the magnetic particles due to the processing error, as described in the above embodiment. The application therefore defines that the spacing between adjacent magnetic film blocks is not less than a predetermined proportion of the magnetic particle diameter, i.e. the spacing distance between the magnetic film blocks is comparable to the magnetic film block diameter.
It should be understood that the NdFeB magnetic particle probe, fePt standard sample and scanning probe microscope system used in the present method are only specific examples for explaining the present application, and are not intended to limit the present application.
Specifically, the magnetic particle probe can comprise NdFeB magnetic particles and a commercial probe (model is NSG 11/probe), and the magnetic particles to be detected are stuck on a cantilever beam of the probe through a high-power optical microscope and are completely magnetized along the direction perpendicular to the cantilever beam as shown in fig. 2.
By way of example, by selecting a proper magnetic material FePt, designing a magnetic film into a pattern structure with a comparable size according to the particle size of NdFeB magnetic particles to be detected, optimally designing the distance between adjacent structures, preparing a standard sample by a micro-processing mode, and making the standard sample along the direction shown in FIG. 2The axial direction is completely magnetized.
Further, in combination with the measurement principle of the scanning probe microscope, a cantilever beam is used as a weak force sensing device to measure the variation of the resonance frequency of the probe caused by the magnetic force between the magnetic particles and the standard sample prepared by micromachining. Giving the variation of the resonant frequency of the probe at different horizontal positions x of the standard sampleSee fig. 3.
Further, based on the measurement data of the resonance frequency variation, fitting experimental measurement data by adopting a multiple linear regression method, and minimizing a fitting residual by using a gradient descent algorithm, see fig. 4, wherein the abscissa of fig. 4 is a horizontal position x, and the ordinate is a magnetic gradientAnd finally, obtaining the equivalent magnetic moment vector and the position of the magnetic particles.
Further, the multiple linear regression fit incorporates electromagnetic correlation theory, including:
the magnetic force between the magnetic particles and the standard sample can be expressed as:
wherein the method comprises the steps ofIs the equivalent magnetic moment of the magnetic particle, +.>For the magnetization of the standard sample, +.>Is the volume element of the standard sample, < >>Is the position relation between the magnetic ball and the standard sample, < >>Is the unit vector of the relative position of the magnetic particles and the standard sample,>is the distance between the bottom of the magnetic ball and the upper surface of the standard sample, < >>Is the permeability in vacuum.
Further processing to obtain the resonance frequency change of the probeWherein->For the resonance frequency of the probe, < >>Is the elastic coefficient of the probe. Finally give->Equivalent magnetic moment of magnetic ball->A functional relationship between them.
Fitting experimental measurement data by adopting a multiple linear regression method, minimizing fitting residual errors by using a gradient descent algorithm, and finally obtaining the equivalent magnetic moment vector of the magnetic particlesAnd its position->。
In particular, because the NdFeB magnetic particle probe and the magnetic film block of the FePt calibration sample can generate magnetic interaction, the change of the resonance frequency of the probe caused by the magnetic force between the NdFeB magnetic particle probe and the FePt calibration sample can be given according to the theory of electromagnetic correlationEquivalent magnetic moment to NdFeB magnetic particles>A functional relationship between them. According to the functional relation, combining magnetic force data measured by a scanning probe microscope, fitting experimental measurement data by adopting a multiple linear regression method, and minimizing fitting residual errors by using a gradient descent algorithm to finally obtain the equivalent magnetic moment vector +.>And its position->。
It will be readily appreciated by those skilled in the art that the foregoing is merely a preferred embodiment of the application and is not intended to limit the application, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the application are intended to be included within the scope of the application.
Claims (10)
1. A method for measuring the equivalent magnetic moment of a magnetic particle, comprising:
measuring the change amount of the resonance frequency of the probe where the magnetic particles are located caused by the magnetic interaction between the magnetic particles and the standard sample; the standard sample comprises an array of magnetic thin film blocks; the probe comprises a cantilever beam and magnetic particles, wherein the cantilever beam is used as a weak force sensor, and when the cantilever beam is acted by magnetic force between the magnetic particles and a standard sample, the resonance frequency of the probe is changed;
determining the relationship between the magnetic force between the magnetic particles and the standard sample and the magnetization intensity of the standard sample, the equivalent magnetic moment of the magnetic particles, the distance between the magnetic particles and the standard sample and the relative position vector; and then fitting based on the relation between the change amount of the resonance frequency of the probe and the magnetic force to obtain the equivalent magnetic moment of the magnetic particles.
2. The method according to claim 1, wherein the magnetic force between the magnetic particles and a standard sampleThe method comprises the following steps:
wherein,is the equivalent magnetic moment of the magnetic particle, +.>For the magnetization of the standard sample, +.>Is the volume element of the standard sample,distance between magnetic particles and standard sample, +.>Is the unit vector of the relative position of the magnetic particles and the standard sample,>for the distance of the magnetic particles from the standard sample, +.>In vacuumIs a magnetic permeability of (c).
3. The method of claim 2, wherein the probe resonance frequency is varied by an amountThe method comprises the following steps:
wherein,for the intrinsic resonance frequency of the probe, < >>Is the elastic coefficient of the probe.
4. A method according to any one of claims 1 to 3, wherein the magnetic thin film bulk material in the standard sample has perpendicular magnetic anisotropy.
5. A method according to any one of claims 1 to 3, wherein the remanence ratio of the magnetic thin film bulk material in the standard sample is greater than a predetermined ratio.
6. A method according to any one of claims 1 to 3, wherein the maximum side length of each magnetic film block in the standard sample is not greater than the diameter of the magnetic particles and/or the distance between two adjacent magnetic film blocks is not less than a predetermined proportion of the diameter of the magnetic particles.
7. A method according to any one of claims 1 to 3, wherein the magnetic force is generated by:
the magnetic particles are controlled to move at a certain height from the surface of the standard sample along the horizontal transverse direction and/or the horizontal longitudinal direction so as to generate the change of the magnetic force between the magnetic particles and the standard sample.
8. A method according to any one of claims 1 to 3, characterized in that the diameter of the magnetic particles is of the order of micrometers and below.
9. A standard sample for magnetic particle equivalent magnetic moment measurement, characterized in that the standard sample comprises an array of magnetic thin film blocks;
the standard sample is used for generating magnetic force with space periodical change between the standard sample and the magnetic particles, so that the resonance frequency of a probe where the magnetic particles are located is changed, and after the relation between the magnetic force between the magnetic particles and the standard sample and the magnetization intensity of the standard sample, the equivalent magnetic moment of the magnetic particles, the distance between the magnetic particles and the standard sample and the relative position vector is determined, the equivalent magnetic moment of the magnetic particles is obtained by fitting based on the relation between the change of the resonance frequency of the probe and the magnetic force.
10. The standard sample according to claim 9, wherein the magnetic thin film bulk material in the standard sample has perpendicular magnetic anisotropy and/or the remanence ratio of the magnetic thin film bulk material in the standard sample is greater than a predetermined ratio.
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