A method for high-precision determination of magnetic moments of micro-nano magnetic structures based on electron holography

Abstract

The invention discloses a method for high-precision determination of magnetic moment of micro-nano magnetic structure based on electron holography, comprising the following steps: S1, observing a sample under a transmission electron microscope, and obtaining two electron holograms before and after magnetization reversal by tilting the sample; S2, in an image processing program, reconstructing a phase map from the two holograms in step S1, subtracting them from the center, and halving them to obtain a sample magnetic phase map; S3, performing circular loop integral fitting and extrapolation to zero on the magnetic phase map obtained in step S2 to obtain an induced magnetic moment, and then obtaining a magnetic moment value according to the relationship between the magnetic induced moment and the magnetic moment. The method of the invention can realize quantitative measurement of high-precision magnetic moment at micro-nano scale.

Description

Technical Field

[0001] The invention relates to a method for measuring the magnetic moment of a micro-nano magnetic structure with high precision based on electron holography. Background Art

[0002] Traditional magnetic moment determination mainly uses vibrating sample magnetometer (VSM) and magnetic balance methods to calibrate the magnetic parameters of magnetic nanoparticles. Similarly, both methods take quantitative materials to measure the magnetic moment and then convert it into magnetic moment per unit mass or volume. However, in the VSM method, the sample is in a state of constant vibration, which will destroy the magnetic dipole interaction between the magnetic nanoparticles, making the measured value smaller than the true value. In addition, when measuring the sample, the measured sample will be selected as the calibration, and the measurement has certain limitations.

[0003] The magnetic moment of magnetic nanomaterials can be measured based on image processing combined with dynamic analysis. By studying the movement of magnetic particles under the action of a gradient magnetic field, the change in the magnitude of the magnetic moment of the magnetic particles is explored, which is used as a method to evaluate the properties of magnetic particles. The force on magnetic particles under a magnetic field is related to the magnitude of its magnetic moment. By recording the movement of magnetic particles under the action of a magnetic field, the velocity and acceleration changes of the particles are calculated through image processing, thereby obtaining the force changes on the magnetic particles, and finally the magnitude of the magnetic moment of the particles is calculated using the magnitude of the magnetic force. However, this method requires a quantitative amount of magnetic nanodroplets to be dripped into a sealed sample tube containing an organic liquid with the same density as the magnetic nanodroplets, and the sample preparation process is complicated and cumbersome. After that, the sample tube is placed vertically in a vertical gradient magnetic field and the trajectory of the movement of the magnetic nanodroplets is recorded by video. The velocity curve and acceleration curve of the magnetic nanodroplets considering the influence of gravity are obtained through digital image processing, thereby calculating the magnetic moment curve of the magnetic nanodroplets. This method cleverly uses the effects of four forces on magnetic nanoparticles: external magnetic field force, gravity, buoyancy, and viscous resistance to measure the magnetic moment of nanoparticles. However, the initial velocity of the magnetic nanoparticles will be given when the sample is placed, and the magnetic nanoparticles will also be subject to a large elastic force when moving to the bottom or wall of the sample tube, which will cause a large error in the magnetic moment measurement. This method can only measure the total magnetic moment of a large number of magnetic nanoparticles, and cannot quantitatively give the magnetic moment of a single nanoparticle. In addition, this method has too many links and is easily disturbed by the external environment, resulting in relatively large errors.

[0004] As a microscope with high spatial resolution, transmission electron microscopy (TEM) applies an external magnetic field to the sample by applying an objective excitation current in the Lorentz mode, observes the change process of the magnetic domain direction and domain wall thickness inside the magnetic sample, and studies the change of the micromagnetic structure inside the magnetic sample. It has been widely used in the characterization of magnetic domain structures at the micro-nano scale, but to date, the high-precision quantitative determination of the magnetic moment of micro-nano magnetic structures is still rarely reported. Electron holography based on transmission electron microscopy can obtain electron optical magnetic phase images of micro-nano magnetic structures with micro-nano scale resolution, and quantitative magnetic parameter information, including magnetization intensity and magnetocrystalline anisotropy, can be obtained by analyzing the magnetic phase image. Electron microscopy techniques based on transmission electron microscopy, including off-axis electron holography and methods based on intensity transfer equations, are used to measure the change in the wave function phase after high-energy electrons penetrate the sample to analyze the magnetic structure information of the sample. It has been widely used to analyze the projection plane magnetic induction map of magnetized nanocrystals, nanostructures, thin films and devices, usually with a spatial resolution better than 10nm. This magnetic phase image can be used to obtain quantitative information about relevant parameters, such as the magnetization or coercivity of the sample area, as well as the magnetic interaction and magnetization transition between single-domain and multi-domain magnetic states. Currently, it is mostly used for high-resolution qualitative analysis of the distribution of magnetic fields. However, to date, there are still very few reports on high-resolution and high-precision determination of the magnetization or magnetic moment of micro-nano magnetic structures.

[0005] 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

[0006] The purpose of the present invention is to provide a method for measuring the magnetic moment of a micro-nano magnetic structure with high precision based on electron holography, thereby overcoming the disadvantage of large error in measuring the magnetic moment of a single nanomagnetic structure or a coupled nanomagnetic structure.

[0007] To achieve the above object, the present invention provides a method for high-precision measurement of the magnetic moment of a micro-nano magnetic structure based on electron holography, comprising the following steps:

[0008] S1: Observe the sample under a transmission electron microscope and obtain two electron holograms before and after the magnetization reversal by tilting the sample;

[0009] S2: In the image processing program, the two holograms in step S1 are reconstructed into a phase map, and then subtracted from each other and halved to obtain the sample magnetic phase map;

[0010] S3: Performing circular loop integral fitting and extrapolating to zero through the magnetic phase diagram obtained in step S2 to obtain the induced magnetic moment, and then obtaining the magnetic moment value according to the relationship between the magnetic induced moment and the magnetic moment.

[0011] Preferably, in the above technical solution, the method of obtaining the electronic hologram in step S1 includes:

[0012] (1) placing a sample on a sample stage of a transmission electron microscope, photographing a hologram of the sample area in a Lorentz mode to obtain a first object hologram; and photographing an empty hologram with the sample removed to obtain a first reference hologram;

[0013] (2) controlling the tilt of the goniometer stage to achieve the tilt of the object in the α direction, applying a strong magnetic field to the objective lens in the Lorentz mode, and taking a second object hologram and a corresponding reference hologram;

[0014] (3) Tilt the sample to -α, move the sample to the same position as step (2), and take the third object hologram and the reference hologram while keeping the objective lens magnetic field and the optical path the same.

[0015] Preferably, in the above technical solution, the thickness of the sample in step (1) is less than 100 nm, and the holographic spatial resolution of the transmission electron microscope used is 2 nm.

[0016] Preferably, in the above technical solution, the method of obtaining the sample magnetic phase image in step S2 includes:

[0017] (1) Importing the two sets of images into an image processing program, and using the real-space reconstruction method to reconstruct two sample phase images from the two sets of object holograms and the reference hologram;

[0018] (2) superimposing the two phase images in an image processing program and aligning the nanoparticles in the two images with pixel-level accuracy by translation, rotation, and scaling;

[0019] (3) Subtract the corresponding pixels of the two aligned images and halve them to obtain the magnetic phase map of the sample.

[0020] Preferably, in the above technical solution, the value of the induced magnetic moment in step S3 is as follows:

[0021] Among them, m B is the induced magnetic moment, φ 0 is the magnetic flux quantum (2.067×10 -15 Tm 2 ), μ 0 Vacuum magnetic permeability

[0022]

[0023] Rate (4π×10 -7 Tm / A), Yes ⊥ The magnetic phase of the position, dl is the infinitesimal element of the loop D;

[0024] Import the image into an image processing program, give the maximum radius and minimum radius, require that all circular loops include the sample, and extrapolate the circular loop integral to zero to obtain the induced magnetic moment;

[0025] According to the relationship between the induced magnetic moment and the magnetic moment, as shown in formula (2):

[0026] m B =mm H (D,M)

[0027] Among them, m H In a sense, it corresponds to the effective magnetic moment of the demagnetization field. The demagnetization factor of the circular loop integral is [1 / 2, 1 / 2, 0], which directly gives equation (3):

[0028]

[0029] Preferably, in the above technical solution, the method for obtaining the magnetic moment value in step S3 includes:

[0030] (1) Importing the image into an image processing program, selecting the maximum radius and the minimum radius of a series of concentric circles containing the sample in the image;

[0031] (2) According to equations (1) to (3), the induced magnetic moment values ​​obtained at different radii are calculated respectively;

[0032] (3) The obtained induced magnetic moment value is converted into the quadratic function y=ax according to the radius 2 +b fitting, and extrapolating the value to zero radius to obtain the induced magnetic moment value of the sample;

[0033] (4) Based on the relationship between the induced magnetic moment value and the magnetic moment, the magnetic moment value can be obtained.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] (1) The present invention is a method for high-precision determination of the magnetic moment of a micro-nano magnetic structure based on electron holography. An electron holography experiment is performed by a transmission electron microscope and a pair of magnetization reversal holograms are photographed. The phase of the hologram is reconstructed using a real-space reconstruction method, which can improve the signal-to-noise ratio and resolution of the phase signal. Then, pixel-level image registration is performed on the phase image of the magnetization reversal, which can greatly improve the accuracy of obtaining the magnetic moment. Then, a circular loop integral fitting is performed to obtain the induced magnetic moment value. According to the relationship between the induced magnetic moment and the magnetic moment, the magnetic moment of the sample at the nanoscale with high precision can be obtained.

[0036] (2) The method of the present invention can measure the magnetic moment of not only simple structures but also complex structures. The method of quantitatively measuring the magnetic moment by circular loop integration does not require any pre-definition of the sample. Compared with other methods, the induced magnetic moment during the measurement of circular loop integration is independent of the position of the magnetized object as long as it is completely within the circular loop.

[0037] (3) The method of the present invention has a high stability against the phase map registration error introduced in the process of image centering by the circular loop integral. The measurement process of the phase map registration error is equivalent to measuring the induced magnetic moment of two identical particles. The induced magnetic moment carried by each particle accounts for half of the total induced magnetic moment, and they are slightly displaced from each other. In uncharged and unpolarized samples, the total (electrostatic + magnetic) phase contribution can be measured separately on two original phase maps without separating them, thereby avoiding phase map registration errors. Directly measuring the magnetic moment of the total phase provides a useful method for evaluating the magnetic state before and after the magnetization reversal process. Utilizing the method of the present invention, quantitative measurement of high-precision magnetic moments at the micro-nano scale can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 is a flow chart of a method for high-precision determination of magnetic moments of micro-nano magnetic structures based on electron holography according to the present invention;

[0039] Figure 2 is a schematic diagram of electron holography based on transmission electron microscopy in the method according to the present invention;

[0040] Figure 3 is a schematic diagram of the operation of the magnetization reversal process in a transmission electron microscope according to the method of the present invention;

[0041] Figure 4 It is the magnetic phase diagram and simulation diagram of induced magnetic moment measurement of spherical magnetic nanoparticles;

[0042] in, Figure 4 (a) is the magnetic phase diagram of spherical magnetic nanoparticles; (b) is the simulation of the induced magnetic moment measurement of spherical magnetic nanoparticles;

[0043] Figure 5 It is the magnetic phase diagram and simulation diagram of induced magnetic moment determination of coupled nanomagnetic particles;

[0044] in, Figure 5 (a) The simulated magnetic phase diagram of the coupled nanomagnetic particles, from left to right, the magnetic moment values ​​are the same at 45°, 30°, and 90°;

[0045] (b) Simulation of the determination of the induced magnetic moment of coupled magnetic nanoparticles;

[0046] Figure 6 It is Fe 3 O 4Magnetic phase diagram of nanorods and simulation diagram of induced magnetic moment determination;

[0047] in, Figure 6 (a)Fe 3 O 4 Magnetic phase diagram of nanorods; (b) Fe 3 O 4 Determination of the magnetic moment of the nanorods. DETAILED DESCRIPTION

[0048] 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.

[0049] 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.

[0050] like Figures 1 to 6 As shown, according to a specific embodiment of the present invention, a method for high-precision determination of the magnetic moment of a micro-nano magnetic structure based on electron holography comprises the following steps:

[0051] S1: Observe the sample under a transmission electron microscope and obtain two electron holograms before and after the magnetization reversal by tilting the sample. Specifically:

[0052] (1) The sample is placed on the sample stage of a transmission electron microscope, and a hologram of the sample area of ​​interest is taken in the Lorentz mode to obtain the first object hologram; and an empty hologram with the sample removed is taken to obtain the first reference hologram.

[0053] (2) controlling the tilt of the goniometer stage to achieve the tilt of the object in the α direction, applying a strong magnetic field to the objective lens in the Lorentz mode, and taking a second object hologram and a corresponding reference hologram;

[0054] (3) Tilt the sample to -α, move the sample to the same position as step (2), and take the third object hologram and the reference hologram while keeping the objective lens magnetic field and the optical path the same.

[0055] The thickness of the sample is less than 100 nm; the electron holographic spatial resolution of the transmission electron microscope used is 2 nm (specifically the general Lorentz electron microscope mode); the objective magnetic field is applied, and the sample is tilted ±α to obtain a pair of magnetization flipped electron holograms, and the reference hologram and the sample hologram are Figure 1 One to one correspondence.

[0056] S2: In the image processing program, the two holograms in step S1 are reconstructed into a phase map, and then subtracted from each other and halved to obtain the sample magnetic phase map.

[0057] The method of obtaining the sample magnetic phase image in step S2 includes:

[0058] (1) Importing the two sets of images into an image processing program, such as computer programming software, and using the real-space reconstruction method to reconstruct two phase images of the sample from the two sets of object holograms and the reference hologram.

[0059] (2) The two phase images are superimposed in an image processing program to align the nanoparticles in the two images with pixel-level accuracy by translation, rotation, and scaling.

[0060] (3) Subtract the corresponding pixels of the two aligned images and halve them to obtain the magnetic phase map of the sample.

[0061] S3: Performing circular loop integral fitting and extrapolating to zero through the magnetic phase diagram obtained in step S2 to obtain the induced magnetic moment, and then obtaining the magnetic moment value according to the relationship between the magnetic induced moment and the magnetic moment.

[0062] The value of the induced magnetic moment in step S3 is as shown in formula (1):

[0063]

[0064] Among them, m B is the induced magnetic moment, φ 0 is the magnetic flux quantum (2.067×10 -15 Tm 2 ), μ 0 is the vacuum permeability (4π×10 -7 Tm / A), yes The magnetic phase of the position, dl is the infinitesimal element of the loop D;

[0065] Import the image into an image processing program, give the maximum radius and minimum radius, require that all circular loops include the sample, and extrapolate the circular loop integral to zero to obtain the induced magnetic moment;

[0066] According to the relationship between the induced magnetic moment and the magnetic moment, as shown in formula (2):

[0067] m B =mm H (D, M)

[0068] Among them, m H In a sense, it corresponds to the effective magnetic moment of the demagnetization field. The demagnetization factor of the circular loop integral is [1 / 2, 1 / 2, 0], which directly gives equation (3):

[0069]

[0070] The method of obtaining the magnetic moment value in step S3 includes:

[0071] (1) Importing the image into an image processing program, selecting the maximum radius and the minimum radius of a series of concentric circles containing the sample in the image;

[0072] (2) According to equations (1) to (3), the induced magnetic moment values ​​obtained at different radii are calculated respectively;

[0073] (3) The obtained induced magnetic moment value is converted into the quadratic function y=ax according to the radius 2 +b fitting, and extrapolating the value to zero radius to obtain the induced magnetic moment value of the sample;

[0074] (4) Based on the relationship between the induced magnetic moment value and the magnetic moment, the magnetic moment value can be obtained.

[0075] Example

[0076] Using the method of the present invention to obtain Fe 3 O 4 Nanorod magnetic moment, the specific steps are as follows:

[0077] S1: Observe the sample under a transmission electron microscope and obtain a pair of holograms by tilting the sample in the Lorentz mode. The thickness of the sample is less than 100nm; the electron holographic spatial resolution of the transmission electron microscope used is 2nm;

[0078] like Figure 2 As shown in the figure, the principle of electron holography is: the coherent electron waves emitted by the electron gun are divided into two beams, one beam propagates in a vacuum and is the reference wave, and the other beam penetrates the sample and propagates and is the object wave. Voltage is applied to the electrostatic holographic wire, so that the object wave and the reference wave are deflected in opposite directions, converge and interfere, thus forming an electron hologram on the image plane.

[0079] When the incident electron wave penetrates a thin sample, it is modulated by the electromagnetic potential of the sample and changes its amplitude and phase. The electron holography method based on the transmission electron microscope records the amplitude and phase changes of the electron wave, thereby obtaining the electromagnetic potential field information of the sample. The distribution of the object wave function can be obtained by reconstructing the electron hologram.

[0080] S1 includes the following steps:

[0081] (1) Figure 3 As shown, Fe 3 O 4 The nanorod sample is placed on the sample stage of a transmission electron microscope. In the Lorentz mode, the objective lens gives the sample a certain magnetic field B, and takes holograms corresponding to several particles in the sample to obtain the first object hologram; and takes a hologram corresponding to the blank space in the sample to obtain the first reference hologram.

[0082] (2) Change the sample tilt angle to a small angle α to ensure that the sample is in the same position as the first object hologram, and take the second object hologram and the reference hologram while keeping other conditions unchanged.

[0083] (3) Reversely tilt the sample to -α to ensure that the sample is in the same position as the first object hologram. Take the third Fe hologram while keeping other conditions unchanged. 3 O 4 Object and reference holograms of a nanorod specimen.

[0084] S2: Acquisition of magnetic phase image

[0085] Specifically: (1) Import the two sets of images into an image processing program, and use the real-space reconstruction method to reconstruct the phase images of the two samples from the two sets of object holograms and the reference hologram.

[0086] (2) The two phase images are superimposed in an image processing program, and the nanodiamond particles in the two images are aligned with pixel-level accuracy through translation, rotation, and scaling.

[0087] (3) Subtract the corresponding pixels of the two aligned images and halve them to obtain the magnetic phase map of the sample.

[0088] S3: The induced magnetic moment is obtained by performing circular loop integration on the obtained magnetic phase diagram, and then the magnetic moment is obtained according to the relationship between the induced magnetic moment and the magnetic moment.

[0089] The value of the induced magnetic moment in step S3 is as shown in formula (1):

[0090]

[0091] Among them, m B is the induced magnetic moment, φ 0 is the magnetic flux quantum (2.067×10 -15 Tm 2 ), μ 0 is the vacuum permeability (4π×10 -7 Tm / A), yes The magnetic phase of the position, dl is the infinitesimal element of the loop D;

[0092] Import the image into an image processing program, give the maximum radius and minimum radius, require that all circular loops include the sample, and extrapolate the circular loop integral to zero to obtain the induced magnetic moment;

[0093] According to the relationship between the induced magnetic moment and the magnetic moment, as shown in formula (2):

[0094] m B =mm H (D,M)

[0095] Among them, m H In a sense, it corresponds to the effective magnetic moment of the demagnetization field. The demagnetization factor of the circular loop integral is [1 / 2, 1 / 2, 0], which directly gives equation (3):

[0096]

[0097] The method of obtaining the magnetic moment value in step S3 includes:

[0098] (1) Importing the image into an image processing program, selecting the maximum radius and the minimum radius of a series of concentric circles containing the sample in the image;

[0099] (2) According to equations (1) to (3), the induced magnetic moment values ​​obtained at different radii are calculated respectively;

[0100] (3) The obtained induced magnetic moment value is converted into the quadratic function y=ax according to the radius 2 +b fitting, and extrapolating the value to zero radius to obtain the induced magnetic moment value of the sample;

[0101] (4) According to the relationship between the induced magnetic moment and the magnetic moment, the magnetic moment value m = [-2.7647, -1.4134] × 10 8 μ B . Where μ B is the Bohr magneton, μ B =9.2732x10 -24 Am 2 .

[0102] The present invention proposes a method for high-precision determination of the magnetic moment of a micro-nano magnetic structure based on electron holography. An electron holography experiment is performed through a transmission electron microscope and a pair of magnetization flipped holograms are photographed. The phase of the hologram is reconstructed using a real space reconstruction method, which can improve the signal-to-noise ratio and resolution of the phase signal. Then, pixel-level image registration is performed on the magnetization flipped phase map, which can greatly improve the accuracy of obtaining the magnetic moment. Then, a circular loop integral fitting is performed to obtain the induced magnetic moment value. According to the relationship between the induced magnetic moment and the magnetic moment, the magnetic moment of the sample at the nanoscale with high precision can be obtained.

[0103] 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 method for high-precision measurement of magnetic moment of micro-nano magnetic structure based on electron holography, characterized in that: The following steps are involved: S1: Observe the sample under a transmission electron microscope, take the object hologram of the sample area and the empty hologram after removing the sample, and obtain the object hologram and empty hologram before and after magnetization reversal by tilting the sample; S2: In the image processing program, the object hologram and the empty hologram before and after flipping in step S1 are reconstructed into two phase images respectively, and then subtracted from each other and halved to obtain the sample magnetic phase image; S3: Performing circular loop integral fitting and extrapolating to zero through the magnetic phase diagram obtained in step S2 to obtain the induced magnetic moment, and then obtaining the magnetic moment value according to the relationship between the magnetic induced moment and the magnetic moment.

2. The method for high-precision measurement of magnetic moment of micro-nano magnetic structure based on electron holography according to claim 1, characterized in that: Step S1: The method for obtaining an electronic hologram comprises: (1) placing a sample on a sample stage of a transmission electron microscope, photographing a hologram of the sample area in a Lorentz mode to obtain a first object hologram; and photographing an empty hologram with the sample removed to obtain a first reference hologram; (2) controlling the tilt of the goniometer stage to achieve the tilt of the object in the α direction, applying a strong magnetic field to the objective lens in the Lorentz mode, and taking a second object hologram and a corresponding reference hologram; (3) Tilt the sample to -α, move the sample to the same position as step (2), and take the third object hologram and the reference hologram while keeping the objective lens magnetic field and the optical path the same.

3. The method for high-precision measurement of magnetic moment of micro-nano magnetic structure based on electron holography according to claim 2, characterized in that: The thickness of the sample in step (1) is less than 100 nm, and the holographic spatial resolution of the transmission electron microscope used is 2 nm.

4. The method for high-precision measurement of magnetic moment of micro-nano magnetic structure based on electron holography according to claim 1, characterized in that: The method of obtaining the sample magnetic phase image in step S2 includes: (1) Importing the two sets of images into an image processing program, and using the real-space reconstruction method to reconstruct two sample phase images from the two sets of object holograms and the reference hologram; (2) superimposing the two phase images in an image processing program and aligning the nanoparticles in the two images with pixel-level accuracy by translation, rotation, and scaling; (3) Subtract the corresponding pixels of the two aligned images and halve them to obtain the magnetic phase map of the sample.

5. The method for high-precision measurement of magnetic moment of micro-nano magnetic structure based on electron holography according to claim 1, characterized in that: The value of the induced magnetic moment in step S3 is as shown in formula (1): Among them, m B is the induced magnetic moment, φ0 is the magnetic flux quantum (2.067×10 -15 Tm 2 ), μ0 is the vacuum permeability (4π×10 - 7 Tm / A), Yes ⊥ The magnetic phase of the position, dl is the infinitesimal element of the loop D; Import the image into an image processing program, give the maximum radius and minimum radius, require that all circular loops include the sample, and extrapolate the circular loop integral to zero to obtain the induced magnetic moment; According to the relationship between the induced magnetic moment and the magnetic moment, as shown in formula (2): m B =m-m H (D,M) Among them, m H In a sense, it corresponds to the effective magnetic moment of the demagnetization field. The demagnetization factor of the circular loop integral is [1 / 2, 1 / 2, 0], which directly gives equation (3):

6. The method for high-precision measurement of magnetic moment of micro-nano magnetic structure based on electron holography according to claim 5, characterized in that: The method of obtaining the magnetic moment value in step S3 includes: (1) Importing the image into an image processing program, selecting the maximum radius and the minimum radius of a series of concentric circles containing the sample in the image; (2) According to equations (1) to (3), the induced magnetic moment values ​​obtained at different radii are calculated respectively; (3) The obtained induced magnetic moment value is converted into the quadratic function y=ax according to the radius 2 +b fitting, and extrapolating to the point where the radius is zero, to obtain the induced magnetic moment value of the sample; (4) Based on the relationship between the induced magnetic moment value and the magnetic moment, the magnetic moment value can be obtained.

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