Measurement technique of magnetic domain wall width based on transmission Lorentz electron microscopy

Abstract

This invention discloses a measurement technique for the width of magnetic domain walls based on a transmission Lorentz electron microscope, comprising the following steps: (1) observing the sample in a transmission electron microscope and obtaining a series of defocus images corresponding to the magnetic domain walls; (2) replacing the sample with a standard sample, obtaining a series of defocus images, and calculating the correction coefficients for magnifications corresponding to different defocus amounts under the current Lorentz imaging mode; (3) selecting a portion of the magnetic domain walls perpendicular to a certain area in a series of defocus images, performing Gaussian linear fitting on the intensity distribution of this area and correcting it to obtain the transverse width of the magnetic domain walls, and then performing linear fitting based on the relationship between the transverse width of the magnetic domain walls and the defocus amount to extrapolate the intrinsic width of the magnetic domain walls; (4) constructing the magnetization distribution of the magnetic domain walls based on the intrinsic width of the magnetic domain walls, simulating a series of Fresnel defocus images of the magnetic domain walls, calculating the correspondence between the width of the magnetic domain walls and the defocus amount, and extrapolating to obtain the width of the simulated magnetic domain walls under positive focus conditions. Using the method of this invention, quantitative measurement of the width of magnetic domain walls in magnetic materials can be achieved.

Description

Technical Field

[0001] This invention relates to the field of transmission electron microscopy, and in particular to a technique for measuring the width of magnetic domain walls based on transmission Lorentz electron microscopy. Background Technology

[0002] Traditional magneto-optical Kerr microscopy (MOKE) utilizes the magneto-optical effect to characterize the magnetic domain structure on the surface of magnetic materials. Its working principle involves a beam of plane-polarized light illuminating the surface of a magnetic sample. After reflection, the polarized light is deflected within a certain angular range. The magnitude 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 exhibit reflected light with different rotation angles, corresponding to domain structure regions with alternating bright and dark contrasts. Therefore, MOKE microscopy can obtain in-plane magnetization direction information of a large range (from several micrometers to millimeters) of magnetic domain structure in magnetic samples. However, due to the limited resolution of its probe light source, the limiting resolution of commercially available MOKE microscopes is approximately 200 nm. For the transition layer between adjacent magnetic domains, i.e., the domain wall, its width is approximately equal to several hundred atomic spacings (about tens of nanometers). Therefore, it is difficult to obtain information about the microstructure of magnetic materials using the magneto-optical effect method.

[0003] With the development of highly coherent and high-brightness electron sources, Lorentz electron microscopy (often referring to the Lorentz imaging mode of transmission electron microscopy) using an electron beam as a probe has achieved a spatial resolution of several nanometers, thus enabling high-resolution imaging observation of the microstructure of magnetic domain walls. The working principle of Lorentz electron microscopy utilizes the magnetic fields generated by the magnetic moments in different directions within a magnetic sample. This causes the incident electron beam to be deflected in different directions by Lorentz forces, ultimately resulting in contrast at the imaging position, corresponding to the location of the magnetic domain walls. The Lorentz force and deflection angle experienced by 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 flux density, sample thickness, and Planck's constant, respectively. The magnetic deflection angle β is typically very small (approximately several μrad), so a large defocusing amount (approximately hundreds of μm to mm) is required to obtain the contrast associated with the magnetic domain structure. In practice, by adjusting the defocusing amount of a transmission electron microscope, Fresnel defocus images of magnetic domain walls on different image planes can be obtained. Specifically, the lateral width of the domain walls is obtained by changing the defocusing amount (commonly represented by the full width at half maximum (FWHM) of the intensity distribution curve perpendicular to the domain wall direction). Based on this, the intrinsic width of the domain walls can be inferred from the relationship between the defocusing amount and the lateral width of the domain walls, and the magnetic parameters of the magnetic material can be estimated. This is of great scientific significance for in-depth analysis of the fundamental magnetic parameters of magnetic materials and understanding the relationship between magnetic structure and magnetic properties.

[0004] The information disclosed in this background section is intended only to enhance the understanding of the overall background of the invention and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide a measurement technique for magnetic domain wall width based on transmission Lorentz electron microscopy, thereby overcoming the problems of large measurement error and low resolution accuracy in traditional magnetic domain wall width measurement techniques.

[0006] To achieve the above objectives, this invention provides a technique for measuring the width of magnetic domain walls based on transmission Lorentz electron microscopy, comprising the following steps:

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

[0008] (2) Replace the sample with a standard sample, obtain a series of defocus images, and calculate the correction coefficients for magnification corresponding to different defocus amounts in the current Lorentz imaging mode;

[0009] (3) Select a portion of the region perpendicular to the domain wall in a series of defocus images, perform Gaussian function linear fitting on the intensity distribution of the region and correct it to obtain the transverse width of the domain wall, and then perform linear fitting based on the relationship between the transverse width of the domain wall and the defocus amount to extrapolate the intrinsic width of the domain wall.

[0010] (4) Based on the intrinsic width of the domain wall, construct the magnetization distribution of the domain wall, simulate the Fresnel defocus diagram of a series of domain walls, calculate the correspondence between the domain wall width and the defocus amount, and extrapolate to obtain the width of the simulated domain wall under positive focus conditions.

[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, where N is the number of series defocus images and N≥10.

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

[0013] 1) Place the sample on the sample stage of the transmission electron microscope and take a positive focus image of the magnetic domain wall region of the sample of interest to obtain the first defocus image with a defocus amount of 0 (N=1).

[0014] 2) Change the defocus amount of the sample, with an increment of 100μm for each defocus image, and take a series of defocus images of the dark contrast magnetic domain wall at the same location (N≥10 images) under the condition that other conditions remain unchanged.

[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 in step (1), and collect and record a series of defocus images;

[0017] 2) Measure the widths L and L of the grid after it is in focus and out of focus, 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) Plot the intensity distribution curve of the selected area using a computer program, perform linear fitting on the intensity distribution curve using a Gaussian function, and calculate the full width at half maximum (FWHM) of the curve. H ;

[0020] 2) Fit the full width at half maximum (WHM) of the intensity distribution curves of the series of defocused images. H And using the correction coefficient α corresponding to different defocus amounts in step (2) i Correcting the actual lateral width W of the magnetic domain walls i =W H / α i ;

[0021] 3) Take the defocus amount of the series of defocus maps as the horizontal axis, and the corrected lateral width W of the magnetic domain wall. i Use it as the ordinate for plotting;

[0022] 4) Perform linear fitting on the graph to obtain the value corresponding to the intersection of the fitted 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 under the simulated magnetic domain wall positive focal condition in step (4) is as follows:

[0024] 1) Based on the domain structure recorded in step (1) and the intrinsic width of the domain wall measured in step (3), construct the magnetization distribution of the domain wall;

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

[0026] 3) Using the method mentioned in step (3), measure the transverse width of a series of magnetic domain walls, calculate the relationship between the width of the magnetic domain wall and the defocusing 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) This invention uses high-resolution Lorentz electron microscopy to obtain images of magnetic domain walls. Compared with the traditional magneto-optical method, it improves the resolution of magnetic domain wall imaging and reduces the error in quantitative measurement of magnetic domain wall width.

[0029] (2) In this invention, correction coefficients corresponding to different defocus amounts are introduced in the Lorentz imaging mode 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 this invention, a Gaussian function is used to linearly fit the transverse intensity distribution curve of the magnetic domain wall and automatically calculate the half-width at half-maximum value of the Gaussian function curve, thereby improving the accuracy of the intrinsic width measurement of the magnetic domain wall.

[0031] (4) The series of Fresnel defocus images of the simulated domain wall in this invention can be used to calculate the correspondence between the 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 Lorentz electron microscope measurement of domain wall width can be corrected. Attached Figure Description

[0032] Figure 1 This is an operation flowchart of the magnetic domain wall width measurement technique based on transmission Lorentz electron microscopy according to the present invention;

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

[0034] Figure 3 This is a diagram of correction coefficients for magnification at different defocus levels; Figure 3 -a is the Au standard sample image with positive focus. Figure 3 -b is an Au standard sample image with a defocusing amount of 1mm;

[0035] Figure 4 This is a flowchart for measuring the width of magnetic domain walls; Figure 4 -a is the defocusing diagram of the magnetic domain walls of the multi-element alloy sample at a defocusing distance of 500 μm. Figure 4 -b is a defocusing diagram of the magnetic domain walls of a simulated multi-element alloy sample at a defocusing distance of 500 μm. Figure 4 -c represents a partial area of ​​the defocused image of the multi-element alloy sample series. Figure 4 -d represents a portion of the defocused image of a series of simulated multi-element alloy samples. Figure 4 -e represents the intensity distribution map for a partial area. Figure 4 -f is a graph showing the relationship between the transverse width and defocusing amount of the magnetic domain walls in experimental and simulated multi-element alloy samples. Detailed Implementation

[0036] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings, but it should be understood that the scope of protection of the present invention is not limited to the specific embodiments.

[0037] Unless otherwise expressly stated, throughout the specification and claims, the term "comprising" or its variations such as "including" or "comprises" shall be understood to include the stated elements or components without excluding other elements or other components.

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

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

[0040] Step 1 includes the following steps:

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

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

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

[0044] Step 2 includes the following steps:

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

[0046] Step 2-2: Measure the widths L and L of the grid after it is in focus 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 region perpendicular to the domain wall in a series of defocus images, perform Gaussian function linear fitting on the intensity distribution of the region and correct it to obtain the lateral width of the domain wall, and then perform linear fitting based on the relationship between the lateral width of the domain wall and the defocus amount to extrapolate the intrinsic width of the domain wall.

[0048] Step 3 includes the following steps:

[0049] Step 3-1: Plot the intensity distribution curve of the selected area using a computer program, perform linear fitting on the intensity distribution curve using a Gaussian function, and calculate the full width at half maximum (FWHM) of the curve. H .

[0050] Step 3-2: Fit the full width at half maximum (WHM) of the intensity distribution curves of the series of defocus images. H And using the correction coefficient α corresponding to different defocus amounts in Step 2 i Correcting the actual lateral width W of the magnetic domain walls i =W H / α i .

[0051] Step 3-3: Take the defocus amount of the series of defocus maps as the horizontal axis, and the corrected lateral width W of the magnetic domain wall. i Use it as the ordinate for plotting;

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

[0053] Step 4: Based on the intrinsic width of the domain walls, construct the magnetization distribution of the domain walls, simulate the Fresnel defocus diagrams of a series of domain walls, calculate the correspondence between the domain wall width and the defocus amount, and extrapolate to obtain the width of the simulated domain wall under positive focus conditions.

[0054] Step 4 includes the following steps:

[0055] Step 4-1: Based on the domain structure recorded in Step 1 and the intrinsic width of the domain walls measured in Step 3, construct the magnetization distribution of the domain walls;

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

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

[0058] Example 1

[0059] The specific steps for measuring the magnetic domain wall width of a multi-element alloy MnFeCoNiAl sample using this invention are as follows:

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

[0061] As one possible implementation, Step 1 includes the following steps:

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

[0063] Steps 1-2: Change the defocus amount in the Lorentz mode, with an increment of 100μm for each defocused image. Under otherwise identical conditions, take a series of defocused images (N≥10) of the same location showing the dark contrast of the magnetic domain walls. Figure 4 (a) is a defocused image of the multi-element alloy sample taken in a Lorentz electron microscope with a defocusing amount of 500 μm. Figure 4 (b) is a defocused image of a magnetic domain wall with a defocusing amount of 500 μm, simulated by a computer program.

[0064] Step 2: According to Figure 3 Replace the sample with an Au standard sample and calculate the correction coefficients for magnification corresponding to different defocus amounts in the current Lorentz mode.

[0065] Step 2 includes the following steps:

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

[0067] Step 2-2: Measure the widths L and L of the grid after it is in focus and out of focus, respectively. D The change in grid width δ = L D -L, calculate the correction factor α i =1 + δ / L. For example... Figure 3 (a) At zero defocus, the width of a single grid is L = 539.3 nm, and the width of a 1 mm defocus grid 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 portion of the same location perpendicular to the magnetic domain wall orientation in the series of defocused images (N>2); according to Figure 4 (e) The transverse width of the domain wall is obtained by linearly fitting a Gaussian function to the intensity distribution in this region and correcting it. Figure 4 (f) By linearly fitting the relationship between the transverse width and defocusing amount of the domain walls of the series of multi-element alloy samples, the intrinsic width of the domain walls under positive focusing conditions is extrapolated.

[0069] Step 3 includes the following steps:

[0070] Step 3-1: Plot the intensity distribution curve of the selected area using a computer program, perform linear fitting on the intensity distribution curve using a Gaussian function, and calculate the full width at half maximum (FWHM) of the curve. H .

[0071] Step 3-2: Fit the full width at half maximum (WHM) of the intensity distribution curves of the series of defocus images. H And using the correction coefficient α corresponding to different defocus amounts in Step 2 i Correcting the actual lateral width W of the magnetic domain walls i =W H / α i .

[0072] Step 3-3: Take the defocus amount of the series of defocus maps as the horizontal axis, and the corrected lateral width W of the magnetic domain wall. i Use the vertical axis as the plotting reference.

[0073] Step 3-4: Perform linear fitting on the graph to obtain the values ​​corresponding to the intersection points of the fitted curve and the vertical axis, which are the intrinsic widths of the magnetic domain walls. For example... Figure 4 (f) The intrinsic width of the magnetic domain walls of the multi-element alloy sample is 64 nm.

[0074] Step 4: According to Figure 2 By combining the intrinsic width of the domain walls, the magnetization distribution of the domain walls is constructed, the Fresnel defocus diagrams of a series of domain walls are simulated, the correspondence between the domain wall width and the defocus amount is calculated, and the width of the simulated domain wall under positive focus conditions is extrapolated.

[0075] Step 4 includes the following steps:

[0076] Step 4-1: Based on the domain structure parameters recorded in Step 1 and the intrinsic width of the domain walls measured in Step 3, construct the magnetization distribution of the domain walls.

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

[0078] Step 4-3: Using the steps mentioned in Step 3, measure the lateral width of a series of domain walls, calculate the relationship between the domain wall width and the defocusing amount, and extrapolate to obtain the width of the simulated domain wall under positive focusing conditions. For example... Figure 4 (f) The simulated domain wall width of the multi-element alloy sample is 55 nm.

[0079] This invention proposes a technique for measuring the width of magnetic domain walls using a transmission Lorentz electron microscope. A series of domain wall images with varying defocus amounts are observed and captured using a transmission electron microscope, and the magnification of Lorentz magnetic contrast images with large defocus amounts is corrected. Using this method to measure the width of magnetic domain walls effectively improves the accuracy of the measurement and reduces measurement errors caused by excessive defocus. When measuring the width of magnetic domain walls, firstly, dark-contrast domain wall regions with different defocus amounts at the same location are selected. The intensity distribution along the direction perpendicular to the domain wall is then fitted with a Gaussian linear curve to obtain the lateral width of the domain wall. Then, based on the correspondence between defocus amount and lateral width of the domain wall, the intrinsic width of the magnetic domain walls inside the magnetic material is obtained through linear extrapolation. Finally, based on experimentally measured domain wall structural parameters, a series of Fresnel defocus images of the domain walls are simulated. By comparing the simulation and measurement results, the systematic error in measuring the width of magnetic domain walls using the Lorentz electron microscope is corrected.

[0080] The foregoing description of specific exemplary embodiments of the invention is for illustrative and explanatory purposes. These descriptions are not intended to limit the invention to the precise forms disclosed, and it will be apparent that many changes and variations can be made in accordance with the foregoing teachings. The exemplary embodiments were chosen and described in order to explain the specific principles of the invention and its practical application, thereby enabling those skilled in the art to implement and utilize various different exemplary embodiments of the invention, as well as various different choices and variations. The scope of the invention is intended to be defined by the claims and their equivalents.

Claims

1. A method for measuring the width of magnetic domain walls based on transmission Lorentz electron microscopy, characterized in that, Includes the following steps: (1) Observe the sample in a transmission Lorentz electron microscope, change the defocus amount in Lorentz mode, and obtain a series of defocus images corresponding to the magnetic domain walls. (2) Replace the sample with a standard sample, obtain a series of defocus images, and calculate the correction coefficients for different defocus amounts corresponding to the magnification in the current Lorentz imaging mode; the method for calculating the correction coefficients is as follows: 1) Replace the sample with a periodic grid Au particle standard, change the defocus amount to the same as in step (1), and collect and record a series of defocus images; 2) Measure the widths L and L of the grid after it is in focus and out of focus, respectively. D The change in grid width δ = L D -L, calculate the correction factor α i =1 + δ / L; (3) Select a portion of the region perpendicular to the domain wall in a series of defocus images, perform Gaussian function linear fitting on the intensity distribution of this portion of the region and correct it to obtain the lateral width of the domain wall, and then perform linear fitting based on the relationship between the lateral width of the domain wall and the defocus amount to extrapolate the intrinsic width of the domain wall; the method for obtaining the intrinsic width of the domain wall is as follows: 1) Plot the intensity distribution curve of the selected area using a computer program, perform linear fitting on the intensity distribution curve using a Gaussian function, and calculate the full width at half maximum (FWHM) of the curve. H ; 2) Fit the full width at half maximum (FWHM) value W of the intensity distribution curves of the series of defocus images. H And using the correction coefficient α corresponding to different defocus amounts in step (2) i Correcting the actual lateral width W of the magnetic domain walls i =W H / α i ; 3) Take the defocus amount of the series of defocus maps as the horizontal axis, and the corrected lateral width W of the magnetic domain wall. i Use it as the ordinate for plotting; 4) Perform linear fitting on the graph to obtain the value corresponding to the intersection of the fitted curve and the vertical axis. This value is the intrinsic width of the magnetic domain wall. (4) Based on the intrinsic width of the domain walls, construct the magnetization distribution of the domain walls, simulate a series of Fresnel defocus maps of the domain walls, calculate the correspondence between the domain wall width and the defocus amount, and extrapolate to obtain the width of the simulated domain walls under positive focus conditions; the method for obtaining the width of the simulated domain walls under positive focus conditions is as follows: 1) Based on the domain structure recorded in step (1) and the intrinsic width of the domain wall measured in step (3), construct the magnetization distribution of the domain wall; 2) Using a computer program, calculate the magnetic phase distribution in the domain wall region and simulate a series of Fresnel defocus images of the domain walls; 3) Using the method mentioned in step (3), measure the transverse width of a series of magnetic domain walls, calculate the relationship between the width of the magnetic domain wall and the defocusing amount, and extrapolate to obtain the width of the simulated magnetic domain wall under positive focus conditions.

2. The method for measuring the domain wall width based on transmission Lorentz electron microscopy according to claim 1, characterized in that, The method for obtaining the defocus map in step (1) is to obtain a series of defocus maps by changing the defocus amount of the sample, where N is the number of series of defocus maps and N≥10.

3. The method for measuring the domain wall width based on transmission Lorentz electron microscopy according to claim 1, characterized in that, The method for obtaining the out-of-focus image in step (1) is as follows: 1) Place the sample on the stage of a transmission electron microscope and take a positive focus image of the magnetic domain wall region of interest to obtain the first defocus image with a defocus amount of 0, N=1; 2) Change the defocus amount of the sample, with an increment of 100μm for each defocus image, 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.

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