A mumax3-based hysteresis loop simulation method
By obtaining the fully saturated and zero-field-strength states of magnetic materials in Mumax3 micromagnetic simulation, and applying alternating field strength to solve the LLG equation, the iteration error problem caused by random initial state assignment is solved, and higher-precision hysteresis loop simulation is achieved.
Patent Information
- Application Number
- CN202610278074.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-03-09
- Publication Date
- 2026-06-05
AI Technical Summary
In the existing technology, the random assignment of the initial magnetic moment state in Mumax3 micromagnetic simulation calculations leads to large errors in iterative calculations and makes it impossible to accurately simulate the hysteresis loop.
By obtaining the fully saturated state of the magnetic material, a demagnetization operation is performed to obtain the zero field strength state. An alternating field strength is then applied in the zero field strength state to solve the LLG equation and obtain the hysteresis loop.
The accuracy of hysteresis loop simulation calculation has been improved, making the magnetic domain morphology more consistent with the actual physical morphology, and the magnetic domain morphology at each point of the loop has high reference value.
Smart Images
Figure CN122154219A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the technical field of simulation calculation, and in particular to a hysteresis loop simulation method based on mumax3. Background Technology
[0002] To study the magnetic properties of magnetic materials from the perspective of domain wall motion and to plot their hysteresis loops, Mumax3 micromagnetic simulation is generally used.
[0003] The most basic principle of Mumax3 micromagnetic simulation calculation is to solve the LLG equation. The LLG equation is calculated by calculating the magnetization state at each time step. It requires the magnetization state of the previous step as the initial condition to continuously iterate and solve the equation. Therefore, the initial state determines whether the calculation is accurate.
[0004] The official simulation hysteresis method provided by the software is to assign an initial magnetic moment as a random state distribution, perform energy relaxation calculations (i.e., disable precession terms in the LLG equations), use the calculation results as the initial state, gradually increase the external field strength until the material reaches saturation, and then gradually decrease the applied external magnetic field until reverse saturation is obtained to obtain the hysteresis.
[0005] This method is fast, but it differs significantly from the actual physical process. The large error is due to incorrect initial conditions, which lead to significant errors in subsequent iterative calculations. Summary of the Invention
[0006] In view of the shortcomings of the prior art, the purpose of this invention is to provide a hysteresis loop simulation method based on mumax3 to solve one or more problems in the prior art.
[0007] To achieve the above objectives, the technical solution of the present invention is as follows: A hysteresis loop simulation method based on mumax3 includes the following steps: Obtain the parameters of the magnetic material and establish a simulation model based on the parameters of the magnetic material; An electric field is applied to the simulation model to obtain the fully saturated state of the magnetic material; To obtain a zero field strength state by demagnetizing a magnetic material that is in a fully saturated state. An alternating field strength is applied to the simulation model in a zero field strength state, and the LLG equation is solved to complete the hysteresis loop simulation and obtain the hysteresis loop. The process of demagnetizing a fully saturated magnetic material to obtain a zero-field-strength state includes the following steps: A cosine field strength with a peak value that gradually decreases over time is applied under saturation conditions, and the LLG equation is solved simultaneously until the peak field strength is reduced to below a preset threshold. The corresponding magnetic moment state is then taken as the zero field strength state.
[0008] Furthermore, applying an electric field to the magnetic material in the orientation direction to obtain a fully saturated state of the magnetic material includes the following steps: Determine whether the parameters of a magnetic material include the corresponding saturation magnetic field parameter. If not, then apply an ever-increasing external field strength until the magnetic moment is completely saturated and no longer changes, and take the corresponding applied field strength as the saturation field strength of the magnetic material. If so, determine the target field strength based on the saturation field strength and apply the target strength until the magnetic moment is completely saturated and no longer changes.
[0009] Furthermore, the cosine-type field strength is: k*Hmax*cos(2ΠFt) Where k is the attenuation coefficient, Hmax is the saturation field strength, F is the demagnetization frequency, and t is time.
[0010] Furthermore, determining the target field strength based on the saturated field strength includes the following steps: Determine the material properties of magnetic materials; Match the appropriate magnification based on the material properties; The target field strength is calculated based on the magnification and saturation field strength.
[0011] Furthermore, the alternating field strength is: Hsin (2Πft) Where H is the preset working field strength, f is the preset working frequency, and t is time.
[0012] Compared with the prior art, the beneficial technical effects of the present invention are as follows: by applying a cosine field strength with decreasing peak value to a fully saturated magnetic material, the magnetic moment distribution of the demagnetized state under zero field strength that conforms to the actual physical situation is finally obtained. Using this state as the basis for Mumax3 micromagnetic simulation calculation, a higher precision hysteresis loop can be obtained. Attached Figure Description
[0013] Figure 1 The flowchart of a hysteresis loop simulation method based on mumax3 provided by an embodiment of the present invention is shown.
[0014] Figure 2 This diagram illustrates the time-varying nature of the first type of cosine field strength provided by an embodiment of the present invention.
[0015] Figure 3A schematic diagram is shown of the initial magnetic moment calculated using the random distribution of the initial state combined with the minimum energy relaxation in the prior art.
[0016] Figure 4 A schematic diagram of the initial magnetic moment obtained under the influence of a first cosine field strength according to an embodiment of the present invention is shown.
[0017] Figure 5 This diagram illustrates the time-varying nature of the second type of cosine field strength provided by an embodiment of the present invention.
[0018] Figure 6 A schematic diagram of the initial magnetic moment obtained under the influence of a second type of cosine field strength according to an embodiment of the present invention is shown. Detailed Implementation
[0019] A simulation method for hysteresis loops based on mumax3, see [link to relevant documentation]. Figure 1 This includes the following steps: S100. Obtain the parameters of the magnetic material and establish a simulation model based on the parameters of the magnetic material.
[0020] Magnetic materials include oriented silicon steel, metal thin films, alloys, and microparticles.
[0021] The acquired parameters include the exchange energy coefficient, anisotropic properties coefficient, orientation direction, model size, and mesh size. The orientation direction can be set based on the specific material properties; for example, microparticles do not require an orientation direction.
[0022] S200: Apply an electric field to the simulation model to obtain the fully saturated state of the magnetic material.
[0023] If the parameters include an orientation direction, the direction of the applied field strength must be consistent with the orientation direction of the magnetic material.
[0024] If no orientation direction is specified in the parameters, there are no restrictions on the direction of the applied field strength, or it can be set manually according to the actual situation.
[0025] A magnetic material reaching full saturation means that all the magnetic moments of the material are pointing in the same direction, and that direction is consistent with the direction of the applied electric field.
[0026] Taking grain-oriented silicon steel as an example, without the application of an external electric field, the direction of the internal magnetic moments in grain-oriented silicon steel has a certain regularity, with most magnetic moment directions being close to or at a small angle to its orientation direction. However, when it reaches full saturation, the directions of all the internal magnetic moments in the grain-oriented silicon steel are the same as the orientation direction.
[0027] As long as the applied external field strength reaches a certain intensity, the magnetic material will enter a fully saturated state. Therefore, the fully saturated state is a certain and completely definite state, so using this state as a basis can ensure the accuracy of subsequent calculations.
[0028] S300: Demagnetize a magnetic material that is in a fully saturated state to obtain a zero field strength state.
[0029] The zero-field-strength state refers to the initial magnetic moment state of a magnetic material when the applied field strength is 0. It is the magnetic moment state of the magnetic material corresponding to the origin of the hysteresis loop. Using this as the starting point for calculation, a more accurate hysteresis loop can be obtained.
[0030] Demagnetization involves gradually reducing the applied external field strength, causing the magnetic moment state of the magnetic material to gradually recover from a fully saturated state to its initial magnetic moment state.
[0031] S400: Apply an alternating field strength to the simulation model in a zero field strength state, and simultaneously perform LLG equation solving to complete the hysteresis loop simulation and obtain the hysteresis loop.
[0032] The alternating field strength is: Hsin(2πft). Where H is the preset operating field strength, f is the preset operating frequency, and t is time.
[0033] Compared to using random initial states and zero-state magnetic moments as initial states, the area enclosed by the loop obtained by the method in this embodiment is closer to the measured curve, and the magnetic domain morphology of the model at each point of the loop closely matches the actual physical morphology, which has high reference value.
[0034] In one embodiment, demagnetizing a magnetic material in a fully saturated state to obtain a zero field strength state includes the following steps: A cosine field strength with a peak value that gradually decreases over time is applied under saturation conditions, and the LLG equation is solved simultaneously until the peak field strength is reduced to below a preset threshold. The corresponding magnetic moment state is then taken as the zero field strength state.
[0035] The preset threshold is a positive number very close to 0. In this embodiment, the preset threshold is 10. -13 This is achieved by setting a preset threshold to compensate for the limitation that the peak value of a gradually decreasing cosine electric field cannot be reduced to zero. When the peak field strength decreases to the preset threshold, the default peak field strength is zero.
[0036] The cosine field strength is: k * Hmax * cos(2πFt). Where k is the attenuation coefficient, Hmax is the saturation field strength, F is the demagnetizing frequency, and t is time. A schematic diagram illustrating the peak field strength versus time can be found here. Figure 2 .
[0037] The attenuation coefficient k is set according to the material properties and the required calculation accuracy. The faster the material responds to changes in field strength, the larger the value of k should be; the higher the required calculation accuracy, the larger the value of k should be. In this embodiment, k is set between 0.6 and 0.98.
[0038] Figure 3 This is a schematic diagram of the initial magnetic moment obtained by combining the initial state random distribution with the minimum energy relaxation calculation in the existing technology. Figure 4 This is a schematic diagram of the initial magnetic moment obtained in this embodiment. It can be seen that the initial magnetic moment obtained using the minimum energy relaxation calculation has irregular domain morphology, distorted domain walls, narrow domain widths, and a large number of domain walls. This state may be the result of local energy minimization but not overall energy minimization. The initial state structure (origin of zero field strength in the initial magnetization curve) obtained using the method of this embodiment has regular domain walls, and the domain width and number are consistent with the actual physical observation results of the material, representing the result of overall energy minimization. The lap application process can better demonstrate the domain wall movement (changes in domain wall position).
[0039] In addition to using the gradually decreasing cosine field strength mentioned above for demagnetization, a gradually decreasing stepped field strength can also be used. A schematic diagram showing the peak value of this field strength changing over time can be found here. Figure 5 A schematic diagram of the corresponding initial magnetic moment can be seen. Figure 6 .
[0040] In terms of computational complexity, the stepped field strength requires less computation than the cosine field strength. However, when the external field strength is 0, the field is still in a near-saturated state without domain walls. From the simulation curves, domain walls are generated during the actual application of the stepped field strength, which is due to the discontinuity of the field strength, resulting in inconsistency between the model simulation and reality.
[0041] In one embodiment, applying an electric field to a magnetic material in the orientation direction to obtain a fully saturated state of the magnetic material includes the following steps: S310. Determine whether the parameters of the magnetic material include the corresponding saturation magnetic field parameters.
[0042] S320. If not, apply an ever-increasing external field strength until the magnetic moment is completely saturated and no longer changes, and take the corresponding applied field strength as the saturation field strength of the magnetic material.
[0043] S330. If so, determine the target field strength based on the saturation field strength and apply the target strength until the magnetic moment is completely saturated and no longer changes.
[0044] The saturation magnetic field parameter refers to the field strength of the saturation magnetic field of the corresponding magnetic material. For magnetic materials without a saturation magnetic field parameter, the saturation field strength needs to be obtained through simulation calculation; for magnetic materials with a saturation magnetic field parameter, the saturation field strength can be used directly.
[0045] In the process of determining the saturation field strength by continuously applying external field strength, the relaxed state is used as the initial calculation, thereby effectively reducing the calculation time.
[0046] In one embodiment, determining the target field strength based on the saturation field strength includes the following steps: S331. Determine the material properties of magnetic materials.
[0047] S332. Match the corresponding magnification based on the material properties.
[0048] S333. Calculate the target field strength based on the magnification and saturation field strength.
[0049] The target field strength can be set to 1.1 to 2 times the saturation field strength, depending on the material properties. The easier the material is to saturate, the closer the peak multiple should be to 1.1, and vice versa.
[0050] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0051] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.
Claims
1. A hysteresis loop simulation method based on mumax3, characterized in that, Includes the following steps: Obtain the parameters of the magnetic material and establish a simulation model based on the parameters of the magnetic material; An electric field is applied to the simulation model to obtain the fully saturated state of the magnetic material; To obtain a zero field strength state by demagnetizing a magnetic material that is in a fully saturated state. An alternating field strength is applied to the simulation model in a zero field strength state, and the LLG equation is solved to complete the hysteresis loop simulation and obtain the hysteresis loop. The process of demagnetizing a fully saturated magnetic material to obtain a zero-field-strength state includes the following steps: A cosine field strength with a peak value that gradually decreases over time is applied under saturation conditions, and the LLG equation is solved simultaneously until the peak field strength is reduced to below a preset threshold. The corresponding magnetic moment state is then taken as the zero field strength state.
2. The hysteresis loop simulation method based on mumax3 as described in claim 1, characterized in that, Applying an electric field to the magnetic material in the orientation direction to obtain a fully saturated state of the magnetic material includes the following steps: Determine whether the parameters of a magnetic material include the corresponding saturation magnetic field parameter. If not, then apply an ever-increasing external field strength until the magnetic moment is completely saturated and no longer changes, and take the corresponding applied field strength as the saturation field strength of the magnetic material. If so, determine the target field strength based on the saturation field strength and apply the target strength until the magnetic moment is completely saturated and no longer changes.
3. The hysteresis loop simulation method based on mumax3 as described in claim 2, characterized in that: The cosine-type electric field strength is: k*Hmax*cos(2ΠFt) Where k is the attenuation coefficient, Hmax is the saturation field strength, F is the demagnetization frequency, and t is time.
4. The hysteresis loop simulation method based on mumax3 as described in claim 2, characterized in that, Determining the target field strength based on the saturated field strength includes the following steps: Determine the material properties of magnetic materials; Match the appropriate magnification based on the material properties; The target field strength is calculated based on the magnification and saturation field strength.
5. The hysteresis loop simulation method based on mumax3 as described in claim 1, characterized in that, The alternating field strength is: Hsin (2Πft) Where H is the preset working field strength, f is the preset working frequency, and t is time.