Magnetic domain wall width measurement technology based on transmission Lorentz electron microscope

Abstract

The invention discloses a technology for measuring the width of a magnetic domain wall based on a transmission Lorentz electron microscope, which comprises the following steps: (1) observing a sample in a transmission electron microscope to obtain a series of defocus images corresponding to the magnetic domain wall; (2) replacing the sample with a standard sample, obtaining a series of defocusing images, and calculating correction coefficients of magnification times corresponding to different defocusing amounts in the current Lorentz imaging mode; (3) selecting a partial region perpendicular to the magnetic domain wall in a series of defocus images, performing Gaussian function linear fitting and correction on the intensity distribution of the region to obtain the transverse width of the magnetic domain wall, performing linear fitting according to the relationship between the transverse width of the magnetic domain wall and the defocus amount, and extrapolating to obtain the intrinsic width of the magnetic domain wall; and (4) according to the intrinsic width of the magnetic domain wall, constructing magnetization distribution of the magnetic domain wall, simulating a Fresnel defocus graph of the series of magnetic domain walls, calculating a corresponding relation between the width of the magnetic domain wall and a defocusing amount, and extrapolating to obtain the width of the simulated magnetic domain wall under a positive focus condition. By using the method of the invention, quantitative measurement of the magnetic domain wall width of the magnetic material can be realized.

Description

Technical Field

[0001] The invention relates to the field of transmission electron microscopy technology, and in particular to a measurement technology for magnetic domain wall width based on a transmission Lorentz electron microscope. Background Art

[0002] The magneto-optical Kerr microscope (MOKE) that traditionally uses the magneto-optical effect is used to characterize the magnetic domain structure on the surface of magnetic materials. Its working principle is that a beam of plane polarized light is irradiated on the surface of a magnetic sample. After reflection, the polarized light will deflect within a certain angle range. The size and direction of the deflection angle are related to the magnetization direction and intensity of the sample surface. Since different magnetic domains have different spontaneous magnetization directions, they will present reflected light with different rotation angles, corresponding to the magnetic domain structure area with alternating light and dark contrast. Therefore, the MOKE microscope can be used to obtain the in-plane magnetization direction information of the magnetic domain structure of a large range (several micrometers to millimeters) of the magnetic sample. However, due to the limited resolution of its detection light source, the limit resolution of the commercial MOKE microscope is about 200nm. For the transition layer between adjacent magnetic domains, that is, the magnetic domain wall, its width is approximately equal to several hundred atomic spacings (about tens of nanometers). Therefore, it is difficult to obtain information on the microstructure of magnetic materials through the magneto-optical effect method.

[0003] With the development of high-coherence and high-brightness electron sources, the spatial resolution of Lorentz electron microscopy (often referring to the Lorentz imaging mode of transmission electron microscopy) using electron beams as probes is as high as several nanometers, so high-resolution imaging observation of the microstructure of magnetic domain walls can be achieved. The working principle of Lorentz electron microscopy is to use the magnetic field generated by the magnetic moments in different directions in the magnetic sample to make the incident electron beam deflect in the corresponding direction under the action of Lorentz forces in different directions, and finally present a bright or dark contrast at the imaging position, corresponding to the position of the magnetic domain wall. The Lorentz force and deflection angle of the electron are expressed as F = e (ν × B) and β = e / hλtB, respectively, where ν and λ are the electron velocity and wavelength; B, t, and h are the magnetic induction intensity, sample thickness, and Planck's constant, respectively. The magnetic deflection angle β is usually very small (about a few μrad), so a large defocus amount (about hundreds of μm to mm) is required to obtain the contrast related to the magnetic domain structure. In actual operation, by adjusting the defocus of the transmission electron microscope, the Fresnel defocus images of the domain wall in different image planes can be obtained. Specifically, the lateral width of the domain wall is obtained by changing the defocus (usually expressed by the half-width of the intensity distribution curve perpendicular to the direction of the domain wall). Based on this, the intrinsic width of the domain wall is inferred through the relationship between the defocus of the domain wall and the lateral width of the domain wall, and then the magnetic parameters of the magnetic material are estimated, which is of great scientific significance for in-depth analysis of the basic magnetic parameters of magnetic materials and mastering the relationship between magnetic structure and magnetic properties.

[0004] The information disclosed in this background technology section is only intended to enhance the understanding of the overall background of the invention and should not be regarded as an acknowledgment or any form of suggestion that the information constitutes the prior art already known to a person skilled in the art. Summary of the invention

[0005] The object of the present invention is to provide a measurement technology of magnetic domain wall width based on a transmission Lorentz electron microscope, thereby overcoming the problems of large measurement error and low resolution accuracy existing in the traditional magnetic domain wall width measurement technology.

[0006] To achieve the above object, the present invention provides a measurement technology of magnetic domain wall width based on a transmission Lorentz electron microscope, comprising the following steps:

[0007] (1) observing the sample in a transmission electron microscope to obtain a series of defocus images corresponding to the magnetic domain wall;

[0008] (2) replacing the sample with a standard sample, obtaining a series of defocus images, and calculating the correction coefficients corresponding to the magnifications of different defocus amounts under the current Lorentz imaging mode;

[0009] (3) Selecting a part of the area perpendicular to the magnetic domain wall in a series of defocus images, performing a Gaussian function linear fit on the intensity distribution of the area and correcting it to obtain the lateral width of the magnetic domain wall, and then performing a linear fit based on the relationship between the lateral width of the magnetic domain wall and the defocus amount, and extrapolating to obtain the intrinsic width of the magnetic domain wall;

[0010] (4) Based on the intrinsic width of the domain wall, the magnetization distribution of the domain wall is constructed, the Fresnel defocus diagrams of a series of domain walls are simulated, the corresponding relationship between the width of the domain wall and the defocus amount is calculated, and the width of the simulated domain wall under positive focus conditions is obtained by extrapolation.

[0011] Preferably, in the above technical solution, the method for obtaining the defocus image in step (1) is to obtain a series of defocus images by changing the defocus amount of the sample, wherein N is the number of the series of defocus images, and N≥10.

[0012] Preferably, in the above technical solution, the method for obtaining the defocus map in step (1) is as follows:

[0013] 1) placing the sample on the sample stage of a transmission electron microscope, taking a positive focus image of the magnetic domain wall region of the sample of interest, and obtaining the first defocus image with a defocus amount of 0 (N=1);

[0014] 2) The defocus amount of the sample is changed, and the increment of each defocus image is 100 μm. When other conditions remain unchanged, a series of defocus images of the dark contrast magnetic domain wall at the same position are taken (N≥10 images).

[0015] Preferably, in the above technical solution, the method for calculating the correction coefficient in step (2) is as follows:

[0016] 1) Replace the sample with a periodic grid Au particle standard, change the defocus amount to the same as step (1), and collect and record a series of defocus images;

[0017] 2) Measure the width L and L of the grid when the grid is focused and defocused respectively D , the change in grid width δ = L D -L, calculate the correction factor α i =1+δ / L.

[0018] Preferably, in the above technical solution, the method for obtaining the intrinsic width of the magnetic domain wall in step (3) is as follows:

[0019] 1) Draw the intensity distribution curve of the selected area through a computer program, use the Gaussian function to perform linear fitting on the intensity distribution curve, and calculate the half-height width W of the curve H ;

[0020] 2) Fit the half-height width W of the intensity distribution curve of the series of defocus images H , and use the correction coefficient α corresponding to the different defocus amounts in step (2) i , correct the actual lateral width W of the domain wall i =W H / α i ;

[0021] 3) Take the defocus amount of the series of defocus images as the horizontal coordinate, and the corrected lateral width W of the magnetic domain wall i As the ordinate, plot;

[0022] 4) Performing a linear fit on the graph, obtaining a value corresponding to the intersection of the fitting curve and the vertical axis, which is the intrinsic width of the magnetic domain wall.

[0023] Preferably, in the above technical solution, the method for obtaining the width of the simulated magnetic domain wall under positive focus conditions in step (4) is as follows:

[0024] 1) constructing the magnetization distribution of the magnetic domain wall according to the magnetic domain structure recorded in step (1) and the intrinsic width of the magnetic domain wall measured in step (3);

[0025] 2) Using a computer program, calculate the magnetic phase distribution in the magnetic domain wall region and simulate the Fresnel defocused images of a series of magnetic domain walls;

[0026] 3) Using the method mentioned in step (3), measure the lateral width of a series of magnetic domain walls, calculate the corresponding relationship between the width of the magnetic domain wall and the defocus amount, and extrapolate to obtain the width of the simulated magnetic domain wall under positive focus conditions.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] (1) The present invention uses high-resolution Lorentz electron microscopy to obtain images of magnetic domain walls. Compared with traditional magneto-optical methods, the resolution of magnetic domain wall imaging is improved and the error in quantitative measurement of magnetic domain wall width is reduced.

[0029] (2) In the present invention, correction coefficients corresponding to different defocus amounts in the Lorentz imaging mode are introduced to correct the magnification of the Lorentz mode in defocus imaging, thereby reducing the systematic error of the magnetic domain wall width measurement.

[0030] (3) In the present invention, a Gaussian function is used to perform linear fitting on the lateral intensity distribution curve of the magnetic domain wall, and the half-width value of the Gaussian function curve is automatically calculated, thereby improving the accuracy of the measurement of the intrinsic width of the magnetic domain wall.

[0031] (4) The present invention simulates a series of Fresnel defocused images of the magnetic domain wall and calculates the corresponding relationship between the magnetic domain wall width and the defocus amount, which can provide a benchmark for the experimental measurement data. By comparing the simulation and measurement results, the systematic error of the Lorentz electron microscope in measuring the magnetic domain wall width can be corrected. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is an operation flow chart of a measurement technique of magnetic domain wall width based on a transmission Lorentz electron microscope according to the present invention;

[0033] Figure 2 is a schematic diagram of a Lorentz electron microscope according to the measurement technology of magnetic domain wall width based on a transmission Lorentz electron microscope of the present invention;

[0034] Figure 3 It is a graph of correction factors for magnification at different defocus amounts; Figure 3 -a is the Au standard sample image at the correct focus. Figure 3 -b is the Au standard sample with a defocus of 1 mm;

[0035] Figure 4 is a flow chart of magnetic domain wall width measurement; Figure 4 -a is the defocus image of the domain wall of the multi-element alloy sample at a defocus amount equal to 500μm, Figure 4 -b is the defocus image of the simulated multi-element alloy sample magnetic domain wall at a defocus equal to 500μm, Figure 4 -c is a partial area diagram of the defocus diagram of the selected multi-element alloy sample series, Figure 4 -d is a partial area diagram of the defocus diagram of the selected simulated multi-element alloy sample series, Figure 4 -e is the intensity distribution diagram of some areas, Figure 4 -f is the corresponding relationship between the lateral width and defocus of the magnetic domain wall of the multi-element alloy sample experiment and simulation. DETAILED DESCRIPTION

[0036] The specific implementation modes of the present invention are described in detail below in conjunction with the accompanying drawings, but it should be understood that the protection scope of the present invention is not limited by the specific implementation modes.

[0037] Unless explicitly stated otherwise, throughout the specification and claims, the term “comprise” or variations such as “include” or “comprising”, etc., will be understood to include the stated elements or components but not to exclude other elements or components.

[0038] like Figures 1 to 4 As shown, according to the measurement technology of magnetic domain wall width based on transmission Lorentz electron microscope according to the specific embodiment of the present invention, the specific detailed scheme is as follows:

[0039] Step 1: Observe the sample in a transmission electron microscope, change the defocus amount in the Lorentz mode, and obtain a series of defocus images corresponding to the magnetic domain wall, N ≥ 10 (N is the number of series of defocus images).

[0040] Wherein, the Step 1 includes the following steps:

[0041] Step 1-1: Place the sample on the sample stage of a transmission electron microscope, take a positive focus image of the sample magnetic domain wall region of interest, and obtain the first defocus image with a defocus amount of 0 (N=1).

[0042] Step 1-2: Change the defocus amount of the sample, the increment of each defocus image is 100 μm, and take a series of defocus images of the dark contrast magnetic domain wall at the same position under the condition that other conditions remain unchanged (N≥10 images).

[0043] Step 2: Replace the sample with a standard sample, obtain a series of defocus images, and calculate the correction coefficients of the magnifications corresponding to different defocus amounts in the current Lorentz imaging mode.

[0044] Wherein, the Step 2 comprises the following steps:

[0045] Step 2-1: Replace the sample with a periodic grid Au particle standard, change the defocus amount to the same as Step 1, and collect and record a series of defocus images.

[0046] Step 2-2: Measure the width L and L of the grid when it is focused and out of focus respectively. D , the change in grid width δ = L D -L, calculate the correction factor α i =1+δ / L.

[0047] Step 3: Select a part of the area perpendicular to the magnetic domain wall in a series of defocus images, perform a Gaussian function linear fit on the intensity distribution of the area and correct it to obtain the lateral width of the magnetic domain wall. Then perform a linear fit based on the relationship between the lateral width of the magnetic domain wall and the defocus amount, and extrapolate to obtain the intrinsic width of the magnetic domain wall.

[0048] Wherein, the Step 3 comprises the following steps:

[0049] Step 3-1: Draw the intensity distribution curve of the selected area through a computer program, use the Gaussian function to linearly fit the intensity distribution curve, and calculate the half-height width W of the curve H .

[0050] Step 3-2: Fit the half-height width W of the intensity distribution curve of the series of defocus images H , and use the correction coefficient α corresponding to the different defocus amounts in Step 2 i , correct the actual lateral width W of the domain wall i =W H / α i .

[0051] Step 3-3: Take the defocus amount of the series of defocus images as the horizontal coordinate, and the corrected lateral width W of the magnetic domain wall i As the ordinate, plot;

[0052] Step 3-4: Perform a linear fit on the graph to obtain the value corresponding to the intersection of the fitting curve and the vertical axis, which is the intrinsic width of the magnetic domain wall.

[0053] Step 4: According to the intrinsic width of the magnetic domain wall, the magnetization distribution of the magnetic domain wall is constructed, the Fresnel defocus diagram of a series of magnetic domain walls is simulated, the corresponding relationship between the width of the magnetic domain wall and the defocus amount is calculated, and the width of the simulated magnetic domain wall under positive focus conditions is extrapolated.

[0054] Wherein, the Step 4 comprises the following steps:

[0055] Step 4-1: Construct the magnetization distribution of the magnetic domain wall according to the magnetic domain structure recorded in Step 1 and the intrinsic width of the magnetic domain wall measured in Step 3;

[0056] Step 4-2: Use a computer program to calculate the magnetic phase distribution in the magnetic domain wall region and simulate the Fresnel defocused images of a series of magnetic domain walls.

[0057] Step 4-3: Using the method mentioned in Step 3, measure the lateral width of a series of magnetic domain walls, calculate the corresponding relationship between the width of the magnetic domain wall and the defocus amount, and extrapolate to obtain the width of the simulated magnetic domain wall under positive focus conditions.

[0058] Example 1

[0059] The present invention is used to measure the magnetic domain wall width of a multi-component alloy MnFeCoNiAl sample, and the specific steps are as follows:

[0060] Step 1: Observe the thin sample in the Lorentz mode of a transmission electron microscope, change the defocus amount in the Lorentz mode, and obtain a series of defocus images corresponding to the magnetic domain wall, N ≥ 10 (N is the number of series of defocus images). Figure 2 This is a schematic diagram of a Lorentz electron microscope.

[0061] As an implementable method, Step 1 includes the following steps:

[0062] Step 1-1: Place the sample on the sample stage of a transmission electron microscope, take a positive focus image of the magnetic domain wall region of interest, and obtain the first defocus image with a defocus amount of 0 (N=1).

[0063] Step 1-2: Change the defocus amount of the Lorentz mode, and the increment of each defocus image is 100μm. Take a series of defocus images of the dark contrast magnetic domain wall at the same position while keeping other conditions unchanged (N≥10 images). Figure 4 (a) is a defocused image of the multi-element alloy sample taken in a Lorentz electron microscope with a defocus equal to 500 μm. Figure 4 (b) is a defocused image of the magnetic domain wall simulated by a computer program at a defocus amount equal to 500 μm.

[0064] Step 2: According to Figure 3 , replace the sample with the Au standard sample, and calculate the correction coefficient of the magnification corresponding to different defocus amounts in the current Lorentz mode.

[0065] Wherein, the Step 2 comprises the following steps:

[0066] Step 2-1: Replace the sample with a standard sample with Au particles in a periodic grid, change the defocus amount to the same as in Step 1, and collect and record a series of defocus images (N is the number of series defocus images, N ≥ 10).

[0067] Step 2-2: Measure the width L and L of the grid when it is focused and out of focus respectively D , the change in grid width δ = L D -L, calculate the correction factor α i =1+δ / L. Figure 3 (a) The width of a single grid at zero defocus is L = 539.3 nm, and the width of the grid at 1 mm defocus is L D =528.6nm, correction factor α i =1.02.

[0068] Step 3: According to Figure 4(c) Import the series of defocused images of the multi-element alloy sample taken in Step 1 into the data analysis software to automatically select a partial area of ​​the same position of the series of defocused images (N>2) perpendicular to the direction of the magnetic domain wall; Figure 4 (e) The intensity distribution of the region is linearly fitted with a Gaussian function and corrected to obtain the lateral width of the magnetic domain wall. Figure 4 (f), by linearly fitting the corresponding relationship between the lateral width of the magnetic domain wall and the defocus amount of a series of multi-element alloy samples, the intrinsic width of the magnetic domain wall under positive focus conditions is extrapolated.

[0069] Wherein, the Step 3 comprises the following steps:

[0070] Step 3-1: Draw the intensity distribution curve of the selected area through a computer program, use the Gaussian function to linearly fit the intensity distribution curve, and calculate the half-height width W of the curve H .

[0071] Step 3-2: Fit the half-height width W of the intensity distribution curve of the series of defocus images H , and use the correction coefficient α corresponding to the different defocus amounts in Step 2 i , correct the actual lateral width W of the domain wall i =W H / α i .

[0072] Step 3-3: Take the defocus amount of the series of defocus images as the horizontal coordinate, and the corrected lateral width W of the magnetic domain wall i As the ordinate, plot .

[0073] Step 3-4: Perform a linear fit on the graph to obtain the value corresponding to the intersection of the fitting curve and the vertical axis, which is the intrinsic width of the magnetic domain wall. Figure 4 (f), the intrinsic width of the magnetic domain wall of the multi-element alloy sample is 64nm.

[0074] Step 4: According to Figure 2 , combined with the intrinsic width of the magnetic domain wall, the magnetization distribution of the magnetic domain wall is constructed, the Fresnel defocus diagram of a series of magnetic domain walls is simulated, the corresponding relationship between the width of the magnetic domain wall and the defocus amount is calculated, and the width of the simulated magnetic domain wall under positive focus conditions is extrapolated.

[0075] Wherein, the Step 4 comprises the following steps:

[0076] Step 4-1: Construct the magnetization distribution of the magnetic domain wall based on the magnetic domain structure parameters recorded in Step 1 and the intrinsic width of the magnetic domain wall measured in Step 3.

[0077] Step 4-2: Use a computer program to calculate the magnetic phase distribution φ in the domain wall regionM , simulated series of Fresnel defocused images of magnetic domain walls I(φ M ).

[0078] Step 4-3: Use the steps mentioned in Step 3 to measure the lateral width of a series of magnetic domain walls, calculate the corresponding relationship between the width of the magnetic domain wall and the defocus amount, and extrapolate to obtain the width of the simulated magnetic domain wall under the condition of positive focus. Figure 4 (f), The simulated magnetic domain wall width of the multi-element alloy sample is 55nm.

[0079] The present invention proposes a measurement technology of magnetic domain wall width based on transmission Lorentz electron microscope, which observes and shoots a series of magnetic domain wall images with defocusing amounts through transmission electron microscope, and performs magnification correction on Lorentz magnetic contrast images with large defocusing amounts. The width of magnetic domain wall can be measured by this method, which can effectively improve the accuracy of magnetic domain wall width measurement and reduce the measurement error caused by excessive defocusing amount. When measuring the width of magnetic domain wall, firstly, dark contrast magnetic domain wall regions with different defocusing amounts at the same position are selected, and the lateral width of the magnetic domain wall is obtained by performing Gaussian function linear curve fitting along the intensity distribution perpendicular to the direction of the magnetic domain wall. Then, according to the corresponding relationship between the defocusing amount and the lateral width of the magnetic domain wall, the intrinsic width of the magnetic domain wall inside the magnetic material is obtained by linear extrapolation. Finally, based on the magnetic domain wall structural parameters measured experimentally, the Fresnel defocusing images of a series of magnetic domain walls are simulated, and the systematic error of the magnetic domain wall width measured by Lorentz electron microscope is corrected by comparing the simulation and measurement results.

[0080] The foregoing description of specific exemplary embodiments of the present invention is for the purpose of illustration and demonstration. These descriptions are not intended to limit the present invention to the precise form disclosed, and it is clear that many changes and variations can be made based on the above teachings. The purpose of selecting and describing the exemplary embodiments is to explain the specific principles of the present invention and its practical application, so that those skilled in the art can realize and utilize various different exemplary embodiments of the present invention and various different selections and changes. The scope of the present invention is intended to be limited by the claims and their equivalents.

Claims

1. A measurement technique for the width of a magnetic domain wall based on a transmission Lorentz electron microscope, characterized in that: The following steps are involved: (1) observing the sample in a transmission electron microscope to obtain a series of defocus images corresponding to the magnetic domain wall; (2) replacing the sample with a standard sample, obtaining a series of defocus images, and calculating the correction coefficients corresponding to the magnifications of different defocus amounts under the current Lorentz imaging mode; (3) Selecting a part of the area perpendicular to the magnetic domain wall in a series of defocus images, performing a Gaussian function linear fit on the intensity distribution of the area and correcting it to obtain the lateral width of the magnetic domain wall, and then performing a linear fit based on the relationship between the lateral width of the magnetic domain wall and the defocus amount, and extrapolating to obtain the intrinsic width of the magnetic domain wall; (4) Based on the intrinsic width of the domain wall, the magnetization distribution of the domain wall is constructed, the Fresnel defocus diagrams of a series of domain walls are simulated, the corresponding relationship between the width of the domain wall and the defocus amount is calculated, and the width of the simulated domain wall under positive focus conditions is obtained by extrapolation.

2. The measurement technique of magnetic domain wall width based on transmission Lorentz electron microscope according to claim 1 is characterized in that: The method for obtaining the defocus image in step (1) is to obtain a series of defocus images by changing the defocus amount of the sample, wherein N is the number of the series of defocus images, and N≥10.

3. The measurement technique of magnetic domain wall width based on transmission Lorentz electron microscope according to claim 1 is characterized in that: The method of obtaining the defocus image in step (1) is as follows: 1) placing the sample on the sample stage of a transmission electron microscope, taking a positive focus image of the magnetic domain wall region of the sample of interest, and obtaining the first defocus image with a defocus amount of 0 (N=1); 2) The defocus amount of the sample is changed, and the increment of each defocus image is 100 μm. When other conditions remain unchanged, a series of defocus images of the dark contrast magnetic domain wall at the same position are taken (N≥10 images).

4. The measurement technique of magnetic domain wall width based on transmission Lorentz electron microscope according to claim 1 is characterized in that: The method for calculating the correction coefficient in step (2) is as follows: 1) Replace the sample with a periodic grid Au particle standard, change the defocus amount to the same as step (1), and collect and record a series of defocus images; 2) Measure the width L and L of the grid when the grid is focused and defocused respectively D , the change in grid width δ = L D -L, calculate the correction factor α i =1+δ / L.

5. The measurement technique of magnetic domain wall width based on transmission Lorentz electron microscope according to claim 1, characterized in that: The method of obtaining the intrinsic width of the magnetic domain wall in step (3) is as follows: 1) Draw the intensity distribution curve of the selected area through a computer program, use the Gaussian function to perform linear fitting on the intensity distribution curve, and calculate the half-height width W of the curve H ; 2) Fit the half-height width W of the intensity distribution curve of the series of defocus images H , and use the correction coefficient α corresponding to the different defocus amounts in step (2) i , correct the actual lateral width W of the domain wall i =W H / α i ; 3) Take the defocus amount of the series of defocus images as the horizontal coordinate, and the corrected lateral width W of the magnetic domain wall i As the ordinate, plot; 4) Performing a linear fit on the graph, obtaining a value corresponding to the intersection of the fitting curve and the vertical axis, which is the intrinsic width of the magnetic domain wall.

6. The measurement technique of magnetic domain wall width based on transmission Lorentz electron microscope according to claim 1, characterized in that: The method for obtaining the width of the simulated magnetic domain wall under the positive focus condition in step (4) is as follows: 1) constructing the magnetization distribution of the magnetic domain wall according to the magnetic domain structure recorded in step (1) and the intrinsic width of the magnetic domain wall measured in step (3); 2) Using a computer program, calculate the magnetic phase distribution in the magnetic domain wall region and simulate the Fresnel defocused images of a series of magnetic domain walls; 3) Using the method mentioned in step (3), measure the lateral width of a series of magnetic domain walls, calculate the corresponding relationship between the width of the magnetic domain wall and the defocus amount, and extrapolate to obtain the width of the simulated magnetic domain wall under positive focus conditions.

Images