JP4578832B2 - Structure factor tensor element determination method and X-ray diffractometer utilization method therefor - Google Patents

Description

  The present invention relates to a method used for evaluating the magnetic structure of a magnetic material (for example, a permanent magnet, a magnetic head, a perpendicular magnetization film, a magnetic semiconductor, a molecular magnetic material, or an organic magnetic material) based on X-ray magnetic scattering. is there. Furthermore, the present invention relates to a method used for elemental selective structure evaluation based on resonance scattering in a crystalline material.

  In particular, in the method of the present invention, linearly polarized X-rays whose polarization direction is controlled are incident on a sample, and the scattered X-ray intensity generated from the sample is measured using a diffractometer while changing the incident polarized light. By analyzing the dependence of scattered X-ray intensity on incident polarization, the structure factor tensor of the sample is analyzed.

The purpose of the X-ray scattering experiment is to determine the structure factor of the object to be measured. The structure factor is a factor that gives the scattering amplitude by the unit structure of the substance, and depends on the scattering vector and the polarization of the X-ray. In the normal scattering process, the scattering amplitude of the scattered wave having the wave number vector k ^f is obtained by projecting the amplitude of the incident wave having the wave number vector k ⁱ onto a plane perpendicular to k ^f , and the classical electron radius (2.818 × 10 ⁻¹⁵ m name physical constant with the value that will) have become multiplied by the r _e a Fourier transform of the charge density ratio and the unit structure of the distance r between the scattering body observation point ρ (k f ^{-k i).} The effect of the projection appears only in the polarized light (π-polarized light) component in the scattering plane stretched by k ⁱ and k ^f, and does not appear in the polarized light (σ-polarized light) component perpendicular to the scattering plane.
If the above is expressed by an expression,

となる。ここで、２θは散乱角（ｋ^ｉとｋ^ｆのなす角）であり、被側定物の構造因子は対角成分のみのテンソル（複数の成分をもち、空間の座標変換に対していくつかのベクトルの成分の積に対応した変換を受けるもの）で与えられる。ところが、（式１）では扱えない特殊な散乱過程が存在する。

It becomes. Here, 2θ is a scattering angle (an angle formed by k ⁱ and k ^f ), and the structure factor of the fixed object is a tensor with only a diagonal component (having a plurality of components, and some coordinate conversion of space Which receives the transformation corresponding to the product of the vector components of However, there is a special scattering process that cannot be handled by (Equation 1).

  Resonant X-ray scattering is scattering caused by the atomic scattering factor exhibiting anomalous dispersion with respect to X-rays having energy near the absorption edge. When the resonance level is anisotropic with respect to the crystal orientation, an off-diagonal term is generated in the structure factor tensor. As such scattering, Templeton-Templeton scattering and resonance magnetic scattering are known, and are used for element-selective structure evaluation of crystalline materials. Non-resonant magnetic scattering is X-ray scattering caused by a magnetic moment and is characterized by a very low scattering intensity. In general, the off-diagonal term of the structure factor tensor for non-resonant magnetic scattering has a finite size. Special scattering in which off-diagonal terms are generated in the structure factor tensor is called scattering by an anisotropic X-ray susceptibility tensor (ATS scattering).

  In order to determine each element of the structure factor tensor, it is necessary to examine the scattering amplitude of each channel of scattering (σ polarization → σ polarization, σ polarization → π polarization, π polarization → σ polarization, π polarization → π polarization). . In the conventional method, linearly polarized X-rays having only a σ (π) polarization component are incident on a sample, and the scattered X-rays are subjected to polarization analysis so that σ (π) polarized light → σ (π) polarized light, σ (π) polarized light → π The element of the structure factor tensor for each channel of (σ) polarization was determined. Polarization analysis of scattered X-rays uses a phenomenon that the polarization component in the scattering plane does not have a scattering amplitude under the condition that the scattering angle is 90 degrees, and uses a non-magnetic and single crystal ellipsometric crystal at a scattering angle of 90 degrees. Thus, it is performed by selectively measuring only the polarization component perpendicular to the scattering plane of the ellipsometric crystal. This is readily understood by imposing the condition 2θ = 90 ° on (Equation 1). The currently known X-ray region ellipsometry method is the only method using a non-magnetic single crystal as the ellipsometry crystal.

Problems to be solved by the invention

As described above, a method for analyzing the polarization of the X-ray region necessary for determining the structure factor tensor has already been proposed. However, in order to quickly determine the structure factor tensor and improve the measurement sensitivity, the following problems caused by using ellipsometric crystals must be solved.
1) The intensity ratio of incident X-rays and scattered X-rays in the diffraction process in the ellipsometric crystal is almost less than 1/100, causing a significant decrease in measurement sensitivity. The reason is that the diffraction line of 2θ = 90 ° used for the ellipsometry has a small atomic scattering factor, and the diffraction line is blurred due to thermal vibration of atoms.

  2) When the integrated intensity is measured very accurately in order to determine the structure factor tensor, it is necessary to obtain not only the sample crystal but also the ellipsometric crystal by a small angle rotation to obtain the integrated intensity. This requires a two-dimensional scanning measurement on a virtual plane stretched by the biaxial rotation angle, and takes a long time for the measurement.

  3) When excluding the effect of diffraction in the ellipsometric crystal to determine the structure factor tensor, it is necessary to deconvolute the ellipsometric crystal resolution function taking into account the angular divergence of the scattered X-rays from the sample. . The analysis is very complicated and depends on the sample and the ellipsometric crystal and is difficult to generalize.

  4) Since the plane spacing of the ellipsometric crystal is discrete and has an upper limit, the energy of X-rays satisfying the condition of a scattering angle of 2θ = 90 ° is also discrete and has a lower limit. This causes a problem that the condition of a scattering angle of 2θ = 90 ° cannot be satisfied in resonance X-ray scattering in which the energy of X-rays used by the absorption edge is limited. In particular, ellipsometry is impossible in the soft X-ray region below the lower limit of the X-ray energy limited by the maximum interplanar spacing of the crystal.

  5) Detectors that can be used for ellipsometry using ellipsometry crystals are limited to zero-dimensional detectors. For this reason, a one-dimensional detector or a two-dimensional detector cannot be used, and the measurement efficiency is extremely low.

Means for solving the problem

  The present invention solves the problems caused by using an ellipsometric crystal for ellipsometric analysis of scattered X-rays from a sample, and promptly determines a structure factor tensor and improves measurement sensitivity. In the conventional method, stationary polarized X-rays are incident on the sample, and the structure factor tensor is determined by analyzing the scattered X-rays. However, in the method of the present invention, the ellipsometric process of the scattered X-rays is abolished. Thus, all the disadvantages of the conventional method are avoided, and the structure factor tensor is determined by measuring the scattered X-ray intensity from the sample without changing the polarization while changing the incident polarization. This avoids loss of scattered X-ray intensity from the sample during the ellipsometric analysis, improves measurement sensitivity, shortens integration time in measurement, and speeds up measurement by using a high-dimensional detector. There is no prior art to determine the structure factor tensor without using ellipsometric crystals, and the present invention is based on a completely new idea.

The invention's effect

  In the method of the present invention, by measuring and analyzing the dependence of the scattered X-ray intensity from the sample on the incident polarization, the structure factor tensor can be determined without using an ellipsometric crystal. Produces a good effect.

  Furthermore, since all the above problems 1) to 5) of the conventional method are avoided, the remarkable effect peculiar to the present invention that the measurement with improved measurement sensitivity is speeded up is produced. In addition, the variable scattering surface method developed as a method for controlling incident polarized light and the algorithm for determining the angle of the six-axis diffractometer necessary for its implementation can be applied to the method of the present invention without modifying the existing radiation source. This produces a remarkable effect peculiar to the present invention.

[Description of polarized light]
A plane formed by the wave vector k ⁱ of incident X-rays and the wave vector k ^f of scattered X-rays is called a scattering plane. The polarized light perpendicular to the scattering plane is called σ polarized light, and the parallel polarized light is called π polarized light.
[Basic idea]
Linearly polarized light is used for incident X-rays. The electric field of the incident X-ray is expressed as E ₀ (e _σ cos θ + e _π sin θ). Here, E ₀ is the electric field amplitude, e _σ , e _x are unit vectors in each polarization direction, and θ is a parameter.

と表される。ここで、ｒ_ｅは古典電子半径である。散乱強度は散乱振幅の自乗で表されるので、以下の式変形

It is expressed. Here, r _e is the classical electron radius. Since the scattering intensity is expressed by the square of the scattering amplitude,

を経て、最終的に

And finally

ある。これよりα≠０の場合は直ちに電荷散乱でないことが結論される。これまでの議論を要約すると次のようになる。散乱強度の入射偏光依存性は一般にＩ（θ）＝Ａ＋Ｂｃｏｓ（２θ＋α）と記述され、位相αの値から電荷散乱か磁気散乱か判別することが可能である。
［テンソル要素の決定］
入射Ｘ線には直線偏光を使用する。後述する方法により偏光を制御し、散乱強度の入射偏光依存性Ｉ（θ）を測定する。散乱強度の入射偏光依存性Ｉ（θ）を示す図１に示されるように、測定結果をフィッティングし、散乱強度の入射偏光依存性Ｉ（θ）の３つのパラメータＡ，Ｂ，αを決定する。構造因子テンソルの４未知変数に対し、フィッティングして得られたパラメータＡ，Ｂ，αに関する３束縛条件が課せられているので、この段階で構造因子テンソルは１パラメータ表示になっている。アジマス角（散乱ベクトルを軸とした試料回転の擬角度（擬角度とは、回折計の有する回転軸と一対一対応の関係がない角度））を別の値に固定し、同様の測定を重ねることで多数の束縛条件を課し、構造因子テンソルの各要素を制度よく決定することが可能である。
［偏光の制御方法］
新規提案の方法では、直線偏光した入射Ｘ線の偏光方法の自在な制御が必要となる。ここでは、３つの実施案を提案する。

is there. From this, it is concluded that when α ≠ 0, it is not charge scattering immediately. The summary of the discussion so far is as follows. The incident polarization dependence of the scattering intensity is generally described as I (θ) = A + Bcos (2θ + α), and it is possible to determine whether it is charge scattering or magnetic scattering from the value of phase α.
[Determination of tensor elements]
Linearly polarized light is used for incident X-rays. Polarization is controlled by a method to be described later, and the incident polarization dependence I (θ) of the scattering intensity is measured. As shown in FIG. 1 showing the incident polarization dependence I (θ) of the scattering intensity, the measurement result is fitted to determine three parameters A, B, and α of the incident polarization dependence I (θ) of the scattering intensity. . Since three constraint conditions regarding parameters A, B, and α obtained by fitting are imposed on the four unknown variables of the structure factor tensor, the structure factor tensor is displayed as one parameter at this stage. Fix the azimuth angle (pseudo-angle of sample rotation with the scattering vector as an axis (the pseudo-angle is an angle that does not have a one-to-one relationship with the rotation axis of the diffractometer)) to another value, and repeat the same measurement. In this way, it is possible to impose many constraints and determine each element of the structural factor tensor systematically.
[Polarization control method]
The newly proposed method requires free control of the polarization method of linearly polarized incident X-rays. Here, three implementation plans are proposed.

(1) Use of undulator with variable polarization plane An insertion light source used to obtain high-intensity light with good monochromaticity in a synchrotron radiation generator is called an undulator. The electron trajectory meanders in a plane perpendicular to the magnetic field created by the regularly arranged magnets, and linearly polarized radiation (because the electric field vector oscillation is confined in the electron trajectory plane) is generated. By making the magnetic field direction of this undulator variable, the polarization direction of incident X-rays can be freely controlled. This method requires modification of an insertion light source incorporated in a large system called a storage ring, and is very technically difficult.

(2) Use of a phase shifter (an optical element that functions to change the polarization of light) In a nearly perfect crystal, X-rays undergo multiple scattering and cause birefringence. In a birefringent crystal, since the refractive indices for the σ-polarized component and the π-polarized component are different, a phase difference proportional to the transmission distance in the crystal is generated between both polarized lights. If the phase difference between the σ polarization component and the π polarization component is controlled using this phenomenon, the polarization direction of incident X-rays can be freely controlled. In this method, the experimental conditions are limited to the optimum energy band of the birefringent crystal, and a separate diffractometer is required for the operation of the target birefringent crystal. There is a drawback that it is necessary to monitor the generated polarized light because of its sensitivity.

(3) Use of a multi-axis diffractometer The polarization direction of incident X-rays to be freely controlled is the polarization direction defined by the scattering surface in the diffraction experiment. This is significant in the relative relationship between the “polarization direction of the incident X-ray” and the “scattering plane of the diffraction experiment”, and has no meaning in the absolute direction (horizontal or vertical) of the polarization of the incident X-ray. Therefore, even if stationary linearly polarized light is used for incident X-rays, polarization can be freely controlled from π-polarized light to σ-polarized light by making the scattering surface variable. The scattering surface can be made variable by using a multi-axis diffractometer having a higher degree of freedom than a commonly used four-axis diffractometer. An advantage of this method is that the polarization direction of incident X-rays can be controlled relatively easily.
[Variable scattering surface method]
The variable scattering surface method is a method of controlling the polarization direction of an incident X-ray with respect to the scattering surface by making the scattering surface variable with a multi-axis diffractometer having a high degree of freedom while using horizontal linearly polarized light for incident X-rays. FIG. 2 shows a conceptual diagram of this variable scattering surface method. FIG. 2A shows a conceptual diagram of a conventional fixed scattering surface using an ellipsometric crystal, and FIG. 2B shows a conceptual diagram of a variable scattering surface method not using an ellipsometric crystal. The inclination angle θ from the vertical plane of the scattering surface with the wave vector direction of the incident X-ray as an axis is an important parameter that describes the polarization state of the incident X-ray. For incident X-rays, horizontal linearly polarized light from an undulator can be used as it is, and the present invention can be implemented only by improving the diffractometer.
(Drawings of apparatus, process, etc. according to invention)
[Diffraction meter used]
HUBER 5020 6-axis diffractometer. It is composed of six axes including a sample axis μ and a detector axis ν added to a normal four-axis diffractometer (sample: η, χ, φ | detector: δ).
FIG. 3 is a diagram showing the definition of the coordinate axis (x, y, z) of the laboratory system and the definition of the origin / rotation direction of each axis (δ, η, χ, φ, μ, ν) of the diffractometer. Each axis in the figure is at the origin, and the positive rotation direction is indicated by an arrow.
[Six Axis Angle Determination Algorithm]
In order to determine the unique six-axis angle of the “sample four-axis-detector two-axis” diffractometer described above, three constraints are required. Although there are an infinite number of ways to impose the constraint conditions, it is most important for the determination of the structure factor tensor element that θ that describes the polarization state by the variable scattering surface method and the azimuth angle Ψ that is important for ATS scattering can be specified as arbitrary angles. convenient. For the remaining one degree of freedom, a constraint condition of ν = 2μ was imposed to reduce the blind spot area. There is no unprecedented control mode of a six-axis diffractometer that can specify pseudo angles θ and Ψ that do not correspond to actual mechanical axes as arbitrary angles, and this will be named “θ-Ψ fixed mode”.
This gives the expression used to calculate each axis angle. The precondition is that the lattice constants a, b, c, α, β, and γ are known, and the UB matrix (crystal orientation matrix: a conversion matrix between the reciprocal lattice of the crystal and the coordinates of the laboratory system. Factors inherent to the crystal B and the factor U that depends on how the crystals are placed.) The algorithm for solving the UB matrix is widely known and will not be described here. The information to be given is the reciprocal lattice vector h, the azimuth angle reference vector n, and the pseudo-angles θ and Ψ that satisfy the diffraction conditions. First, the scattering angle 2θ is calculated from the lattice constant and h. this is,

で与えられる。これより、検出器の２軸の角度が

Given in. From this, the angle of the two axes of the detector

と与えられる。また、試料の４軸の角度は

And given. The angle of the four axes of the sample is

で与えられる。ここで、Ｖ_ｉｊは

Given in. Where V _ij is

より与えられる。また、ベクトルｕのｘ成分を［ｕ］_χと表している。軸方向の定義は、図３に与えてある。以上の表式を用いると、任意の擬角度θとΨに対する、六軸角を一意に決定することが可能である。これについては、実際にθ−Ψ固定モードで回折実験を行い、計算された位置に反射が観測されることを確認している。

Given more. Further, the x component of the vector u is represented as [u] _χ . The definition of the axial direction is given in FIG. Using the above expression, it is possible to uniquely determine the six-axis angles for arbitrary pseudo angles θ and Ψ. For this, a diffraction experiment is actually performed in the θ-Ψ fixed mode, and it is confirmed that reflection is observed at the calculated position.

The Example of this invention is typically shown with a figure. The magnetic structure of rare earth metal dysprosium was evaluated. In this case, the scattered X-ray intensity is scanned by changing the scattering vector along the reciprocal lattice vector c ^* of the sample (dysprosium). Moreover, the temperature of the sample was kept at 120K for measurement.

FIG. 4 is a diffraction profile along c ^* of (008) fundamental reflection. The slope of the scattering surface measured is θ = −60 ° and the azimuth angle is ψ = 180 °. The area of the shaded portion in the figure is the integrated intensity of this reflection.

5, (008) ^- is a diffraction profile along the magnetic satellite reflections ^{c *.} The slope of the scattering surface where the measurement was performed was θ = −60 °, and the azimuth angle was ψ = 180 °. The area of the shaded portion in the figure is the integrated intensity of this reflection.

(008) ^- performing normalized integrated intensity of the magnetic satellite reflections (008) and dividing the integrated intensity of the fundamental reflection. Thereby, the effect of the sample volume related to scattering, the Debye-Waller factor, and the Lorentz factor are offset. (008) the basic reflection (008) ^- showed azimuth angle dependence of the integrated intensity ratio of the magnetic satellites reflected in Figure 6. The temperature of the sample was kept at 120K, and the measurement was performed with the scattering plane tilt angle fixed at -70 °. The azimuth angle dependence becomes a constant value only when the direction of the helical axis and the direction of the scattering vector coincide with each other in the helical magnetic structure. Therefore, dysprosium has a helical magnetic structure and the helical axis is c-axis. It is immediately concluded that they are parallel. In that case, sin α = 0.

(008) the basic reflection (008) ^- the scattering plane inclination angle dependence of the integrated intensity ratio of the magnetic satellite reflection

This is shown in FIG.

Number 4

Of the equation (008) as a basic reflection (008) ^- expression for the integrated intensity ratio of the magnetic satellite reflections,

となる。ここで、格子定数ｃ＝５．６５５８５Åと波長λ＝０．６２１１６３Åを使用した。Ｂの必要条件「非負数」を満たすためにはα＝πでなくてはならない。図７中の実線は上式による回帰分析の結果を示したもので、Ａ＝０．００２１４（１０）とＢ＝０．０００４７（１４）とが得られた。α≠０であることから、測定した衛星反射の起源が磁気散乱であることが直ちに結論される。

It becomes. Here, the lattice constant c = 5.66555Å and the wavelength λ = 0.621163Å were used. In order to satisfy the necessary condition “non-negative number” of B, α = π must be satisfied. The solid line in FIG. 7 shows the result of regression analysis by the above equation, and A = 0.00214 (10) and B = 0.00047 (14) were obtained. Since α ≠ 0, it is immediately concluded that the origin of the measured satellite reflection is magnetic scattering.

角を別の値に固定した測定を行えば束縛条件が増えるので、構造因子テンソルの要素を精度良く決定することが可能である。From the measurement with the azimuth angle fixed at 180 ° shown in FIG.

If the measurement is performed with the angle fixed at a different value, the constraint condition increases, so the elements of the structure factor tensor can be determined with high accuracy.

  The synchrotron radiation facility for carrying out the present invention includes a storage ring in which accelerated electrons circulate, a light source for generating synchrotron radiation (a deflection electromagnet, an undulator, and a wiggler), and double crystal spectroscopy for monochromating the synchrotron radiation obtained from the light source An experimental apparatus using monochromatic light obtained from a spectroscope and a spectroscope is installed, and a schematic diagram of the whole is shown in FIG.

  FIG. 3 shows the overall structure of the apparatus (multi-axis diffractometer), FIG. 2 is a schematic view of how to use the apparatus (multi-axis diffractometer), and the horizontal axis in FIG. The vertical axis represents the integrated reflection intensity measured by a detector mounted on the diffractometer. A, B, α are the slopes of the scattering surface of the integrated reflection intensity

Angular dependence

Number 4

It is obtained by analyzing with.

  It is a figure which shows I ((theta)-) about the incident polarization dependence of a scattered intensity.

  It is a figure which shows the concept of a variable scattering surface method.

  It is a figure which shows the definition of the origin and rotation direction of each axis | shaft of a diffractometer.

  It is a figure which shows the diffraction intensity curve of (008) basic reflection.

(008) ^- it is a diagram showing a diffraction intensity curve of the magnetic satellite reflections.

  It is a figure which shows the azimuth angle dependence of integral intensity ratio.

  It is a figure which shows the scattering surface inclination-angle dependence of an integral intensity ratio.

  It is a figure which shows the outline of a synchrotron radiation facility.

Claims (3)

Instead of examining the scattering amplitude of each scattering channel (σ-polarized light, σ-polarized light, σ-polarized light, π-polarized light, π-polarized light, σ-polarized light, and π-polarized light, then π-polarized light) using an ellipsometric crystal, the polarization direction is controlled. the X-rays of linearly polarized light incident on the sample, using a diffractometer scattered X-ray strength of contribution is the square of the scattering amplitude synthesized from each channel generated from the sample while changing the incident polarized light And determining the structure factor tensor of the sample by analyzing the dependence of the scattered X-ray intensity on the incident polarization.   Method according to claim 1, characterized in that it allows the use of a one-dimensional or two-dimensional detector for the determination of the structure factor tensor.   The method according to claim 1, wherein a scattering experiment on a scattering surface inclined at an arbitrary angle is enabled by using a multi-axis diffractometer, and a polarization direction is controlled.

Images