Magnetic domain wall width quantitative measurement method based on transmission electron microscope electron holography

Abstract

The invention discloses a magnetic domain wall width quantitative measurement method based on transmission electron microscope electron holography, and the method comprises the steps: observing a sample in a transmission electron microscope, obtaining an electron hologram containing a magnetic domain wall region, the electron hologram at least comprising an object hologram and a reference hologram; importing the object hologram and the reference hologram into an image processing program, and performing phase reconstruction to obtain a phase diagram of the sample; performing phase gradient calculation on the phase diagram to obtain a phase gradient diagram, selecting a region of interest containing a magnetic domain wall in the phase gradient diagram, extracting a one-dimensional gradient profile, and fitting the one-dimensional gradient profile by adopting a hyperbolic tangent function to obtain characteristic parameters of the magnetic domain wall; and calculating the width of the magnetic domain wall according to the feature parameters obtained by fitting, and outputting a width result of the magnetic domain wall and a fitting curve image. According to the method, the magnetic phase information is directly reconstructed based on the electronic holography, higher spatial resolution and phase sensitivity are achieved, and the measurement error of the magnetic domain wall width is remarkably reduced.

Description

Technical Field

[0001] This invention relates to the field of transmission electron microscopy, and in particular to a method for quantitatively measuring the width of magnetic domain walls based on transmission electron microscopy electron holography. This method can be applied to the characterization of the microscopic magnetic structure of magnetic materials in transmission electron microscopy. Background Technology

[0002] The magnetic domains and their domain wall structures in magnetic materials directly affect key physical properties and device performance, such as magnetization reversal mechanisms, coercivity, and spin transport. Domain walls, as regions where the magnetization direction transitions continuously between adjacent domains, typically have intrinsic widths on the nanoscale and depend on various factors including exchange interactions, magnetic anisotropy, sample thickness, and temperature. Therefore, achieving high spatial resolution, quantitative, and repeatable precise measurements of domain wall width is crucial for a deeper understanding of the microscopic mechanisms of magnetic materials and their applications in devices.

[0003] Currently, the characterization of magnetic domain structures mainly relies on methods such as magneto-optical Kerr microscopy and Lorentz transmission electron microscopy. Magneto-optical Kerr microscopy can rapidly acquire qualitative information on the distribution of magnetic domains within a large field of view, but its spatial resolution is limited by the optical diffraction limit, making it difficult to accurately resolve the intrinsic width of domain walls and internal details on the order of tens of nanometers. In Lorentz transmission electron microscopy, Fresnel defocusing imaging mode is often used. By deflecting the electron beam under different defocusing conditions caused by the magnetic field inside the sample, contrast fringes related to the domain walls are formed. The domain wall width is then indirectly estimated by using the relationship between the apparent width of the intensity profile (e.g., half-width at half-maximum) and the amount of defocusing. However, this method usually requires a large amount of defocusing to obtain sufficient contrast, making the measured "apparent width" susceptible to multiple factors such as the choice of defocusing amount, lens aberrations, sample thickness and tilt angle, electron scattering, and noise. In addition, the measurement process often relies on empirical interpretation or indirect inference based on specific models, resulting in non-uniqueness and insufficient repeatability of the results, making it difficult to meet the requirements of high-precision, automated quantitative measurement.

[0004] Off-axis electron holography, a transmission electron microscopy technique based on the principle of interference, can directly reconstruct the phase of electron waves transmitted through a sample, thereby obtaining quantitative phase information related to the sample's internal potential distribution and magnetic induction intensity. For magnetic materials, phase changes caused by the magnetic structure can be converted into phase gradients, establishing a clear correspondence with the magnetic flux along the electron beam direction. Compared to indirect measurement methods relying on optical diffraction or defocus contrast, electron holography possesses nanometer-level spatial resolution and high phase sensitivity, completely preserving the continuous transition characteristics of domain walls within the same phase image. This technique is easily combined with numerical analysis methods; by fitting a parametric model to the phase or phase gradient profile, the intrinsic width of magnetic domain walls can be stably and directly extracted.

[0005] In summary, to overcome the limitations of existing magneto-optical Kerr microscopy and Lorentz defocusing imaging techniques in domain wall width measurement, such as insufficient spatial resolution, susceptibility to imaging conditions, reliance on subjective experience, and low quantitative consistency, it is urgent to develop a magnetic domain wall width measurement method and corresponding system based on electronic holographic phase information to achieve high-resolution, low-noise, and repeatable accurate measurement of the intrinsic width of magnetic domain walls.

[0006] 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

[0007] The purpose of this invention is to provide a quantitative measurement method for magnetic domain wall width based on transmission electron microscopy electron holography, so as to solve the problems of large errors, insufficient resolution and accuracy in traditional measurements.

[0008] To achieve the above objectives, this invention provides a method for quantitatively measuring magnetic domain wall width based on transmission electron microscopy (TEM) electron holography, comprising the following steps:

[0009] (1) The sample is observed in a transmission electron microscope to obtain an electron hologram containing the domain wall region, wherein the electron hologram includes at least an object hologram and a reference hologram;

[0010] (2) Import the object hologram and the reference hologram into the image processing program and perform phase reconstruction to obtain the phase map of the sample;

[0011] (3) Perform phase gradient calculation on the phase map to obtain the phase gradient map. Select the region of interest containing the domain wall in the phase gradient map, extract the one-dimensional gradient profile, and use the hyperbolic tangent function to fit the one-dimensional gradient profile to obtain the characteristic parameters of the domain wall.

[0012] (4) Calculate the domain wall width based on the fitted feature parameters, and output the domain wall width result and the fitted curve image.

[0013] Preferably, in the above technical solution, the method for obtaining the electronic hologram in step (1) includes:

[0014] 1) Place the sample on the stage of a transmission electron microscope and take a hologram of the object containing the magnetic domain walls in Lorentz mode;

[0015] 2) While keeping other imaging conditions unchanged, remove the sample or select a sample-free area to take a reference hologram.

[0016] Preferably, in the above technical solution, the object hologram and the reference hologram are obtained through multi-frame acquisition, drift correction and image averaging processing, respectively.

[0017] Preferably, in the above technical solution, the phase reconstruction method in step (2) includes:

[0018] 1) The object hologram and the reference hologram are processed using the real space reconstruction method or an equivalent algorithm to reconstruct the phase map;

[0019] 2) Perform coordinate unification processing on the phase map, including rotation and / or flipping operations, so that the domain wall normal direction is consistent with the subsequent profile extraction direction.

[0020] Preferably, in the above technical solution, step (3) uses a hyperbolic tangent function model to fit the one-dimensional gradient profile, and the fitting function is in the form of:

[0021] ,

[0022] Where A is the amplitude parameter and B is the slope parameter. C represents the center position of the domain wall, and C is the background offset parameter.

[0023] Preferably, in the above technical solution, the region of interest of the domain wall in step (3) is rectangular, and the rectangular region is such that its short side extends along the domain wall direction and its long side extends along the domain wall normal direction.

[0024] Preferably, in the above technical solution, the method for extracting the one-dimensional gradient profile in step (3) is to spatially average the gradient data in the region of interest of the rectangle along its short side.

[0025] Preferably, in the above technical solution, the method for calculating the domain wall width in step (4) is as follows: based on the slope parameter B obtained from the fitting, calculate according to the formula... Calculate the domain wall width w, and output the result in nanometers.

[0026] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0027] (1) The present invention provides a quantitative measurement method for magnetic domain wall width based on transmission electron microscopy (TEM) electron holography. First, the magnetic phase information corresponding to the magnetic domain wall structure is recorded using electron holography. Then, phase gradient analysis is performed on the reconstructed phase map, and hyperbolic tangent function fitting is combined to accurately obtain the intrinsic width of the magnetic domain wall, achieving high-precision and high-resolution quantitative measurement. This method directly reconstructs magnetic phase information based on electron holography, which has higher spatial resolution and phase sensitivity compared to traditional magneto-optical imaging or defocus fringe analysis in Lorentz microscopy, thus significantly reducing the measurement error of the magnetic domain wall width.

[0028] (2) By performing gradient calculations on the phase map and averaging it along the domain wall extension direction in the selected region of interest, the method of the present invention can effectively suppress the interference of random noise and local defects in the sample, and improve the repeatability and reliability of the measurement results.

[0029] (3) The present invention uses the hyperbolic tangent function to automatically fit the gradient profile. By directly and objectively converting the domain wall width through the fitting parameters, the measurement process is automated and quantified, avoiding the problem of inconsistent results caused by subjective threshold selection in the traditional manual interpretation method.

[0030] (4) This invention makes full use of the high sensitivity of electronic holography to characterize magnetic phase changes and the precise positioning of the domain wall transition region by phase gradient analysis. It can accurately measure the intrinsic width of magnetic domain walls at the nanoscale, providing a high-precision quantitative analysis tool for the study of micro-nano magnetic structures, the development of high-performance magnetic storage materials and related fields. Attached Figure Description

[0031] Figure 1 This is a flowchart illustrating the quantitative measurement method for magnetic domain wall width based on transmission electron microscopy electron holography according to the present invention.

[0032] Figure 2 This is a schematic diagram illustrating the working principle of the off-axis electronic holography technology employed in this invention;

[0033] Figure 3 This is a schematic diagram illustrating the verification of the method of the present invention based on simulated data in Example 1;

[0034] in, Figure 3 (a) The simulated magnetic moment distribution of the 180° Bloch domain wall structure (top) and its corresponding simulated phase diagram (bottom); Figure 3 (b) for Figure 3 (a) is the gradient distribution map obtained after performing phase gradient calculation on the simulated phase map; Figure 3 (c) is for Figure 3 (b) shows the curve of the gradient profile fitted to the region indicated by the rectangle, and the domain wall width calculated based on the fitting result.

[0035] Figure 4 This is a diagram showing the quantitative measurement results of the magnetic domain wall width based on an off-axis electron holographic experiment using a real transmission electron microscope, as described in Example 1.

[0036] in, Figure 4 (a) is the phase diagram of the sample reconstructed by off-axis electron holography; Figure 4 (b) for Figure 4(a) shows the phase gradient map obtained after performing phase gradient calculation on the phase map. The rectangle in the figure marks the region of interest (ROI) containing the target domain wall selected for extracting the profile data. Figure 4 (c) to make Figure 4 (b) shows the one-dimensional gradient profile curve obtained by averaging the two-dimensional gradient data in the ROI region along the domain wall extension direction (scatter points represent the original data), and the result of fitting with the hyperbolic tangent function model (solid line is the fitted curve). The dashed line in the figure is used to indicate the range of the magnetic domain wall transition region determined according to the fitting parameters. Detailed Implementation

[0037] The following detailed description of specific embodiments is provided in conjunction with the accompanying drawings, but it should be understood that the scope of protection of the present invention is not limited to the specific embodiments.

[0038] 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.

[0039] like Figures 1 to 4 As shown, this invention discloses a method for quantitatively measuring magnetic domain wall width based on transmission electron microscopy (TEM) electron holography, performed in Lorentz mode. The core principle of this method is that for continuously rotating magnetic domain walls (e.g., 180° Bloch walls), the distribution of their magnetic phase gradient along the domain wall normal direction satisfies a hyperbolic tangent function relationship. The specific implementation steps are as follows:

[0040] Step 1: Acquire images from the electron holographic experiment

[0041] The sample is observed in Lorentz mode of a transmission electron microscope to obtain an electron hologram containing the target magnetic domain wall region. The electron hologram comprises at least one pair of images: an object hologram and a reference hologram. The object hologram records the phase modulation of the electron waves caused by the sample (including its magnetic domain structure); the reference hologram is taken in a region without a sample or outside the sample to provide a phase reference and eliminate background phase interference introduced by the instrument.

[0042] This step specifically includes:

[0043] 1. Place the sample to be tested on the transmission electron microscope stage, and take pictures of the region of interest containing the magnetic domain walls in Lorentz mode to obtain a hologram of the object.

[0044] 2. Keeping other imaging conditions (such as magnification, lens current, bias voltage, etc.) completely unchanged, remove the sample or select a vacuum area without a sample, and take a reference hologram.

[0045] 3. To improve the image signal-to-noise ratio, multiple frames can be acquired from the object hologram and the reference hologram, and the acquired image sequence can be processed by drift correction and frame averaging.

[0046] Step 2: Phase Map Reconstruction and Processing

[0047] The object hologram and reference hologram obtained in step 1 are imported into an image processing program (e.g., computer software based on a specific algorithm). Using the real-space reconstruction method or other equivalent holographic reconstruction algorithms, a phase map φ(x, y) reflecting the internal information of the sample is calculated and reconstructed. Since the magnetic field strength distribution generated by the domain walls produces additional magnetic phase modulation on the electron waves passing through the sample, the magnetic phase φmag in the reconstructed phase map contains spatial transition information of the domain walls, providing a data basis for subsequent quantitative measurements.

[0048] This step specifically includes:

[0049] 1. Using an image processing program, perform phase unwrapping and reconstruction operations on the object hologram and the reference hologram to obtain the original phase distribution map of the sample.

[0050] 2. Perform necessary coordinate unification processing (such as rotation, flipping, etc.) on the obtained phase map to ensure that the coordinate directions of the phase map (especially the x and y directions) accurately correspond to the normal directions of the domain walls and the profile extraction directions in subsequent analysis.

[0051] Step 3: Phase gradient analysis and characteristic parameter fitting

[0052] Spatial gradient calculation is performed on the phase map obtained in step 2 to obtain the phase gradient map. Within the phase gradient map, a rectangular region of interest (ROI) is selected that completely encompasses the target domain wall transition region. Then, the two-dimensional gradient data within this ROI are spatially averaged along the domain wall extension direction to extract a one-dimensional gradient profile curve g(x) along the domain wall normal direction. Finally, a hyperbolic tangent function model is used to perform nonlinear fitting on this profile curve to obtain key parameters characterizing the domain wall transition features.

[0053] For a typical 180° Bloch domain wall, the variation of its magnetic phase gradient along the normal direction follows a hyperbolic tangent function form:

[0054] ;

[0055] in I represents the phase information within the sample, and I represents the amplitude parameter. The parameter represents the center position of the domain wall. Let ϕ be the domain wall width. The left side of the equation is the gradient operation performed on the phase map ϕ to obtain the phase gradient map. The fitting model is obtained based on this formula.

[0056] The fitted model is:

[0057] ;

[0058] Where A is the amplitude parameter and B is the slope parameter (directly related to the domain wall width). Let C be the center position parameter of the domain wall, and C be the background offset parameter. These parameters can be accurately obtained through fitting.

[0059] Therefore, by fitting the one-dimensional phase gradient profile with a hyperbolic tangent function to obtain the fitting parameters, the intrinsic width of the magnetic domain wall can be calculated.

[0060] Step 3 can be broken down into the following sub-steps:

[0061] 1. The phase map obtained in step 2 Perform spatial gradient calculations to obtain the phase gradient distribution map; preferably, calculate the component aligned with the domain wall normal direction, for example... or .

[0062] 2. In the phase gradient map, select a rectangular region of interest that includes the complete domain wall transition features. The short side of this region should preferably be parallel to the extension direction of the domain wall, and the long side should preferably be parallel to the normal direction of the domain wall.

[0063] 3. Spatially average the two-dimensional gradient data in the region of interest along its short side direction (i.e., the domain wall extension direction) to obtain a one-dimensional gradient profile curve g(x) distributed along the long side direction (i.e., the domain wall normal direction).

[0064] 4. The obtained one-dimensional gradient profile curve g(x) is nonlinearly fitted using a hyperbolic tangent function model. The fitting function is in the form of:

[0065] ;

[0066] Where A is the amplitude parameter, B is the slope parameter, x0 is the center position of the domain wall, and C is the background offset. Through the fitting process, the values ​​of parameters A, B, x0, and C are accurately obtained.

[0067] Step 4: Calculation and Output of Domain Wall Width

[0068] This step calculates the domain wall width based on the feature parameters obtained from step 3, and outputs quantitative results and related illustrations. Specifically, it includes:

[0069] 1. Calculate the width w of the domain wall based on the slope parameter B obtained from the fitting. The preferred definition and calculation formula are as follows: .

[0070] 2. Output the final numerical result of the domain wall width w, which should be clearly labeled in nanometers (nm). Simultaneously, generate and output a comparison image containing the original gradient profile data points and the fitted curve to visually demonstrate the fitting quality and the transition characteristics of the domain walls. Example

[0071] The method described in this invention is used to process alloys The magnetic domain wall width of the sample was measured, and the specific implementation steps are as follows:

[0072] Step 1: Acquire electronic holographic images

[0073] Observation in Lorentz mode of transmission electron microscopy A thin-film sample was used to obtain an off-axis electron hologram containing the target magnetic domain wall region. The hologram included:

[0074] The sample is placed on the sample stage, and the region of interest containing the magnetic domain walls is photographed in Lorentz mode to obtain a hologram of the object.

[0075] While keeping all other imaging parameters exactly the same, remove the sample or select a vacuum region without a sample and take a reference hologram.

[0076] Step 2: Phase map reconstruction and preprocessing

[0077] The object hologram and reference hologram obtained in step 1 are imported into an image processing program, and phase extraction is performed using an off-axis holographic reconstruction algorithm to obtain a phase map reflecting the internal magnetic structure of the sample. The phase map was then subjected to necessary coordinate unification processing (such as rotation and flipping) to ensure that its spatial coordinate direction (x, y) was consistent with the normal direction of the domain wall and the profile extraction direction in the subsequent analysis.

[0078] Step 3: Phase gradient analysis and feature fitting

[0079] This step aims to extract quantitative features of domain walls from the phase map.

[0080] Preprocessed phase map Perform spatial gradient calculations to obtain the phase gradient map. Preferably, calculate the gradient components along the domain wall normal direction (e.g., the x-direction). .

[0081] In the obtained phase gradient map, select a rectangular region of interest that completely covers the domain wall transition region. This region should be set so that its short side is parallel to the extension direction of the domain wall and its long side is parallel to the normal direction of the domain wall.

[0082] The two-dimensional gradient data within this rectangular region are spatially averaged along its shorter side (domain wall extension direction) to obtain a one-dimensional gradient profile curve g(x) distributed along its longer side (domain wall normal direction).

[0083] A hyperbolic tangent function model is used to perform nonlinear fitting on the above one-dimensional profile curve g(x). The fitting formula is:

[0084] ;

[0085] By fitting, the amplitude parameter A, slope parameter B, domain wall center position x0, and background offset parameter C are accurately obtained.

[0086] Step 4: Width Calculation and Result Output

[0087] Based on the fitting parameters obtained in step 3, calculate and output the final result.

[0088] Based on the slope parameter B obtained from the fitting, the intrinsic width w of the domain wall is calculated using the following formula: In this embodiment, the measured The domain wall width of the sample is 26.1 nm. The specific value of the domain wall width (in nm) is output, and a comparison image showing the original gradient profile data and the fitted curve is generated to visually verify the fitting quality and the reliability of the measurement results.

[0089] like Figure 3 and Figure 4 As shown, the method proposed in this invention can effectively achieve quantitative measurement of the width of magnetic domain walls in both simulation and experimental data.

[0090] Figure 3 The feasibility of the method of the present invention was verified based on simulation data: wherein, Figure 3 (a) The simulated magnetic moment distribution of the 180° Bloch domain wall structure (top) and its corresponding simulated phase diagram (bottom) are shown, clearly presenting the phase change characteristics of the domain wall region; Figure 3 (b) for Figure 3 (a) The gradient distribution map obtained after performing phase gradient calculation on the phase map shows that the gradient value is significantly enhanced in the domain wall transition region, which accurately marks the spatial position of the domain wall. Figure 3 (c) Figure 3 (b) The gradient profile within the rectangular frame was fitted, and the simulated domain wall width was calculated to be 84.7 nm based on the fitting results, indicating that the method can accurately extract the domain wall scale information in the simulated data.

[0091] Figure 4 The applicability of this method was further verified through actual off-axis electron holographic experiments using transmission electron microscopy: Figure 4(a) is the experimentally reconstructed phase diagram of the sample, showing the true magnetic domain structure and phase distribution; Figure 4 (b) is the corresponding phase gradient map, where the rectangle marks the region of interest containing the target magnetic domain walls; Figure 4 (c) The hyperbolic tangent function model was used to fit the region (solid line). The fitting results are in high agreement with the experimental data (scatter plots). Based on the fitting parameters, the domain wall width in the actual sample can be deduced to be 26.1 nm.

[0092] In conclusion, Figure 3 and Figure 4 The results collectively demonstrate that this invention, based on electron holography using transmission electron microscopy, achieves quantitative measurement of magnetic domain wall width through a combination of phase gradient and function fitting.

[0093] This invention proposes a high-precision quantitative measurement method for magnetic domain wall width based on off-axis electron holography using transmission electron microscopy. The method involves acquiring a hologram of the object containing the magnetic domain wall region and a reference hologram in Lorentz mode of a transmission electron microscope. Phase reconstruction is then performed to obtain the phase distribution map of the sample. The phase gradient is calculated, and key parameters are obtained by fitting a hyperbolic tangent function to selected feature regions. Based on these parameters, the intrinsic width of the magnetic domain wall is calculated. Compared with existing methods based on the magneto-optical Kerr effect (MOKE) or Lorentz defocus Fresnel fringes, this invention does not rely on the apparent broadening of domain wall contrast under large defocus conditions, nor does it require extrapolation estimation through multiple defocus sequences, thus providing a more direct and fundamental approach to width extraction.

[0094] This method has the advantages of high spatial resolution, strong noise resistance, and easy automation. It can significantly improve the accuracy and consistency of magnetic domain wall width measurement, and provide a reliable technical means for the characterization of the microscopic magnetic structure of magnetic materials and the engineering evaluation of key performance parameters of related devices.

[0095] 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 quantitatively measuring the width of magnetic domain walls based on transmission electron microscopy (TEM) electron holography, characterized in that, Includes the following steps: (1) The sample is observed in a transmission electron microscope to obtain an electron hologram containing the domain wall region, wherein the electron hologram includes at least an object hologram and a reference hologram; (2) Import the object hologram and the reference hologram into the image processing program and perform phase reconstruction to obtain the phase map of the sample; (3) Perform phase gradient calculation on the phase map to obtain the phase gradient map. Select the region of interest containing the domain wall in the phase gradient map, extract the one-dimensional gradient profile, and use the hyperbolic tangent function to fit the one-dimensional gradient profile to obtain the characteristic parameters of the domain wall. (4) Calculate the domain wall width based on the fitted feature parameters, and output the domain wall width result and the fitted curve image.

2. The method for quantitatively measuring the width of magnetic domain walls based on transmission electron microscopy (TEM) electron holography according to claim 1, characterized in that, Step (1) of obtaining the electronic hologram includes: 1) Place the sample on the stage of a transmission electron microscope and take a hologram of the object containing the magnetic domain walls in Lorentz mode; 2) While keeping other imaging conditions unchanged, remove the sample or select a sample-free area to take a reference hologram.

3. The method for quantitatively measuring the width of magnetic domain walls based on transmission electron microscopy (TEM) electron holography according to claim 2, characterized in that, The object hologram and the reference hologram were obtained through multi-frame acquisition, drift correction, and image averaging processing, respectively.

4. The method for quantitative measurement of magnetic domain wall width based on transmission electron microscopy electron holography according to claim 1, characterized in that, Step (2) Phase reconstruction methods include: 1) The object hologram and the reference hologram are processed using the real space reconstruction method or an equivalent algorithm to reconstruct the phase map; 2) Perform coordinate unification processing on the phase map, including rotation and / or flipping operations, so that the domain wall normal direction is consistent with the subsequent profile extraction direction.

5. The method for quantitatively measuring the width of magnetic domain walls based on transmission electron microscopy electron holography according to claim 1, characterized in that, Step (3) uses a hyperbolic tangent function model to fit the one-dimensional gradient profile. The fitting function has the following form: ， Where A is the amplitude parameter and B is the slope parameter. C represents the center position of the domain wall, and C is the background offset parameter.

6. The method for quantitatively measuring the width of magnetic domain walls based on transmission electron microscopy electron holography according to claim 1, characterized in that, Step (3) The region of interest of the domain wall is a rectangle, and the rectangular region is such that its short side extends along the domain wall direction and its long side extends along the domain wall normal direction.

7. The method for quantitatively measuring the width of magnetic domain walls based on transmission electron microscopy electron holography according to claim 6, characterized in that, Step (3) involves extracting a one-dimensional gradient profile by averaging the gradient data within the rectangular region of interest along its shorter side.

8. The method for quantitatively measuring the width of magnetic domain walls based on transmission electron microscopy electron holography according to claim 1, characterized in that, Step (4) The method for calculating the domain wall width is as follows: based on the slope parameter B obtained from the fitting, calculate according to the formula... Calculate the domain wall width w, and output the result in nanometers.

Images