A micromagnetic method for predicting magnetic characteristics of magnetic samples

Abstract

The present invention relates to the field of electromagnetism, and in particular to a micromagnetic method for predicting the magnetic characteristics of a magnetic sample, the method comprising: (1) constructing a plurality of magnet models with different magnetic domain sizes, shapes, and numbers of magnetic domains, and determining the magnetic parameters of the magnet models; (2) placing a magnet to be tested under predetermined external field conditions, obtaining its magnetization intensity, and comparing the magnetization intensity with the measurement results of each model under the same external field conditions; (3) determining the similarity between the magnet to be tested and each model, finding the model with the highest similarity, and retrieving various magnetic parameters of the model; and (4) determining the external field conditions of the magnet to be tested in a new target environment.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetism, and in particular to a micromagnetism method for predicting magnetic characteristics of magnetic samples. Background Art

[0002] For samples with fixed composition and structure, their magnetic characteristics are essentially determined under specific temperature and pressure conditions. However, these characteristics are usually based on the sample's performance in a saturated state, or the residual magnetic properties after experiencing a saturated state. However, relatively little research has been conducted on the effects of weaker magnetic fields on the magnetic properties of samples. This is especially true for samples exposed to geomagnetic environments for long periods of time. Due to changes in their position and orientation, the weak external magnetic field environment they are exposed to will also change accordingly. In recent years, a growing number of studies have shown that under specific conditions, the effects of such weak external magnetic fields can accumulate and may have a certain impact on the magnetic properties of the sample.

[0003] However, there is currently no good method to predict the specific impact of weak magnetic fields on magnetic bodies. Summary of the Invention

[0004] Introduction to related concepts:

[0005] Saturation magnetization refers to the maximum value and state of the magnetization intensity of a ferromagnetic material that can be reached under the action of an external magnetic field. In this state, the ferromagnetism of the material no longer increases with the increase of the external magnetic field.

[0006] A magnetic domain is a small area within a magnetic material with the same magnetization direction. Within these areas, the electron spins align, forming a localized magnetic field. Often, multiple magnetic domains exist within a material, and their magnetization directions may differ, resulting in the overall material appearing non-magnetic or weakly magnetic.

[0007] A magnetic domain wall is the interface between two adjacent magnetic domains. Within this region, the magnetization direction transitions and gradually changes, gradually shifting from one domain's orientation to another. The presence of domain walls enables materials to switch between different magnetic domains and states. Typically, under the influence of an external magnetic field, domain walls move, causing changes in the material's macroscopic magnetic properties. The evolution of microscopic magnetic domains begins with the movement of domain walls.

[0008] The magnetism of macroscopic matter originates from the spin of each electron at the microscopic scale. In other words, magnetism is the result of the combined contribution of each electron's spin. Each electron possesses a spin, representing the smallest unit of magnetic dipole. When many electrons are clustered together, following the connections of atoms or molecules, their spins interact and superimpose, causing the entire material to exhibit macroscopic magnetism.

[0009] As mentioned above, the research methods and results of macroscopic magnetism are relatively rich and there is no relevant research on the influence of weak magnetic fields on inherent magnetism. The present invention will study the physical principles and mechanisms of the influence of weak magnetic fields on inherent magnetism from the perspective of microscopic magnetism rather than macroscopic magnetism.

[0010] The present invention first models a variety of possible microscopic magnetic structures. Magnetic domains of various shapes, such as common spherical and layered structures, are created, along with their size and diameter. Magnetic domain parameters, such as the spin exchange coefficient, magnetic anisotropy, and saturation magnetization, are established. The center of magnetic domain appearance, as well as the relative distances and orientations between various domains, are determined. Next, based on the LLG equation, micromagnetic simulations are performed on the various designed microscopic magnetic structures. The results are compared with the actual changes in magnetic samples after exposure to weak magnetic fields. The objective laws governing the changes and evolution of intrinsic magnetic properties are summarized, and the relationship between these changes and microscopic magnetic structures is established.

[0011] The technical solutions of the present invention are as follows:

[0012] Based on the LLG equation of micromagnetism, various models were designed, including circular magnetic domains, lamellar magnetic domains, long columnar magnetic domains, and multi-domain hybrids. Simulations were performed under various preset parameters, including saturation magnetization, spin exchange energy, anisotropy constant, and the magnitude and direction of the external magnetic field, to identify the factor that most significantly alters the induced magnetic field. Simultaneously, the measured data was compared with the simulation results to identify the closest model. The selected model can be used to predict the microscopic magnetic structure of the research object and its response behavior in other magnetic field environments.

[0013] Specifically, the present invention provides a micromagnetic method for predicting the magnetic characteristics of a magnetic sample, characterized in that the method comprises:

[0014] (1) constructing multiple magnet models with different magnetic domain sizes, shapes, and numbers of magnetic domains, and determining the magnetic parameters of the magnet models;

[0015] (2) placing the magnet to be measured under predetermined external field conditions to obtain its magnetization intensity, and comparing the magnetization intensity with the measurement results of each model under the same external field conditions;

[0016] (3) Determine the similarity between the magnet to be tested and each model, find the model with the highest similarity, and retrieve the magnetic parameters of the model;

[0017] (4) Determine the external field conditions of the magnet to be tested in the new target environment, and substitute the external field conditions and the magnetic parameters of the model into the following formula:

[0018]

[0019] Where m is the magnetization intensity, Heff is the effective magnetic field, γ is the gyromagnetic ratio, α is the spin damping coefficient, u is the speed of the spin-polarized current, and β is a constant related to the spin transfer torque, which is used to express the influence of the spin current on the magnetic moment.

[0020] H eff =H ext +H an +H ex

[0021]

[0022] Effective magnetic field H eff It consists of three parts: exchange field H ex , anisotropy field H an and the external magnetic field H ext

[0023] (5) Solve the parameters in step (4) to obtain the magnetization intensity of the magnet to be measured under the target external field conditions.

[0024] Preferably, the method further comprises selecting a type of magnetic domain in the model for the magnet to be measured according to the material of the magnet to be measured.

[0025] Preferably, the magnet to be measured is made of stainless steel, and the maximum magnetic domain size in the constructed model is 2 μm.

[0026] Preferably, the minimum magnetic domain size in the model is 10 nm and the magnetic anisotropy constant range is about 10E 4 ~10E 6 J / m.

[0027] The method of the present invention provides guidance for the impact of weak magnetic fields on the intrinsic magnetism of samples. For example, it can provide an assessment and prediction of changes in the weak magnetism of a sample after it has been exposed to the geomagnetic field for a long time and in different regions. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 Flowchart of a micromagnetic modeling method for evaluating the intrinsic magnetic characteristics of magnetic samples

[0029] Figure 2 For: A micromagnetic modeling model initial state and spin distribution diagram

[0030] Figure 3 For: A micromagnetic modeling model evolution process 1 Unsaturated micromagnetic state and spin distribution diagram

[0031] Figure 4 For: A micromagnetic modeling model evolution process 2 unsaturated micromagnetic state and spin distribution diagram

[0032] Figure 5 For: A micromagnetic modeling model evolution process 3 unsaturated micromagnetic state and spin distribution diagram

[0033] Figure 6 For: A micromagnetic modeling model evolution process 4 unsaturated micromagnetic state and spin distribution diagram

[0034] Figure 7 For: A micromagnetic modeling model evolution process 5 unsaturated micromagnetic state and spin distribution diagram

[0035] Figure 8 The final saturation magnetization micromagnetic state and spin distribution diagram of a micromagnetic model

[0036] Figure 9 Simulation results of the 100mT magnetic field reciprocating hysteresis loop model

[0037] Figure 10 Simulation results of the 50mT magnetic field reciprocating hysteresis loop model

[0038] Figure 11 Simulation results of the 10mT magnetic field reciprocating hysteresis loop model DETAILED DESCRIPTION

[0039] The present invention will be described in further detail below with reference to the embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0040] Figure 1 Schematic flow chart of the method of the present invention.

[0041] As shown in the figure, the method of the present invention includes:

[0042] (1) constructing multiple magnet models with different magnetic domain sizes, shapes, and numbers of magnetic domains, and determining the magnetic parameters of the magnet models;

[0043] (2) placing the magnet to be measured under predetermined external field conditions to obtain its magnetization intensity, and comparing the magnetization intensity with the measurement results of each model under the same external field conditions;

[0044] (3) Determine the similarity between the magnet to be tested and each model, find the model with the highest similarity, and retrieve the magnetic parameters of the model;

[0045] (4) Determine the external field conditions of the magnet to be tested in the new target environment, and

[0046] Substitute the magnetic parameters of the model into the following formula:

[0047]

[0048] Among them, the right side of the equation consists of three terms, namely the effective term, the spin damping term, and the spin transfer torque term. The latter two terms have little effect. m is the magnetization intensity, H eff is the effective magnetic field, γ is the gyromagnetic ratio, α is the spin damping coefficient, u is the speed of the spin-polarized current, and β is a constant related to the spin transfer torque, which is used to express the influence of the spin current on the magnetic moment.

[0049] H eff =H ext +H an +H ex

[0050]

[0051] Effective magnetic field H eff It consists of three parts: exchange field H ex , anisotropy field H an and the external magnetic field H ext ,

[0052] (5) Solve the parameters in step (4) to obtain the magnetization intensity of the magnet to be measured under the target external field conditions.

[0053] A region 320 nm long, 160 nm wide, and 20 nm thick was selected as the micromagnetic research area, corresponding to the size of the region in the spin distribution map. Outside the research area is a magnetic shielding region. In the center of this region lies a magnetic domain with a radius of 50 nm and high magnetic anisotropy. The region outside this domain has zero magnetic anisotropy, allowing it to freely undergo ferromagnetic reversals along the direction of the external field.

[0054] Taking this embodiment as an example, the magnetocrystalline anisotropy parameter of the magnetic domain is k=500000 J / m, and the saturation magnetization intensity is M D = 1.4E6 A / m, and the saturation magnetization of the non-magnetic domain region is M = 8E5 A / m. The initial magnetization direction is {-100} along the negative X-axis, and {100} along the positive X-axis. The external magnetic field is applied from zero field to the maximum positive applied magnetic field B (directed along the X-axis). After reaching the maximum positive magnetic field, the applied magnetic field gradually decreases to the maximum negative field -B, and then gradually increases to the maximum positive field B. Various maximum external field B values ​​are calculated in this example: 100mT, 50mT, and 10mT.

[0055] The evolution of the microscopic magnetic structure under an external field. As mentioned above, the spin direction of the magnetic domain is in the negative X-axis direction, while the spin direction in the non-magnetic domain area outside the magnetic domain is opposite, in the positive X-axis direction.

[0056] Figures 2 to 8It shows the evolution process of microscopic spins such as magnetic domains after the application of an external field. The direction of the arrow in the figure represents the direction of the spin, and the size of the arrow represents the size of the magnetic moment. Figure 2 This is close to the sample's initial magnetic state. The circular magnetic domains have a strong magnetic moment, indicated by larger arrows, and are primarily oriented in the -X direction. The non-magnetic domains have a smaller magnetic moment, oriented in the +X direction. The interface between the magnetic domains and non-magnetic domains is clear and distinct.

[0057] Figure 3 After applying an external magnetic field, the magnetic domain wall begins to evolve and move. The magnetization direction inside the magnetic domain basically maintains the initial -X direction, while the orientation of the area outside the magnetic domain has begun to become disordered, and even two new spin "vortices" appear in the positive and negative directions of the Y axis outside the magnetic domain. Figure 4 The magnetization direction of the central magnetic domain begins to deflect, and the positions of the two vortices move. Figures 5 and 6 This is the process of the magnetization direction of the magnetic domain reversing and the external vortex continuing to evolve. The vortex slowly moves to the boundary of the region and disappears, as shown in Figure 7 As shown, the consistency of magnetization direction is achieved. Figure 8 This is the final evolution result after the final saturation magnetization, where the magnetic domain and the outside of the magnetic domain are magnetized roughly along the direction of the external field.

[0058] The following are the test results under different external magnetic fields

[0059] 1. Set the external magnetic field to 100 mT and apply the external magnetic field in the same manner as the aforementioned hysteresis loop test. Figure 9 The hysteresis loop results of the simulation calculation are shown in Figure 2. After normalizing the magnetization intensity, the maximum relative permeability or magnetic field that can exist in the model sample is 98% of the saturation magnetization and 98.86% in the reverse direction.

[0060] 2. Set the external magnetic field to 50 mT. Figure 10 The hysteresis loop of the model sample under these conditions shows that the sample's intrinsic magnetism no longer reverses with the external field. Throughout the process, the sample's magnetization remains in the positive direction, with the possible extremes of magnetization intensity reaching 97% of the saturation magnetization and 58% of the positive direction.

[0061] 3. Set the external magnetic field to 10 mT. Figure 11 The results of the hysteresis loop of the model sample under this condition. It can be seen that the change in the sample's own magnetism is much smaller than the maximum saturation magnetization, which are 21.3% and -21.94% respectively. In this case, the final micromagnetic structure and spin distribution are similar. Figure 5 As a result, the magnetization direction of the magnetic domain basically changes to the Y-axis direction. This is why in practical applications, the residual magnetic field of the sample sometimes decreases after being magnetized by an external field.

[0062] Regarding magnetic domains, taking stainless steel as an example, most of these domains originate from grain boundaries or material defects. Common stainless steel grain sizes range from 2 to 10 μm, so the model considers a maximum magnetic domain size of 2 μm. Defects in stainless steel typically originate from pores, cracks, inclusions, and copper or carbon precipitates, so the model considers a minimum magnetic domain size of 10 nm.

[0063] The shape and symmetry of stainless steel grains are closely related to the forging process. Common stainless steel grain shapes include equiaxed grains (spherical); rectangular columnar grains; long, thin needle-like grains; and lamellar, thin grains. Therefore, at least four basic magnetic domain shapes are selected for modeling.

[0064] The shape-dependent magnetic anisotropy constant in stainless steel ranges from approximately 10E4 to 10E6 J / m.

[0065] The main consideration is the ferromagnetic effect, and the ferromagnetism in stainless steel mainly comes from Fe. The magnetic exchange coupling constant of Fe varies in a small range. According to the exchange constant J(10 -9 J) plan.

[0066] Different types of stainless steel have different saturation magnetization intensities. For example, stainless steel has a saturation magnetization of 0.8x10 6 A / m, high carbon steel is 1.6x10 6 A / m, mild steel is 1.8x10 6 A / m, pure iron is 2.2x10 6 A / m. Therefore, the saturation magnetization of the magnetic domain in the model is M s According to the range of 0.8~2.2x10 6 A / m range selection.

[0067] Table 1 is an example of some models in the present invention.

[0068] Table 1 Some model examples

[0069]

[0070]

[0071] The method of the present invention will conduct actual testing on a stainless steel sample with a fixed composition and process, and compare the measured results with the simulation results of various models to find the closest model. Once the model is determined, it can be substituted into the equation of the present invention to obtain the magnetization results under any environmental conditions. The effective magnetic field consists of three parts, namely, the exchange field H ex , anisotropy field H an and the external magnetic field H extThe exchange field is related to the Bohr magneton constant μ0, the saturation magnetization Ms, and the exchange constant J, while the anisotropy field is related to the anisotropy coefficient k determined by the model. In other words, once an applicable model is established, the magnetic field magnitude of a target object under specific circumstances can be predicted.

[0072] By designing and modeling a model containing different magnetic parameters, the present invention can truly predict and simulate the changes in the magnetic properties of magnetic samples in a weak magnetic field environment, and can provide an evaluation basis for similar situations, such as the evolution of the magnetic properties of metal targets in a geomagnetic environment.

[0073] Although the principles of the present invention have been described in detail above in conjunction with the preferred embodiments of the present invention, those skilled in the art should understand that the above embodiments are merely illustrative of the present invention and are not intended to limit the scope of the present invention. The details in the embodiments do not constitute a limitation on the scope of the present invention. Without departing from the spirit and scope of the present invention, any obvious changes such as equivalent transformations and simple substitutions based on the technical solution of the present invention fall within the scope of protection of the present invention.

Claims

1. A micromagnetic method for predicting the magnetic characteristics of a magnetic sample, characterized in that: The method includes: (1) constructing multiple magnet models with different magnetic domain sizes, shapes, and numbers of magnetic domains, and determining the magnetic parameters of the magnet models; (2) placing the magnet to be measured under predetermined external field conditions to obtain its magnetization intensity, and comparing the magnetization intensity with the measurement results of each model under the same external field conditions; (3) Determine the similarity between the magnet to be tested and each model, find the model with the highest similarity, and retrieve the magnetic parameters of the model; (4) Determine the external field conditions of the magnet to be tested in the new target environment, and substitute the external field conditions and the magnetic parameters of the model into the following formula: Where m is the magnetization intensity, H eff is the effective magnetic field, γ is the gyromagnetic ratio, α is the spin damping coefficient, u is the speed of the spin-polarized current, and β is a constant related to the spin transfer torque, which is used to express the influence of the spin current on the magnetic moment. H eff =H ext +H an +H ex Effective magnetic field H eff It consists of three parts: exchange field H ex , anisotropy field H an and the external magnetic field H ext (5) Solve the parameters in step (4) to obtain the magnetization intensity of the magnet to be measured under the target external field conditions.

2. The micromagnetic method for predicting magnetic characteristics of a magnetic sample according to claim 1, characterized in that: The method further includes selecting a type of magnetic domain in the model for the magnet to be measured based on the material of the magnet to be measured.

3. The micromagnetic method for predicting magnetic characteristics of a magnetic sample according to claim 1, characterized in that: The magnet to be tested is made of stainless steel, and the maximum magnetic domain size in the constructed model is 2 μm.

4. The micromagnetic method for predicting magnetic characteristics of a magnetic sample according to claim 3, characterized in that: The minimum magnetic domain size in the model is 10nm and the magnetic anisotropy constant range is 10E 4 ~10E 6 J / m.

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