Model construction and parameter optimization methods, devices, and storage media for magnetic systems

Abstract

The present application discloses a method, device and storage medium for model construction and parameter optimization of a magnetic system, relating to the technical field of magnetic materials. The method includes: obtaining Hamiltonian parameters of the magnetic system, where the Hamiltonian parameters include spin exchange interaction parameters, Landau self-energy parameters, anisotropy parameters and biquadratic exchange interaction parameters, and the Landau self-energy parameters can be used to describe spin density fluctuations, and the spin exchange interaction parameters include long-range exchange interactions; respectively constructing expressions for the spin exchange interaction energy and Landau self-energy of the magnetic system according to the spin exchange interaction parameters and Landau self-energy parameters; using the expressions for the spin exchange interaction energy and Landau self-energy to represent the total energy of the system, and constructing a magnetic Hamiltonian model of the magnetic system. The technical solution of the present application can solve the problem that the existing nearest-neighbor Heisenberg model for describing a magnetic system is difficult to reflect the spin density fluctuations and long-range interactions of magnetic materials.

Description

Technical Field

[0001] This application relates to the technical field of magnetic materials, and particularly to a method, device, and storage medium for constructing a model and optimizing parameters of a magnetic system. Background Art

[0002] Magnetic materials refer to substances that directly or indirectly generate magnetism from transition elements such as iron, cobalt, nickel, and their alloys. To study magnetic materials, it is necessary to understand the corresponding magnetic systems. Magnetic systems involve the microscopic structure, interactions of magnetic materials, as well as the response and evolution process of magnetic materials under an external magnetic field.

[0003] To study a magnetic system, it is necessary to construct a magnetic system model, namely a magnetic Hamiltonian model; the use of a magnetic system model can design magnetic materials with better performance, such as magnetic transformers, magnetic motors, magnetic storage, and magnetic photosensitive materials. Existing technologies for the construction and optimization of the magnetic Hamiltonian model mainly include the first-principles and model Hamiltonian methods. Such model construction and optimization methods mainly include the energy mapping method and the Green's function method based on the magnetic force principle. Among them, the Green's function method is a method for solving non-homogeneous differential equations with initial conditions or boundary conditions according to the magnetic force principle; for the exchange parameters of magnetic materials, the energy mapping method is usually selected for calculation. The energy mapping method mainly includes the following steps: determining the structure of magnetic atoms in the system; presetting the distribution of N magnetic moments, calculating the energy of this N-magnetic moment distribution, and subtracting them pairwise to obtain N - 1 independent energy differences; expressing the energy expressions of the N-magnetic moment distribution according to the Heisenberg model and the DM model, and outputting the relationship between the above N - 1 energy differences and the exchange parameters under the two models; finally, fitting the magnitude of the above exchange parameters by the least squares method.

[0004] The above energy mapping method and the Green's function method based on the magnetic force principle usually limit the description of the magnetic Hamiltonian model to the local short-range nearest-neighbor Heisenberg model. The nearest-neighbor Heisenberg model uses spin exchange interactions for model processing. Due to the nature of the model itself, when solving the spin exchange interaction, the model normalizes the spin, which makes it difficult for the model itself to reflect the fluctuations of the spin density. Since the model is difficult to reflect the spin density fluctuations of magnetic materials, it is difficult to accurately describe the properties of magnetic materials using existing magnetic system models, and it is even more difficult to design magnetic materials with better performance, which limits the application of magnetic materials in electricity, storage, communication, etc.

[0005] The above content is only used to assist in understanding the technical solution of this application, and does not represent an admission that the above content is prior art. Summary of the Invention

[0006] The main objective of this application is to provide a method for constructing a model of a magnetic system, a method for optimizing model parameters, a device, and a readable storage medium, aiming to solve the technical problem that existing methods are limited to the nearest-neighbor Heisenberg model, which is difficult to reflect the spin density fluctuations of magnetic materials.

[0007] To achieve the above objective, this application proposes a method for constructing a model of a magnetic system, which includes:

[0008] Obtain the Hamiltonian parameters of the magnetic system, where the Hamiltonian parameters include spin exchange interaction parameters and Landau self-energy parameters. The Landau self-energy parameters are used to describe spin density fluctuations, and the spin exchange interaction parameters include the description of long-range exchange interactions;

[0009] According to the spin exchange interaction parameters and Landau self-energy parameters, respectively construct expressions for the spin exchange interaction energy and Landau self-energy of the magnetic system;

[0010] Use the expressions of the spin exchange interaction energy and Landau self-energy to represent the total energy of the magnetic system, and construct the magnetic Hamiltonian model of the magnetic system.

[0011] In one embodiment, the Hamiltonian parameters further include anisotropy parameters and biquadratic exchange interaction parameters; the above step of respectively constructing expressions for the spin exchange interaction energy and Landau self-energy of the magnetic system according to the spin exchange interaction parameters and Landau self-energy parameters includes:

[0012] Use the spin exchange interaction parameters and spin configurations to construct an expression for the spin exchange interaction energy:

[0013]

[0014] Where, represents the spin exchange interaction energy, represents d the spin exchange interaction parameter of the and respectively represent the i th and j th spin configurations;

[0015] Use the Landau self-energy parameters and spin configurations to construct an expression for the Landau self-energy:

[0016]

[0017] Where, represents the Landau self-energy, represents d the Landau self-energy parameter of the

[0018] Construct an expression for the anisotropy energy using the anisotropy parameter and the spin configuration:

[0019]

[0020] where, represents the anisotropy energy, A represents the anisotropy parameter;

[0021] And, construct an expression for the biquadratic exchange interaction energy using the biquadratic exchange interaction parameter and the spin configuration:

[0022]

[0023] where, represents the biquadratic exchange energy, represents d the biquadratic exchange interaction parameter for the

[0024] In one embodiment, the steps of constructing the magnetic Hamiltonian model of the magnetic system using the expressions of the spin exchange interaction energy and the Landau self-energy to represent the total energy of the magnetic system include:

[0025] Construct the magnetic Hamiltonian model of the magnetic system using the spin exchange interaction energy, the anisotropy energy, the Landau self-energy, and the biquadratic exchange interaction energy of the magnetic system:

[0026]

[0027] where, represents the total energy of the magnetic system, represents the reference state energy of the magnetic system, represents the spin exchange interaction energy, represents the anisotropy energy, represents the Landau self-energy, represents the biquadratic exchange interaction energy;

[0028] Configure the orders corresponding to the spin exchange interaction parameter J , the Landau self-energy parameter L and the biquadratic exchange interaction parameter K respectively.

[0029] In one embodiment, after the steps of constructing the magnetic Hamiltonian model of the magnetic system above, the model construction method of the magnetic system further includes:

[0030] Randomly flip the number of spins of the magnetic system according to the random number flipping method to generate multiple data sets of spin configurations respectively;

[0031] According to the replica exchange simulated annealing algorithm, combined with a data set of various spin configurations and a magnetic Hamiltonian model, the optimal Hamiltonian parameters of the magnetic system are solved and obtained.

[0032] In one embodiment, the step of randomly flipping the number of spins of the magnetic system according to the random number flipping method to generate a data set of various spin configurations respectively includes:

[0033] According to the interactions included in the magnetic system, analyze the magnetic state types of the spin configurations in the magnetic system, where the magnetic state types include ferromagnetic state FM, collinear non-ferromagnetic state NFM, and non-collinear magnetic state NCM;

[0034] For the ferromagnetic state FM, generate NC FM spin configurations of the FM state by constraining the magnitude of the magnetic moment;

[0035] For the collinear non-ferromagnetic state NFM, use random numbers to flip the spin directions of the corresponding number and positions in the given number of spins to generate NC NFM spin configurations of the NFM state;

[0036] For the non-collinear magnetic state NCM, use random numbers to flip the spin directions of the corresponding number and positions in the given number of spins to generate spin configurations of the NCM state;

[0037] Sum up the spin configurations of the FM state, the spin configurations of the NFM state, and the spin configurations of the NCM state to obtain the data set of all spin configurations in the magnetic system.

[0038] In one embodiment, the step of solving and obtaining the optimal Hamiltonian parameters of the magnetic system according to the replica exchange simulated annealing algorithm, combined with a data set of various spin configurations and a magnetic Hamiltonian model, includes:

[0039] Configure the parameter optimization framework corresponding to the replica exchange simulated annealing algorithm, where the parameter optimization framework includes recursive iteration, exchange iteration, and scanning iteration, and the recursive iteration, exchange iteration, and scanning iteration are nested in sequence;

[0040] Define the temperature interval of the replica exchange simulated annealing algorithm according to the value range of each Hamiltonian parameter in the magnetic system;

[0041] Select multiple system replicas respectively, where each system replica represents a set of temperature distributions within the temperature interval, and each set of temperature distributions includes multiple different temperatures, and each temperature is used to fit a set of Hamiltonian parameter values;

[0042] In the recursive iteration, use multiple system replicas in parallel to execute the simulated annealing algorithm, and adjust the temperature distribution represented by the system replicas each time a recursive iteration is executed;

[0043] In the exchange iteration, two adjacent temperatures in the system replicas are exchanged according to a predetermined temperature exchange strategy.

[0044] In the scan iteration, the simulated annealing algorithm is executed using the data set of spin configurations and the model parameter values at the temperature, and the Hamiltonian parameter values at the temperature are updated in each scan iteration.

[0045] In one embodiment, the steps of solving for the optimal Hamiltonian parameters of the magnetic system according to the replica exchange simulated annealing algorithm, in combination with the data set of various spin configurations and the magnetic Hamiltonian model, include:

[0046] Define the orders required for the spin exchange interaction parameter, the Landau self-energy parameter, and the biquadratic exchange interaction parameter.

[0047] Determine the nearest neighbor relationship according to the distance between spins, and select spin configurations from the data set of various spin configurations according to the nearest neighbor relationship and input them into the magnetic Hamiltonian model.

[0048] Using the magnetic Hamiltonian model, calculate the total energy of the system corresponding to each set of Hamiltonian parameter values at the spin configuration and order, where each set of Hamiltonian parameter values includes the spin exchange interaction parameter value, the anisotropy parameter value, the Landau self-energy parameter value, and the biquadratic exchange interaction parameter value.

[0049] Use the weighted energy difference calculation formula as the loss function of the simulated annealing algorithm:

[0050]

[0051] Solve for the energy difference of the magnetic system; where, represents the weight factor of the i th spin configuration, represents the total energy of the system calculated by the magnetic Hamiltonian model, represents the total energy of the system calculated using the first-principles density functional theory, N represents the total number of spin configurations;

[0052] When the energy difference is minimized, select the Hamiltonian parameter values corresponding to the minimized energy difference as the optimal Hamiltonian parameters of the magnetic system.

[0053] In one embodiment, the steps of determining the nearest neighbor relationship according to the distance between spins, selecting spin configurations from the data set of various spin configurations according to the nearest neighbor relationship, and inputting them into the magnetic Hamiltonian model include:

[0054] Define the spin center of the data set and select the central spin configuration from the spin center.

[0055] Search for other spin configurations that are nearest neighbors in all directions of the spin configuration at the center of the search distance according to a predetermined search distance;

[0056] Input the central spin configuration and other nearest-neighbor spin configurations into the magnetic Hamiltonian model to solve for the total energy of the system;

[0057] After obtaining the total energy of the system by solving, use other spin configurations as the central spin configuration, and re-execute the steps of searching for other spin configurations that are nearest neighbors in all directions of the spin configuration at the center of the search distance and subsequent steps until the data set of spin configurations is traversed.

[0058] In addition, to achieve the above object, the present application also provides a device for constructing a model and optimizing parameters of a magnetic system. The device includes: a memory, a processor, and a computer program stored on the memory and executable on the processor. The computer program is configured to implement the steps of the method for constructing a model of a magnetic system provided by any one of the above technical solutions.

[0059] In addition, to achieve the above object, the present application also provides a storage medium. The storage medium is a computer-readable storage medium, and a computer program is stored on the storage medium. When the computer program is executed by a processor, it implements the steps of the method for constructing a model of a magnetic system provided by any one of the above technical solutions.

[0060] One or more technical solutions proposed by the present application have at least the following technical effects:

[0061] Obtain the spin exchange interaction parameter and the Landau self-energy parameter. The spin exchange interaction parameter can be used to describe the spin exchange interaction of a magnetic material, and the spin exchange interaction includes a long-range exchange interaction. The Landau self-energy parameter can describe the spin density fluctuation. In a magnetic system, the magnetic interaction of a magnetic material mainly comes from the nearest-neighbor exchange interaction J between local spins; in a magnetic metal material, electrons in the magnetic system have both charge degrees of freedom and spin degrees of freedom, and electrons can move freely in the magnetic system. The magnetic exchange interaction range is relatively long, and the spin density may fluctuate. Therefore, the Landau self-energy can accurately describe the spin density fluctuation. Use the spin exchange interaction parameter to construct an expression for the spin exchange interaction energy, and use the Landau self-energy parameter to construct an expression for the Landau self-energy; then use the above spin exchange interaction energy and Landau self-energy to construct a magnetic Hamiltonian model. In this way, the magnetic Hamiltonian model can consider as much as possible the magnetic system of the magnetic material with the above spin density fluctuation. Compared with the existing nearest-neighbor Heisenberg model, this magnetic Hamiltonian model can not only reflect the spin exchange interaction of the magnetic material, but also reflect the spin density fluctuation of the magnetic material, and thus can more accurately describe the interaction energy of the magnetic system and has a stronger interpretability for the energy distribution of the magnetic material. Description of the Drawings

[0062] The accompanying drawings here are incorporated into the description and form a part of this description, showing embodiments consistent with this application, and are used together with the description to explain the principles of this application.

[0063] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the following will briefly introduce the accompanying drawings required for use in the description of the embodiments or the prior art. Obviously, for those of ordinary skill in the art, other accompanying drawings can also be obtained based on these accompanying drawings without creative efforts.

[0064] Figure 1 Flow diagram of the method for constructing the model of the first magnetic system provided by the embodiment of this application;

[0065] Figure 2 For this application Figure 1 Flow diagram of a method for constructing a multi-spin energy;

[0066] Figure 3 For this application Figure 1 Flow diagram of the method for constructing the magnetic Hamiltonian model of a magnetic system provided by the shown embodiment;

[0067] Figure 4 Flow diagram of the method for constructing the model of the second magnetic system provided by the embodiment of this application;

[0068] Figure 5 For Figure 4 Flow diagram of the method for generating a data set of multi-spin configurations provided by the shown embodiment;

[0069] Figure 6 Is Figure 4 Flow diagram of the method for solving the first optimal Hamiltonian parameter provided by the shown embodiment;

[0070] Figure 7 Is Figure 4 Flow diagram of the method for solving the second optimal Hamiltonian parameter provided by the shown embodiment;

[0071] Figure 8 Is Figure 7 Flow diagram of the method for selecting and inputting a spin configuration provided by the shown embodiment;

[0072] Figure 9 Structural diagram of the model generation system of a magnetic system provided by the embodiment of this application;

[0073] Figure 10 Flow diagram of the method for optimizing the model parameters of a magnetic system provided by the embodiment of this application;

[0074] Figure 11 is a data distribution diagram of a spin configuration provided by an embodiment of the present application;

[0075] Figure 12 is a curve graph of energy versus magnetic moment provided by an embodiment of the present application;

[0076] Figure 13 is a schematic structural diagram of a model construction device for a magnetic system provided by an embodiment of the present application.

[0077] The realization of the purpose, functional characteristics and advantages of the present application will be further described with reference to the embodiments and the accompanying drawings. Detailed implementation manners

[0078] It should be understood that the specific embodiments described herein are only used to explain the technical solutions of the present application and are not used to limit the present application.

[0079] For a better understanding of the technical solutions of the present application, the following will be described in detail in conjunction with the accompanying drawings of the specification and specific implementation manners.

[0080] The main solution of the embodiment of the present application is: by obtaining the Hamiltonian parameters of the magnetic system, these Hamiltonian parameters are energy contribution parameters related to spin-dependent interactions, specifically including spin exchange interaction parameters, anisotropy parameters, Landau self-energy parameters, and biquadratic exchange interaction parameters; according to the above Hamiltonian parameters, models of the spin exchange interaction energy, anisotropy energy, Landau self-energy, and biquadratic exchange interaction energy of the magnetic system are respectively constructed; finally, using the above spin exchange interaction energy, anisotropy energy, Landau self-energy, and biquadratic exchange interaction energy to represent the total energy of the system, a magnetic Hamiltonian model of the magnetic system can be constructed.

[0081] The following technical problems exist in the prior art: The methods for constructing and parameter optimizing the magnetic Hamiltonian model provided by the prior art mainly include the energy mapping method and the Green's function method based on the magnetic force principle. The energy mapping method and the Green's function method based on the magnetic force principle are limited in describing the magnetic Hamiltonian model to the local nearest-neighbor Heisenberg model. The nearest-neighbor Heisenberg model uses spin exchange interaction for model processing. Due to the nature of the model itself, when solving the spin exchange interaction, the model must normalize the spin, which makes it difficult for the model itself to reflect the fluctuations of the spin density. Since the model is difficult to reflect the spin density fluctuations of magnetic materials, it is difficult to accurately describe the properties of magnetic materials using the existing magnetic system model, and it is even more difficult to design magnetic materials with better performance, which limits the application of magnetic materials in electricity, storage, communication, etc.

[0082] To solve the above technical problems, the present application provides a solution that uses the spin-exchange interaction parameter and the Landau self-energy parameter. The spin-exchange interaction parameter can be used to describe the spin-exchange interaction of magnetic materials, and this spin-exchange interaction includes long-range exchange interaction. The Landau self-energy parameter can describe the spin density fluctuation. In a magnetic system, the magnetic interaction of magnetic materials mainly comes from the nearest-neighbor exchange interaction between local spins; in magnetic metal materials, the electrons in the magnetic system have both charge degrees of freedom and spin degrees of freedom, and the electrons can move freely in the magnetic system. The magnetic exchange interaction range is relatively long, and there may be fluctuations in the spin density. Therefore, using the Landau self-energy can accurately describe the spin density fluctuation situation and can accurately describe the materials with spin density fluctuations.

[0083] In summary, the present application uses the spin-exchange interaction parameter to construct an expression for the spin-exchange interaction energy, and uses the Landau self-energy parameter to construct an expression for the Landau self-energy; then uses the above spin-exchange interaction energy and Landau self-energy to construct a magnetic Hamiltonian model, so that the magnetic Hamiltonian model can consider as much as possible the magnetic system of the magnetic materials with the above spin density fluctuations. Compared with the existing nearest-neighbor Heisenberg model, this magnetic Hamiltonian model can not only reflect the spin-exchange interaction of magnetic materials, but also reflect the spin density fluctuation situation of magnetic materials, and thus can more accurately describe the interaction energy of the magnetic system and has stronger interpretability for the energy distribution of magnetic materials.

[0084] It should be noted that the execution subject of this embodiment can be a computing service device with data processing, network communication, and program running functions, such as a tablet computer, a personal computer, a mobile phone, etc., or an electronic device, a computer-readable storage medium, etc. that can implement the above functions.

[0085] To better understand the above technical solution, the exemplary embodiments of the present application will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present application are shown in the drawings, it should be understood that the present application can be implemented in various forms and should not be limited by the embodiments shown here. On the contrary, these embodiments are provided to enable a more thorough understanding of the present application and to fully convey the scope of the present application to those skilled in the art.

[0086] To achieve the above technical purpose, see Figure 1 , Figure 1 This application provides a method for constructing a model of a magnetic system. To achieve the above purpose, the present application proposes a method for constructing a model of a magnetic system. The method for constructing a model of a magnetic system includes:

[0087] S110: Obtain the Hamiltonian parameters of the magnetic system, where the Hamiltonian parameters include spin-exchange interaction parameters, anisotropy parameters, Landau self-energy parameters, and biquadratic exchange interaction parameters. To implement the technical solution of this application, at least the spin-exchange interaction parameters and Landau self-energy parameters are selected in this application. The Landau self-energy parameters are used to describe spin density fluctuations, and the spin-exchange interaction parameters include long-range exchange interactions.

[0088] In the prior art, the description of the magnetic system mainly focuses on the nearest-neighbor Heisenberg model, that is, it mainly includes the nearest-neighbor spin-exchange interaction and anisotropy, which makes it difficult for the prior art to accurately describe various magnetic interactions contained in the magnetic system. However, in the embodiments of this application, by obtaining the Hamiltonian parameters of the magnetic system, including spin-exchange interaction parameters, anisotropy parameters, Landau self-energy parameters, and biquadratic exchange interaction parameters, these Hamiltonian parameters can be used to describe spin-exchange interaction, anisotropy, Landau self-energy, and biquadratic exchange interaction respectively, so as to construct a magnetic Hamiltonian model of the magnetic system that is as general as possible, making the constructed magnetic Hamiltonian model able to describe various interaction energies of the magnetic system as comprehensively and accurately as possible.

[0089] S120: According to the spin-exchange interaction parameters, anisotropy parameters, Landau self-energy parameters, and biquadratic exchange interaction parameters, construct the spin-exchange interaction energy, anisotropy energy, Landau self-energy, and biquadratic exchange interaction energy of the magnetic system respectively. Among them, at least the spin-exchange interaction energy and Landau self-energy need to be constructed in this application. The spin-exchange interaction energy and Landau self-energy constructed by the above spin-exchange interaction parameters and Landau self-energy parameters can solve the problem that the nearest-neighbor Heisenberg model describing the magnetic system in the prior art is difficult to reflect the spin density fluctuations and long-range interactions of magnetic materials.

[0090] The above spin-exchange interaction parameters, anisotropy parameters, Landau self-energy parameters, and biquadratic exchange interaction parameters can be used to describe spin-exchange interaction, anisotropy energy, Landau self-energy, and biquadratic exchange interaction respectively. Therefore, by using the above spin-exchange interaction parameters, anisotropy parameters, Landau self-energy parameters, and biquadratic exchange interaction parameters, the spin-exchange interaction energy, anisotropy energy, Landau self-energy, and biquadratic exchange interaction energy of the magnetic system can be constructed respectively. Specifically, the spin-exchange interaction parameters combined with the spin configuration can construct a model of the spin-exchange interaction energy; the anisotropy parameters combined with the spin configuration can construct a model of the anisotropy energy; the Landau self-energy parameters combined with the spin configuration can construct a model of the Landau self-energy; the biquadratic exchange interaction parameters combined with the spin configuration can construct a model of the biquadratic exchange interaction energy. For the specific construction methods of various magnetic exchange interaction energies, see Figure 2The technical steps provided by the illustrated embodiments.

[0091] S130: Express the total energy of the magnetic system using the spin-exchange interaction energy, anisotropy energy, Landau self-energy, and biquadratic exchange interaction energy of the magnetic system, and construct a magnetic Hamiltonian model of the magnetic system. To implement the technical solution of this application, in the magnetic Hamiltonian model of the magnetic system constructed above, the total energy of the system includes at least the spin-exchange interaction energy and the Landau self-energy.

[0092] The magnetic system includes magnetic insulators and some semiconductors, magnetic metal materials, low-dimensional magnetic materials, and magnetic materials of transition metals. For magnetic insulators and some semiconductors: the magnetic moments are highly localized, and the sources of magnetic interactions in the magnetic system mainly come from the spin-exchange interactions between local spins; in magnetic metal materials, the range of magnetic exchange interactions is relatively long, and there are fluctuations in the spin density, so it is necessary to introduce the Landau self-energy to describe; in low-dimensional magnetic materials, there is strong anisotropy energy in the magnetic system; in magnetic materials of transition metals, there is a biquadratic exchange interaction caused by electron transitions. The technical solution of this application uses the spin-exchange interaction energy, anisotropy energy, Landau self-energy, and biquadratic exchange interaction energy to express the total energy of the magnetic system. The magnetic Hamiltonian model constructed in this way can describe various magnetic systems as comprehensively and accurately as possible, and describe various interactions of the magnetic system as accurately as possible.

[0093] In summary, the technical solution provided by the embodiments of this application constructs a magnetic Hamiltonian model including the spin-exchange interaction energy, anisotropy energy, Landau self-energy, and biquadratic exchange interaction energy, which can describe the spin-exchange interaction, anisotropic interaction, Landau self-energy, and biquadratic exchange interaction; therefore, the magnetic Hamiltonian model can consider the magnetic systems of the above various materials as much as possible, construct a spin Hamiltonian model as universal as possible, and cover the interaction energy that can accurately describe the magnetic system. In addition, the magnetic Hamiltonian model constructed by the embodiments of this application introduces the Landau self-energy and biquadratic exchange interaction energy, which can describe the fluctuation of the spin density and the energy contribution caused by electron transitions.

[0094] Among them, in an exemplary embodiment, refer to Figure 2 , the above step S120: The steps of constructing the spin-exchange interaction energy, anisotropy energy, Landau self-energy, and biquadratic exchange interaction energy of the magnetic system according to the spin-exchange interaction parameter, anisotropy parameter, Landau self-energy parameter, and biquadratic exchange interaction parameter respectively, include:

[0095] S121: Use the spin-exchange interaction parameter and the spin configuration to construct an expression for the spin-exchange interaction energy:

[0096]

[0097] Among them, represents the spin-exchange interaction energy, represents d the spin-exchange interaction parameter of the -th nearest neighbor, and i respectively represent the j -th and i -th spin configurations. The j -th and -th spin configurations cannot be the same spin configuration. In the expression of this spin-exchange interaction energy, is the tensor of , representing the magnetic exchange interaction. can be written in the form of the diagonal term and the non-diagonal term

[0098]

[0099] Among them, A represents the anisotropy parameter. The J and Γ with subscripts are the matrix elements of the tensor . The diagonal term of this tensor is related to the nearest-neighbor exchange interaction in the ordinary Heisenberg model, and the non-diagonal term of this tensor is related to the DMI interaction. Because there is a DMI interaction in the symmetry-broken magnetic system, it plays an important role in the description of the ground state of the magnetic system. Therefore, using this spin-exchange interaction parameter can reflect the DMI interaction. DMI is a magnetic interaction between spin magnetic moments. Generally, magnetic materials usually have ferromagnetism or antiferromagnetism. In these materials, the magnetic moments are arranged parallel or antiparallel, and the interaction between the magnetic moments is also called ferromagnetic exchange interaction or Heisenberg exchange interaction.

[0100] In addition, usually, the -th and -th spin configurations and

[0101] S122: Use the anisotropy parameter and the spin configuration to construct an expression for the anisotropy energy:

[0102]

[0103] where, represents the anisotropy energy, A represents the anisotropy parameter, which is also a 3 × 3 tensor, and its expansion form is as follows:

[0104]

[0105] A represents the anisotropy parameter. Similarly, the anisotropy parameter represents the anisotropic interaction. Therefore, using the anisotropy parameter and the spin configuration, the anisotropy energy can be constructed. Using the anisotropy parameter can simulate the anisotropy energy. For low-dimensional magnetic materials, there is a strong anisotropy energy in the magnetic system , so by using the anisotropy parameter and the spin configuration to construct the anisotropy energy, the low-dimensional magnetic materials can be accurately described using this anisotropy energy.

[0106] S123: Use the Landau self-energy parameter and the spin configuration to construct an expression for the Landau self-energy:

[0107]

[0108] where, represents the Landau self-energy, represents d -order Landau self-energy parameter, and this is a scalar. The Landau self-energy can be constructed by combining the Landau self-energy parameter and the spin configuration. Because in magnetic metal materials, the electrons in the magnetic system have both charge degrees of freedom and spin degrees of freedom, the electrons can move freely in the magnetic system, the range of the magnetic exchange interaction is relatively long, and the spin density may fluctuate. Therefore, in order to accurately describe the properties of magnetic metal materials, the embodiments of the present application construct the Landau self-energy to describe magnetic metal materials.

[0109] Moreover,

[0110] S124: Use the biquadratic exchange interaction parameter and the spin configuration to construct an expression for the biquadratic exchange interaction energy:

[0111]

[0112] where, represents the biquadratic exchange energy, represents d -order nearest-neighbor biquadratic exchange interaction parameter, It is also a scalar that can represent the biquadratic exchange interaction. In magnetic materials containing transition metals, there is a biquadratic exchange interaction caused by electron transitions, and this interaction can induce some topological phase transitions. Therefore, in the embodiments of this application, the biquadratic exchange interaction parameter is used to construct the biquadratic exchange interaction energy, which can accurately describe the properties of magnetic materials containing transition metals.

[0113] In the technical solutions provided by the embodiments of this application, the spin exchange interaction parameter, the anisotropy parameter, the Landau self-energy parameter, and the biquadratic exchange interaction parameter are respectively used to describe the spin exchange interaction, the anisotropy interaction, the Landau self-energy, and the biquadratic exchange interaction. Therefore, by using the spin exchange interaction parameter, the anisotropy parameter, the Landau self-energy parameter, and the biquadratic exchange interaction parameter respectively, and combining the above formulas, the spin exchange interaction energy, the anisotropy energy, the Landau self-energy, and the biquadratic exchange interaction energy of the magnetic system can be constructed respectively. Among them, the spin exchange interaction energy can be used to describe the magnetism of magnetic insulators and some semiconductors; the anisotropy energy can be used to describe the magnetism of low-dimensional magnetic materials; the Landau self-energy can be used to describe the magnetism of magnetic metal materials; the biquadratic exchange interaction energy can be used to describe magnetic materials containing transition metals. In addition, the above Hamiltonian parameters can describe various interactions of the magnetic system as accurately as possible, including long-range interactions, which mainly depend on the i-th and the j spin configurations and values. If the interaction range between two spin configurations is long, that is, the distance between spins is long, it can also describe the long-range interaction between the above spin configurations. The long-range interaction means that the distance between these two spins is long. If the distance is the nearest neighbor, it is not a long-range interaction. Specifically, d order nearest neighbor, d d = 1 represents the nearest neighbor, d = 2 represents the next-nearest neighbor, d d = 3 represents the next-next-nearest neighbor, and so on, d = n d represents the n-th order nearest neighbor. When d the value is relatively large, it is long-range. And whether the specific spins are in long-range interaction depends on the stacking mode and lattice constant of the actual crystal material, and the value needs to be determined according to the properties of different materials.

[0114] and can both describe the fluctuations of the spin density using this spin exchange interaction parameter; It can also reflect the DMI interaction, thereby describing a magnetic system with symmetry breaking.

[0115] In summary, the Hamiltonian model constructed in this application considers the above possible magnetic systems and constructs a spin Hamiltonian model that is as general as possible, covering the interaction energy that can accurately describe the magnetic system.

[0116] Among them, in one embodiment, referring to Figure 3 , the above step S130: using the spin exchange interaction energy, anisotropy energy, Landau self-energy, and biquadratic exchange interaction energy of the magnetic system to represent the total energy of the magnetic system, and constructing the magnetic Hamiltonian model of the magnetic system includes:

[0117] S131: Using the spin exchange interaction energy, anisotropy energy, Landau self-energy, and biquadratic exchange interaction energy of the magnetic system, construct the magnetic Hamiltonian model of the magnetic system:

[0118]

[0119] Where represents the total energy of the magnetic system, and the total energy of this magnetic system can be calculated based on the first-principles density functional theory; represents the reference state energy of the magnetic system, that is, the system energy independent of spin; represents the energy caused by the spin exchange interaction, that is, the spin exchange interaction energy; represents the energy caused by anisotropy, that is, the anisotropy energy; represents the Landau self-energy; represents the energy caused by the biquadratic exchange interaction, that is, the biquadratic exchange interaction energy.

[0120] Of course, in order to reflect the spin exchange interaction and describe the spin density fluctuation in the magnetic system, the simplest form of the above magnetic Hamiltonian model includes: .

[0121] S132: Configure the orders of the spin exchange interaction parameter J , the Landau self-energy parameter L , and the biquadratic exchange interaction parameter K respectively.

[0122] The spin exchange interaction J , the Landau self-energy parameter L , and the biquadratic exchange interaction parameter K can be configured with corresponding orders; the orders of the above interactions are respectively used to consider the range of action of the spin exchange interaction, the accuracy of the Landau self-energy correction, and the range of action of the biquadratic exchange interaction in the magnetic Hamiltonian model. The specific form of the Hamiltonian here determines the basic framework for subsequent model optimization.

[0123] In the technical solution provided by the embodiment of the present application, represents the energy caused by spin-exchange interaction. Since the magnetic interaction between magnetic insulators and some semiconductors mainly comes from spin-exchange interaction J , therefore it can describe the magnetic properties of magnetic insulators and some semiconductors; represents the energy caused by anisotropy. Since there is a strong anisotropy energy in low-dimensional magnetic materials A , therefore it can describe the magnetic properties of low-dimensional magnetic materials; represents the Landau self-energy, which can describe the long-range magnetic exchange interaction and spin density fluctuation in magnetic metal materials; represents the energy caused by biquadratic exchange, which can describe the magnetic properties of magnetic materials containing transition metals with biquadratic exchange interaction caused by electron transition. In addition, the above can also describe the magnetic system with symmetry breaking of DMI interaction. In summary, the Hamiltonian model constructed by the technical solution of the present application can comprehensively consider the above possible magnetic systems, construct a spin Hamiltonian model as general as possible, and cover the interaction energy that can accurately describe the magnetic system.

[0124] The technical solution provided by the present application, in addition to constructing the magnetic Hamiltonian model of the magnetic system, also needs to generate a data set of spin configurations and optimize the magnetic Hamiltonian model.

[0125] Specifically, refer to Figure 4 , in an embodiment, after the step S130 of the model construction method of the magnetic system: the step of constructing the magnetic Hamiltonian model of the magnetic system, the model construction method of the magnetic system further includes:

[0126] S140: Randomly flip the number of spins of the magnetic system according to the random number flipping method to generate multiple data sets of spin configurations respectively.

[0127] The existing method for optimizing the model parameters of a magnetic system is mainly the energy mapping method. This energy mapping method optimizes the system parameters based on the first principles and the model Hamiltonian. However, the energy mapping method depends on the artificial selection of spin configurations, which will result in fewer spin configurations and it is difficult to cover the excited states of the spin system. To solve this problem, the embodiments of the present application flip the number of spins of the magnetic system according to the random number flipping method to generate a data set of various spin configurations. Generally, as long as the random numbers are sufficient, all the spins of the spin configuration can be covered, effectively avoiding the deviation of parameter fitting caused by the artificial intervention in the selection of spin configurations. The data set of spin configurations generated by the embodiments of the present application includes the ground state and various possible high-energy states, considering the influence of various energy states on the model parameters of the magnetic system, and can cover the excited states of the spin system.

[0128] S150: According to the replica exchange simulated annealing algorithm, combined with the data set of various spin configurations and the magnetic Hamiltonian model, solve to obtain the optimal Hamiltonian parameters of the magnetic system.

[0129] The replica exchange simulated annealing algorithm provided by the embodiments of the present application, which combines the data set of various spin configurations and the above magnetic Hamiltonian model to solve the method for the optimal Hamiltonian parameters of the magnetic system, substitutes the spin configurations in the data set into the magnetic Hamiltonian model, specifically substitutes them into Figure 2 the steps S121 - S124 provided in the illustrated embodiment, and sets the order of each Hamiltonian parameter. By using this replica exchange simulated annealing algorithm to select system replicas (there are multiple combinations of Hamiltonian parameters in the system replicas), the above magnetic Hamiltonian model can be operated in parallel using the system replicas, so as to obtain the total energy of multiple magnetic systems, and then subtract the total energy obtained according to the first principles density functional theory to construct a loss function of the energy difference. When the energy difference is the smallest, the Hamiltonian parameters corresponding to the smallest energy difference are the optimal Hamiltonian parameters.

[0130] It should be noted that the Replica Exchange Simulated Annealing (RESA) is a variant of the simulated annealing algorithm, mainly used to solve complex optimization problems, especially those with multiple local optimal solutions. In the traditional simulated annealing algorithm, the system starts from an initial state and conducts random searches at a series of temperatures, accepting inferior solutions with a certain probability to avoid being trapped in local optima. RESA, however, introduces the concept of "replicas", and further improves the global search ability by exchanging states among multiple replicas at different temperatures. In this application, for the purpose of describing the magnetic system, the "replicas" are uniformly named system replicas. In the embodiments of this application, since the Hamiltonian parameters include multiple ones, in order to avoid being trapped in local optima, the replica exchange simulated annealing algorithm is selected to extract multiple system replicas and exchange the Hamiltonian parameters in the system replicas, so as to achieve the purpose of rationalizing the temperature distribution and obtaining the optimal Hamiltonian parameters.

[0131] Among them, regarding the method of using the random number flipping method to flip the number of spins in the magnetic system to generate a data set, please refer to Figure 5 . In one embodiment, the above step S140: The step of randomly flipping the number of spins in the magnetic system according to the random number flipping method to generate data sets of various spin configurations respectively includes:

[0132] S141: Analyze the magnetic state types of the spin configurations in the magnetic system according to the interactions included in the magnetic system, where the magnetic state types include ferromagnetic state FM, collinear non-ferromagnetic state NFM, and non-collinear magnetic state NCM.

[0133] Different magnetic state types correspond to different interactions in the magnetic Hamiltonian model. Generally, in the magnetic Hamiltonian model, the anisotropy parameter A mainly depends on the data set of the non-collinear magnetic state NCM; the spin exchange parameter J mainly depends on the data set of the collinear non-ferromagnetic state NFM, while the Landau parameter L mainly depends on the data set of the collinear ferromagnetic state FM, and the biquadratic exchange interaction parameter K mainly depends on the data set of the non-collinear data set and the

[0134] S142: For the ferromagnetic state FM, generate NC by constraining the magnitude of the magnetic moment FMFM state spin configurations. The spin configuration of the ferromagnetic state FM can generate NC by a method that only requires the magnitude of the magnetic moment. FM FM state spin configurations with different spin magnitudes.

[0135] S143: For the collinear non-ferromagnetic state NFM, use random numbers to flip the spin directions of the corresponding number and positions in the given number of spins to generate NC NFM NFM state spin configurations. In the embodiments of the present application, by generating random numbers and flipping i spins in the above-mentioned given number of spins according to the random numbers, NFM state spin configurations can be generated.

[0136] S144: For the non-collinear magnetic state NCM, use random numbers to flip the spin directions of the corresponding number and positions in the given number of spins to generate NCM state spin configurations. Similarly, by randomly flipping the spin directions of the corresponding number and positions in the given number of spins, NCM state spin configurations with different spins can be generated.

[0137] S145: Sum up the FM state spin configurations, NFM state spin configurations, and NCM state spin configurations to obtain the data set of all spin configurations in the magnetic system.

[0138] In the embodiments of the present application, spin configurations are generated by the random number method to generate a data set of spin configurations. Assume that for a magnetic system with a given number of spins it is expected to generate spin configurations. For the ferromagnetic state FM, generate NC FM FM state spin configurations with spins; for the collinear non-ferromagnetic state NFM, generate NC NFM NFM state spin configurations with spins; for the non-collinear magnetic state NCM, generate NCM state spin configurations with spins; then the finally generated data set of spin configurations contains the total number of spins as follows: .

[0139] Since random numbers are used to flip the spins, as long as the random numbers are sufficient, this data set can cover the excited state configurations, solving the problem that the existing Green's function method based on the magnetic force principle depends on the ground state selection and is difficult to accurately describe the excited state, and does not depend on manual configuration to select spin configurations, and the generated spin configurations can meet the requirements of the magnetic Hamiltonian model.

[0140] In addition, as Figure 6As shown, for the method of solving the optimal Hamiltonian model of a magnetic system using the replica exchange simulated annealing algorithm, in one embodiment, the above step S150: The step of solving for the optimal Hamiltonian parameters of the magnetic system according to the replica exchange simulated annealing algorithm, in combination with a data set of various spin configurations and a magnetic Hamiltonian model, includes:

[0141] S151: Configure the parameter optimization framework corresponding to the replica exchange simulated annealing algorithm, where the parameter optimization framework includes recursive iteration, exchange iteration, and scan iteration; the recursive iteration, exchange iteration, and scan iteration are nested in sequence.

[0142] The replica exchange simulated annealing algorithm (RESA), also often referred to as parallel tempering or multiple Markov chain Monte Carlo, is an efficient global optimization algorithm designed to overcome the problem that traditional simulated annealing algorithms are prone to getting trapped in local optima in complex energy landscapes by simultaneously simulating multiple system replicas (each replica has a different temperature). The main operating steps of the replica exchange simulated annealing algorithm are as follows: Initialize multiple temperature replicas, and each replica runs under different temperature parameter settings. Each independent replica performs simulated annealing simulation. After a certain number of periodic steps, two replicas are selected to attempt to exchange states (such as temperature). The acceptance probability of the exchange is usually based on the Metropolis criterion, ensuring that the entire process satisfies the detailed balance condition and the correctness of the statistical results.

[0143] For the parameter optimization framework of the replica exchange simulated annealing algorithm in the embodiments of this application, see Figure 9 , and the parameter optimization framework includes recursive iteration, exchange iteration, and scan iteration. These three iterations are the three-layer loop logic of the replica exchange simulated annealing algorithm: the recursive loop (recursive iteration), the outermost loop that adjusts the temperature distribution, which can rationalize the temperature distribution and make the next-layer exchange loop more reasonable; the exchange loop (exchange iteration), the loop that exchanges adjacent temperatures, which can avoid being trapped in local minima; the scan loop (scan iteration), the innermost loop, which updates all parameters in each loop, executes a simulated annealing algorithm once, and obtains the parameters that minimize the objective function. Among them, the scan loop includes a simulated annealing solver, a minimum energy solver, and a Hamiltonian energy solver. The three solvers are carried out in sequence to solve for the Hamiltonian parameters. For the specific steps of optimizing the Hamiltonian parameters, see Figure 6 .

[0144] S152: Define the temperature interval of the replica exchange simulated annealing algorithm according to the value range of each Hamiltonian parameter in the magnetic system.

[0145] The Hamiltonian parameters in the embodiments of the present application include spin-exchange interaction parameters, anisotropy parameters, Landau self-energy parameters, and biquadratic exchange interaction parameters. Different Hamiltonian parameters have different value ranges, and temperature represents a set of values of Hamiltonian parameters. Therefore, it is necessary to delimit a temperature interval within the value ranges of the above-mentioned various Hamiltonian parameters, that is, the value space of the above-mentioned set of Hamiltonians. Specifically, the present application can define a temperature exchange strategy through relevant parameters, specifically defining the highest temperature and the lowest temperature through relevant parameters. The highest temperature is the highest value of a set of Hamiltonian parameter values, and the lowest temperature is the lowest value of a set of Hamiltonian parameter values. The range between the highest temperature and the lowest temperature is the temperature interval.

[0146] S153: Select multiple system replicas respectively, where each system replica represents a set of temperature distributions within the temperature interval. Each set of temperature distributions includes multiple different temperatures, and each temperature is used to fit a set of Hamiltonian parameter values.

[0147] The temperature distribution is to select a temperature region of a certain size within the temperature interval defined by the replica exchange simulated annealing algorithm described above. This temperature region includes multiple different temperatures, that is, it contains multiple sets of different Hamiltonian parameter values.

[0148] S154: In the recursive iteration, use multiple system replicas in parallel to execute the simulated annealing algorithm, and adjust the temperature distribution represented by the system replicas each time a recursive iteration is performed.

[0149] The recursive loop is the outermost layer of the replica exchange simulated annealing algorithm. The present application needs to define the number of recursive iterations to be performed through certain parameters. Each recursive iteration requires adjustment of the temperature distribution. Here, the adjustment step size can be selected. Each time a recursive iteration is performed, a certain step size is moved within the temperature interval, and different temperature regions are selected to obtain different system replicas. In this way, the simulated annealing algorithm is executed using multiple system replicas in parallel during the recursive iteration. Each system replica contains multiple sets of different Hamiltonian parameter values, and during the scanning iteration included in the recursive iteration, the simulated annealing algorithm is executed using the Hamiltonian parameter values.

[0150] S155: In the exchange iteration, exchange two adjacent temperatures in the system replicas according to a predetermined temperature exchange strategy. During each exchange iteration, the temperature exchange strategy is defined by relevant parameters. Executing this temperature exchange strategy performs an exchange operation on two adjacent temperatures or temperatures separated by a predetermined value, thereby avoiding being trapped in a local minimum.

[0151] S156: In the scanning iteration, perform the simulated annealing algorithm using the data set of spin configurations and the values of the model parameters at the temperature, and update the values of the Hamiltonian parameters at the temperature in each scanning iteration. The values of the model parameters at the temperature are also the Hamiltonian parameter values in this temperature distribution. The scanning loop is the innermost layer of the replica exchange simulated annealing algorithm. In each scanning iteration, all the Hamiltonian parameters of this layer are executed, so as to perform a simulated annealing algorithm to obtain the minimized objective function value. For the steps of performing the simulated annealing algorithm to obtain the minimized objective function parameters, see Figure 7 and Figure 8 .

[0152] The technical solution provided by the embodiment of the present application uses the replica exchange simulated annealing method, which can efficiently fit the model parameters, ensure that the model parameters are the global optimal solution, and the obtained model parameters consider the comprehensive influence of various magnetic states and various magnetic interactions.

[0153] Specifically, as can be seen from the embodiment shown in Figure 9 , the embodiment of the present application selects the REMPOS software to perform the above operations. The software includes an input layer 100, a function layer 200, and an output layer 300; among them, the input layer inputs an execution control file, an index mapping file, a spin distance matrix file, a configuration energy file, and a configuration spin file; among them, the spin distance matrix file inputs the distances between spin configurations, and the configuration spin file inputs spin configurations. The configuration energy file inputs the interaction energies corresponding to various Hamiltonian model parameters. The function layer 200 includes an input acquisition module 201, a random number acquisition module 202, a recursive loop module 203, and a resource release module 204. The output layer includes phase diagram simulation data, energy optimization results, optimization paths, and resume calculation parameters.

[0154] Specifically, the parameter optimization framework corresponding to the replica exchange simulated annealing algorithm adopted by the embodiment of the present application is controlled by the parameters in the INPUT file, which involves the control of recursive iteration, exchange iteration, and scanning iteration parameters. Among them, the "n_scheme" parameter defines the temperature exchange strategy, indicating how many temperature points are exchanged at intervals each time. The highest temperature is defined by the parameter "beta_min", and the lowest temperature is defined by the "beta_max". The "n_recursion" parameter defines how many rounds of recursive iteration are performed in total ( C recursion ), which is the outermost loop parameter, and the temperature distribution is adjusted in each recursive iteration. The "stop_recursion" parameter defines how many rounds to iterate until the temperature distribution is no longer updated. The value of this parameter is less than the value of "n_recursion". "n_exchange1" and "n_exchange2" define the number of iterations of the attempted exchange ( C exchange), in each exchange iteration, two temperatures in the temperature exchange strategy defined by the "n_scheme" parameter attempt to exchange. The "n_sweep1" and "n_sweep2" parameters define the number of sweep iterations ( C sweep ), in each sweep iteration, attempt updates of all Hamiltonian parameters are performed, and a complete CSA calculation is carried out. The "n_equil1" and "n_equil2" parameters define the number of thermal equilibration times before performing the formal calculation ( C equip ), in each iteration, attempt updates of all parameters are performed once. In summary, the number of parameter updates is C = C recursion × C exchange × C sweep + C equip .

[0155] In one embodiment, as Figure 7 shown, the above step S150: According to the replica exchange simulated annealing algorithm, combining a data set of various spin configurations and a magnetic Hamiltonian model, the step of solving for the optimal Hamiltonian parameters of the magnetic system includes:

[0156] S157: Define the orders required for the spin exchange interaction parameter, the Landau self-energy parameter, and the biquadratic exchange interaction parameter.

[0157] As described above, the spin exchange interaction J , the Landau self-energy coefficient L , the biquadratic exchange interaction parameter K can configure the corresponding orders to consider the range of action of the spin exchange interaction in the Hamiltonian model, the accuracy of the Landau self-energy correction, and the range of action of the biquadratic exchange interaction.

[0158] S158: Determine the nearest neighbor relationship according to the distance between spins, select spin configurations from the data set of various spin configurations according to the nearest neighbor relationship, and input them into the magnetic Hamiltonian model. The nearest neighbor relationship can be determined by using the K-nearest neighbor search algorithm, that is, transforming the data set of various spin configurations into a three-dimensional spin configuration interval. Since the spin configuration is represented as a 1*3 vector in three-dimensional space, the data set of spin configurations can be transformed into a three-dimensional spin configuration interval. By selecting any spin configuration S i in this spin configuration region, and then using the K-nearest neighbor search algorithm to find the spin configuration with the closest distance between spins in this three-dimensional spin configuration interval S j, select the spin configuration through the above method and input it into the magnetic Hamiltonian model. The nearest-neighbor relationship and the representation by the above d order are not elaborated here.

[0159] S159: Use the magnetic Hamiltonian model to calculate the total energy of the system corresponding to each set of Hamiltonian parameter values under the spin configuration and order respectively. Among them, each set of Hamiltonian parameter values includes the spin exchange interaction parameter value, the anisotropy parameter value, the Landau self-energy parameter value, and the biquadratic exchange interaction parameter value.

[0160] After selecting the spin configuration and determining the order of the corresponding Hamiltonian parameters, input the spin configuration and order into the above magnetic Hamiltonian model. Then, both the spin configuration and order are known quantities. Next, call each set of Hamiltonian parameters and input them into the above magnetic Hamiltonian model, and the spin exchange interaction energy, anisotropy energy, Landau self-energy, and biquadratic exchange interaction energy of the magnetic system can be calculated respectively, and then the total energy of the magnetic system can be calculated.

[0161] S1510: Use the first-principles density functional theory to calculate the total energy of the magnetic system. The density functional, i.e., the DFT theory, is a kind of first-principles. This density functional theory means that the chemical properties are determined by the electron cloud density, and it is not necessary to solve the orbitals of each atom. The total energy of the system is strictly calculated through the KS equation. The specific method of calculating the total energy of the system by the first-principles density functional theory is known and will not be elaborated here.

[0162] S1511: Use the weighted energy difference calculation formula as the loss function of the simulated annealing algorithm

[0163]

[0164] , and solve the energy difference of the magnetic system; among them, represents the weight factor of the i-th spin configuration, represents the total energy of the system calculated by the magnetic Hamiltonian model, represents the total energy of the system calculated by using the first-principles density functional theory, N represents the total number of spin configurations.

[0165] Using this energy difference calculation formula as the loss function of the simulated annealing algorithm, the total energy of the system calculated by the magnetic Hamiltonian model is closer to the total energy of the system calculated by the first-principles density functional theory , which indicates that the calculation accuracy of this magnetic Hamiltonian model is higher and it can describe the magnetic system more accurately.

[0166] S1512: When the energy difference is minimized, select the Hamiltonian parameter value corresponding to the minimized energy difference as the optimal Hamiltonian parameter of the magnetic system.

[0167] In the embodiments of the present application, an optimization framework is configured according to the magnetic Hamiltonian model and the data set of spin configurations, and the optimization convergence criterion is determined by the data volume of the data set and the number of model parameters. The model parameters are based on the replica exchange simulated annealing algorithm and can adaptively solve the optimal solution of the parameters of a given model. The parameter solution can be directly used to analyze the interactions of the magnetic system.

[0168] Specifically, referring to Figure 8 , in one embodiment, the above step S158: determining the nearest neighbor relationship according to the distance between spins, and selecting the spin configuration from the data set of various spin configurations according to the nearest neighbor relationship and inputting it into the magnetic Hamiltonian model includes:

[0169] S1581: Define the spin lattice and the spin center of the data set, and use the spin lattice to select the central spin configuration from the spin center.

[0170] S1582: Search for other spin configurations neighboring in each direction of the spin lattice according to a predetermined search distance. Of course, the predetermined search distance can be set according to actual needs. If the nearest neighboring spin configurations are selected, the search distance can be set as small as possible. The algorithm used here preferably selects the K-nearest neighbor search algorithm.

[0171] S1583: Input the central spin configuration and other neighboring spin configurations into the magnetic Hamiltonian model to solve the total energy of the system.

[0172] After the total energy of the system is solved, use other spin configurations as the central spin configuration and re-execute the steps of searching for other spin configurations neighboring in each direction of the spin lattice according to the predetermined search distance and subsequent steps until the data set of spin configurations is traversed.

[0173] The technical solution provided by the embodiments of the present application is to transform the data set of spin configurations into a three-dimensional spin configuration interval. Since the spin configuration is embodied as a 1*3 vector in three-dimensional space, the data set of spin configurations can be transformed into a three-dimensional spin configuration interval. Define a spin center in the spin configuration region corresponding to the data set, and define a spin lattice. The spin lattice is a three-dimensional structure. First, the spin lattice frames the spin configuration at the spin center , and through the K-nearest neighbor algorithm, search for other spin configurations adjacent in each direction according to a predetermined search radius , and finally input the above spin configurations and into the magnetic Hamiltonian model, for example, substitute them into the expression of the spin exchange interaction energy.

[0174] Specifically, in the application of related parameter optimization of magnetic systems, define the number of input spin configurations, which is determined by the parameter "configs_number". Define the number of spins in each lattice (determined by the parameter "spins_number") and the total number of spins (determined by the parameter "total_spins"). Define the spin lattice, and specify the number of lattices a, b, and c respectively by the parameter "spin_lattice", such as "spin_lattice 2 2 2" means that a 2 × 2 × 2 square lattice is defined. Define the search path for finding neighboring atoms, and specify the number of lattices to search in the lattice a, b, and c directions respectively by the parameter "traverse_lattice", such as "traverse_lattice -1 1 -1 1 -1 1" means spin In the grid By searching [ -1, +1] range of spin configuration To determine whether it is a neighbor spin. When "if_exchange" or "if_biquadratic" is ".true.", it is necessary to define the neighbor order (controlled by the parameter "neighbour_order") and the neighbor distance (controlled by the parameter "neighbour_distance") to be solved. For example, "neighbour_order 1", "neighbour_distance 2.00" means that only the first-order neighbor is calculated, and the distance between the two spins of this neighbor is 2.00 Å. When "if_landau" or "if_biquadratic" is ".true.", it is necessary to define the spin center. For example, setting "spin_center 0.0 0.0 2.3" means that the spin center is at (0.0,0.0,2.3).

[0175] In summary, the magnetic Hamiltonian model of the magnetic system constructed by the technical solution of this application can cover various magnetic exchange interactions as much as possible, and can accurately describe magnetic insulators, metals, low-dimensional magnetic materials, and materials with fluctuating spin density. The total energy of the magnetic system is calculated based on the density functional of the first principle. The spin configuration data set can effectively avoid the deviation of parameter fitting caused by artificial intervention in the selection of spin configuration through a reasonable random number method. The data set of spin configurations contains the ground state and various possible high-energy states, and comprehensively considers the influence of various energy states on the model parameters of the magnetic system. Finally, the replica exchange simulated annealing algorithm is selected, which can efficiently fit the model parameters, ensure that the model parameters are the global optimal solution, and the obtained model parameters consider the comprehensive influence of various magnetic states and various magnetic interactions. The technical solution of this application has a good description of various magnetic systems, especially for metal magnetic systems, complex magnetic state magnetic systems, and low-dimensional magnetic systems, and is an efficient model optimization method.

[0176] In addition, combining Figure 10 the model parameter optimization method of the magnetic system provided by the embodiments shown, it can be seen that the model parameter optimization method provided by the embodiments of this application includes S200: model construction, S300: data set generation, and S400: model optimization. Specifically:

[0177] For the S200 model construction part: According to the given magnetic system, analyze the possible interactions to determine whether to add the corresponding interaction parameters, and add the corresponding energy contribution terms to the magnetic Hamiltonian model. Among them, the spin exchange interaction J, the Landau self-energy coefficient L, and the biquadratic exchange interaction parameter K can configure the corresponding orders, and the above orders are used to consider the range of action of the spin exchange interaction, the accuracy of the Landau self-energy correction, and the range of action of the biquadratic exchange interaction in the magnetic Hamiltonian model. The specific form of the Hamiltonian here determines the basic framework for subsequent model optimization.

[0178] Specifically, as Figure 10 shown, the above step S200: model construction includes:

[0179] S201: Interaction analysis. Analyze the possible interactions of the given magnetic system.

[0180] S202: Initialize the model and add E 0 . After determining the included interactions, initialize the above magnetic Hamiltonian model. For example, if it is determined that the magnetic system only contains the reference state energy, the magnetic Hamiltonian model is initialized as follows:

[0181] S203: Determine whether it contains the J interaction.

[0182] S204: Configure the order of J and add E J 。

[0183] S205: Determine whether it contains the A interaction.

[0184] S206: Add E A 。Add this to the magnetic Hamiltonian model E A 。

[0185] S207: Determine whether it contains the L interaction.

[0186] S208: Configure the order of L and add E L 。

[0187] S209: Determine whether it contains the K interaction.

[0188] S210: Configure the order of K and add E K 。

[0189] S211: The construction of the final Hamiltonian model is completed.

[0190] For the generation part of the S300 dataset: According to the specific form of the magnetic Hamiltonian model, generate a data set of spin configurations. The anisotropy A parameter in the magnetic Hamiltonian model mainly depends on the non - collinear data set, the spin - exchange parameter J mainly depends on the collinear non - FM state data set, and the Landau parameter L mainly depends on the collinear FM state data set, and the biquadratic exchange interaction parameter K mainly depends on the non - collinear data set and the collinear FM state data set. The mutual combination of these data sets has a comprehensive impact on the accuracy of the Hamiltonian parameters, and a specific magnetic system can flexibly configure the composition and data volume of the data set.

[0191] Specifically, as Figure 10 shown, the above - mentioned S300: dataset generation steps include:

[0192] S301: Analyze the dataset composition.

[0193] S302: Generate FM - state configurations.

[0194] S303: Configure the spin configuration NC FM 。

[0195] S304: Generate NFM - state configurations.

[0196] S305: Configure the spin configuration NC NFM

[0197] S306: Generate the NCM state configuration.

[0198] S307: Configure the spin configuration NC NCM

[0199] S308: Generate the final data set NC configs 。

[0200] For the above S400 model optimization part, configure the optimization framework according to the model and data set, that is, the replica exchange simulated annealing algorithm mentioned above, and determine the optimization convergence criterion based on the data volume of the data set and the number of model parameters. The model parameters adaptively solve the optimal solution of the parameters of the given model based on the replica exchange simulated annealing algorithm. The parameter solution can be directly used to analyze the interaction of the magnetic system. See Figure 10 :

[0201] S401: Analyze the optimization framework.

[0202] S402: Configure the parameter optimization framework of the magnetic system. Here, the parameter optimization framework of the magnetic system and the three iterative processes of the above simulated annealing algorithm.

[0203] S403: Configure the parameter optimization convergence criterion, and the convergence criterion is the above formula for calculating the energy difference.

[0204] S404: Analyze the optimization results. The Hamiltonian parameters corresponding to the minimized energy difference, that is, the optimal Hamiltonian model parameters.

[0205] In addition, as a preferred embodiment, combined with Figure 11 the data distribution diagram shown and Figure 12 the curve of energy versus magnetic moment shown, it can be seen that: the specific implementation manner of the present application is described in detail with body-centered cubic Fe as an example.

[0206] Body-centered cubic Fe is a metallic ferromagnetic system and a three-dimensional system. The anisotropy of Fe is weak, and its magnetic Hamiltonian model mainly includes spin exchange interaction J , Landau self-energy parameter L and reference state energy E 0 . The magnetic Hamiltonian model of Fe is constructed as follows:

[0207]

[0208] In the current system the non-diagonal term is very small, and the parameters can be fitted based on collinear spins. The optimization formula is:

[0209]

[0210] Among them, is the system energy of the magnetic system obtained by first-principles calculation, is a scalar, is the actual magnetic moment of the system, non-normalized, and the parameter optimization considers the results of different orders of J and L .

[0211] In the part of generating the data set of spin configurations:

[0212] In the embodiment of the present application, the first-principles software ABACUS is used as the software for generating the data set of spin configurations, and the calculated Fe magnetic moment is 2.26 , which is close to the experimental result. The body-centered cubic Fe unit cell contains 2 atoms, and the a, b, and c axes are expanded by a factor of 4 respectively, and a total of 128 spins are included. The generated configuration magnetic moments are in the range of 1.2 to 3.0 . Among them, , . The total data set size is . The distribution of the data is as shown in Figure 11 .

[0213] In the part of optimizing the parameters of the magnetic Hamiltonian model:

[0214] Considering that the order of J is 5, 7; the order of L is 2, 3, 4, based on the above data set and Hamiltonian model (the Hamiltonian model is denoted as E0_Ji_Lj; where i represents the optimization of J to the i-th order and j represents the optimization of L to the j-th order), the following model parameters are obtained:

[0215]

[0216] Plot the L parameter of the E0_J5_L2 model as a curve of energy versus magnetic moment E(S) as shown in Figure 12 ; It can be seen from Figure 12 that:

[0217] The lowest energy state of the final curve is near 2.2 , which can reproduce the magnetic moment of the ground state of the system. The largest J is negative, and at the same time, several neighboring J values are also negative. It is analyzed that this system is a strong ferromagnetic system, which is consistent with the actual situation.

[0218] In summary, for the technical solution provided by the above embodiments of the present application, by using the spin-exchange interaction parameter, the anisotropy parameter, the Landau self-energy parameter, and the biquadratic exchange interaction parameter, these parameters can cover various magnetic exchange interactions as much as possible. Using these Hamiltonian parameters, the spin-exchange interaction energy, the anisotropy energy, the Landau self-energy, and the biquadratic exchange interaction energy of the magnetic system can be constructed, and it can accurately describe magnetic insulators, metals, low-dimensional magnetic materials, and materials with fluctuating spin density. Specifically, the magnetic system includes magnetic insulators and some semiconductors, magnetic metal materials, low-dimensional magnetic materials, and magnetic materials of transition metals. In addition, there is also a DMI interaction in the magnetic system with symmetry breaking. The magnetic Hamiltonian model constructed in the present application includes the spin-exchange interaction energy, the anisotropy energy, the Landau self-energy, and the biquadratic exchange interaction energy, and can describe the spin-exchange interaction, the anisotropy interaction, the Landau self-energy, and the biquadratic exchange interaction. Therefore, the magnetic Hamiltonian model can consider the magnetic systems of the above various materials as much as possible and construct a spin Hamiltonian model as universal as possible, covering the interaction energy that can accurately describe the magnetic system. In addition, the magnetic Hamiltonian model constructed in the present application introduces the Landau self-energy and the biquadratic exchange interaction energy, and can describe the fluctuation of the spin density.

[0219] It should be noted that the above examples are only for understanding the present application and do not constitute a limitation on the model construction method of the magnetic system of the present application. Based on this technical concept, more forms of simple transformations are within the protection scope of the present application.

[0220] The present application provides a device for model construction and parameter optimization of a magnetic system. The device for model construction and parameter optimization of a magnetic system includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the model construction and parameter optimization method of the magnetic system in the first embodiment above.

[0221] Next, refer to Figure 13, which shows a schematic structural diagram of a device for model construction and parameter optimization of a magnetic system suitable for implementing the embodiments of the present application. The device for model construction and parameter optimization in the embodiments of the present application can include, but is not limited to, mobile terminals such as mobile phones, laptop computers, digital broadcast receivers, PDAs (Personal Digital Assistant), PADs (Portable Application Description), PMPs (Portable Media Players), in-vehicle terminals (such as in-vehicle navigation terminals), etc., and fixed terminals such as digital TVs, desktop computers, etc. Figure 13 The device for model construction and parameter optimization of the shown magnetic system is merely an example and should not impose any limitations on the functions and usage scope of the embodiments of the present application.

[0222] As Figure 13 shown, the device for model construction and parameter optimization of the magnetic system can include a processing device 1001 (such as a central processing unit, a graphics processing unit, etc.), which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM: Read Only Memory) 1002 or a program loaded from a storage device 1003 into a random access memory (RAM: Random Access Memory) 1004. In the RAM 1004, various programs and data required for device operation are also stored. The processing device 1001, the ROM 1002, and the RAM 1004 are connected to each other through a bus 1005. An input / output (I / O) interface 1006 is also connected to the bus. Generally, the following systems can be connected to the I / O interface 1006: an input device 1007 including, for example, a touch screen, a touch pad, a keyboard, a mouse, an image sensor, a microphone, an accelerometer, a gyroscope, etc.; an output device 1008 including, for example, a liquid crystal display (LCD: Liquid Crystal Display), a speaker, a vibrator, etc.; a storage device 1003 including, for example, a magnetic tape, a hard disk, etc.; and a communication device 1009. The communication device 1009 can enable the device for model construction and parameter optimization of the magnetic system to communicate with other devices wirelessly or wiredly to exchange data. Although the figure shows a device for model construction and parameter optimization with various systems, it should be understood that it is not required to implement or have all the shown systems. More or fewer systems can be alternatively implemented or had.

[0223] In particular, according to the embodiments disclosed in the present application, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, the embodiments disclosed in the present application include a computer program product that includes a computer program carried on a computer-readable medium, and the computer program contains program codes for executing the methods shown in the flowcharts. In such an embodiment, the computer program can be downloaded and installed from a network through a communication device, or installed from a storage device 1003, or installed from a ROM 1002. When the computer program is executed by a processing device 1001, the above functions defined in the methods of the embodiments disclosed in the present application are executed.

[0224] The model construction and parameter optimization device for the magnetic system provided by the present application adopts the model construction and parameter optimization method for the magnetic system in the above embodiments, and can solve the technical problems that the existing technical methods can only fit a small number of nearest-neighbor interactions, it is difficult to accurately describe the magnetic system with other interactions, and the model is difficult to reflect the spin density fluctuations. Compared with the prior art, the beneficial effects of the model construction and parameter optimization device for the magnetic system provided by the present application are the same as those of the model construction and parameter optimization method for the magnetic system provided by the above embodiments, and other technical features in the model construction and parameter optimization device are the same as the features disclosed in the method of the previous embodiment, and will not be elaborated here.

[0225] It should be understood that the various parts disclosed in the present application can be implemented by hardware, software, firmware, or a combination thereof. In the description of the above embodiments, specific features, structures, materials, or characteristics can be combined in a suitable manner in any one or more embodiments or examples.

[0226] The above is only the specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed in the present application, and all should be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

[0227] The present application provides a computer-readable storage medium having computer-readable program instructions (i.e., computer programs) stored thereon, and the computer-readable program instructions are used to execute the model construction and parameter optimization method for the magnetic system in the above embodiments.

[0228] The computer-readable storage medium provided by this application can, for example, be a USB flash drive, but is not limited to electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or components, or any combination of the above. More specific examples of computer-readable storage media can include, but are not limited to: electrical connections with one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM) or flash memory, optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the above. In this embodiment, the computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, device, or component. The program code contained on the computer-readable storage medium can be transmitted using any appropriate medium, including but not limited to: wires, optical cables, RF (Radio Frequency), etc., or any suitable combination of the above.

[0229] The above computer-readable storage medium can be included in a device for model building and parameter optimization of a magnetic system; it can also exist independently and not be assembled into a device for model building and parameter optimization of a magnetic system.

[0230] The above computer-readable storage medium carries one or more programs. When the one or more programs are executed by a device for model building and parameter optimization, the device is caused to: obtain Hamiltonian parameters of a magnetic system, where the Hamiltonian parameters include spin-exchange interaction parameters, anisotropy parameters, Landau self-energy parameters, and biquadratic exchange interaction parameters; respectively construct the spin-exchange interaction energy, anisotropy energy, Landau self-energy, and biquadratic exchange interaction energy of the magnetic system according to the spin-exchange interaction parameters, anisotropy parameters, Landau self-energy parameters, and biquadratic exchange interaction parameters; use the spin-exchange interaction energy, anisotropy energy, Landau self-energy, and biquadratic exchange interaction energy to represent the total energy of the system, and construct a magnetic Hamiltonian model of the magnetic system.

[0231] Computer program code for performing the operations of this application can be written in one or more programming languages or combinations thereof. The programming languages include object-oriented programming languages such as Java, Smalltalk, C++, and also include conventional procedural programming languages such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, executed as a stand-alone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computer (e.g., by connecting through the Internet using an Internet service provider).

[0232] The flowcharts and block diagrams in the accompanying drawings illustrate the possible architectures, functions, and operations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in the flowchart or block diagram can represent a module, a program segment, or a part of code that contains one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks can occur in a different order than that marked in the accompanying drawings. For example, two consecutive blocks shown can actually be executed substantially in parallel, and they can sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, and combinations of blocks in the block diagram and / or flowchart, can be implemented by a dedicated hardware-based system for performing the specified functions or operations, or can be implemented by a combination of dedicated hardware and computer instructions.

[0233] The modules described in the embodiments of this application can be implemented in software or in hardware. Among them, the name of the module does not constitute a limitation to the unit itself in some cases.

[0234] The readable storage medium provided by this application is a computer-readable storage medium. The computer-readable storage medium stores computer-readable program instructions (i.e., computer programs) for executing the model construction and parameter optimization method of the above magnetic system, which can solve the technical problems that the existing model construction and parameter optimization solutions based on the nearest-neighbor Heisenberg model can only fit a small number of nearest-neighbor interactions, are difficult to accurately describe magnetic systems with other interactions, and the model is difficult to reflect spin density fluctuations. Compared with the prior art, the beneficial effects of the computer-readable storage medium provided by this application are the same as those of the model construction method of the magnetic system provided in the above embodiments, and will not be elaborated here.

[0235] This application also provides a computer program product, including a computer program, and the steps of the model construction and parameter optimization method of the magnetic system as described above are implemented when the computer program is executed by a processor.

[0236] The computer program product provided by this application can solve the technical problems that the existing methods can only fit a small number of nearest-neighbor interactions, are difficult to accurately describe magnetic systems with other interactions, and the model is difficult to reflect spin density fluctuations. Compared with the prior art, the beneficial effects of the computer program product provided by this application are the same as those of the model construction and parameter optimization method of the magnetic system provided in the above embodiments, and will not be elaborated here.

[0237] The above are only partial embodiments of this application, and thus do not limit the patent scope of this application. Any equivalent structural transformation made under the technical concept of this application by using the content of the specification and drawings of this application, or any direct / indirect application in other related technical fields, is included in the patent protection scope of this application.

Claims

1. A method for model construction and parameter optimization of a magnetic system, characterized in that: The method comprises: Obtaining Hamiltonian parameters of a magnetic system, wherein the Hamiltonian parameters include spin exchange interaction parameters, Landau self-energy parameters, anisotropy parameters, and biquadratic exchange interaction parameters, wherein the Landau self-energy parameters are used to describe spin density fluctuations, and the spin exchange interaction parameters include long-range exchange interactions; According to the spin exchange interaction parameter and the Landau self-energy parameter, expressions of the spin exchange interaction energy and the Landau self-energy of the magnetic system are respectively constructed, including: Using the spin exchange interaction parameters and the spin configuration, an expression for the spin exchange interaction energy is constructed: Among them, E J represents the spin exchange interaction energy, J d represents the spin exchange interaction parameter of the d-order neighbor, S i and S j Respectively represent the i-th and j-th spin configurations, and the i-th and j-th spin configurations cannot be the same spin; using the Landau self-energy parameters and spin configurations, construct the expression of Landau self-energy: Among them, E L represents the Landau self-energy, L d represents the Landau self-energy parameter of order d; Using the anisotropy parameters and the spin configuration, an expression for the anisotropy energy is constructed: Among them, E A represents anisotropy energy, A represents anisotropy parameter; And, using the biquadratic exchange interaction parameters and spin configuration, construct an expression for the biquadratic exchange interaction energy: Among them, E K represents the secondary exchange energy, K d represents the biquadratic exchange interaction parameter of the d-order nearest neighbor; The total system energy of the magnetic system is expressed by using the expressions of the spin exchange interaction energy and the Landau self-energy, and a magnetic Hamiltonian model of the magnetic system is constructed, including: The magnetic Hamiltonian model of the magnetic system is constructed using the spin exchange interaction energy, anisotropy energy, Landau self-energy and biquadratic exchange interaction energy of the magnetic system: E DFT =E0+E J +E A +E L +E K Among them, E DFT represents the total system energy of the magnetic system, E0 represents the reference state energy of the magnetic system, and E J represents the spin exchange interaction energy, E A represents the anisotropy energy, E L represents the Landau self-energy, E K represents the biquadratic exchange interaction energy; The number of spins of the magnetic system is randomly flipped according to the random number flipping method to generate data sets of various spin configurations; According to the replica exchange simulated annealing algorithm, the data sets of the multiple spin configurations and the magnetic Hamiltonian model are combined to solve and obtain the optimal Hamiltonian parameters of the magnetic system.

2. The method according to claim 1, characterized in that The step of randomly flipping the number of spins of the magnetic system according to the random number flipping method to generate data sets of multiple spin configurations respectively includes: Analyzing the magnetic state type of the spin configuration in the magnetic system according to the interactions contained in the magnetic system, wherein the magnetic state type includes a ferromagnetic state FM, a collinear non-ferromagnetic state NFM and a non-collinear magnetic state NCM; For the ferromagnetic state FM, NC is generated by constraining the magnetic moment size FM FM state spin configuration; For the collinear non-ferromagnetic state NFM, a random number is used to flip the spin direction of the corresponding number and position in the given spin number to generate NC NFM NFM state spin configuration; For non-collinear magnetic states NCM, random numbers are used to flip the spin directions of the corresponding number and position in the given number of spins to generate NC NCM NCM state spin configuration; The FM state spin configuration, the NFM state spin configuration and the NCM state spin configuration are summed up to obtain a data set of all spin configurations in the magnetic system.

3. The method according to claim 2, characterized in that The step of solving the optimal Hamiltonian parameters of the magnetic system according to the replica exchange simulated annealing algorithm, combining the data sets of the multiple spin configurations and the magnetic Hamiltonian model, comprises: Configuring a parameter optimization framework corresponding to the replica exchange simulated annealing algorithm, wherein the parameter optimization framework includes recursive iteration, exchange iteration and scanning iteration, and the recursive iteration, exchange iteration and scanning iteration are nested in sequence; Defining a temperature range of the replica exchange simulated annealing algorithm according to the value range of each Hamiltonian parameter in the magnetic system; Selecting a set of temperature distributions within the temperature range of the system, each set of the temperature distributions includes a plurality of different temperatures, and each temperature is used to fit a set of Hamiltonian parameter values; In the recursive iteration, the system replicas are used in parallel to execute a simulated annealing algorithm, and the temperature distribution represented by the system replicas is adjusted each time a recursive iteration is executed; In the exchange iteration, two adjacent temperatures in the system replica are exchanged according to a predetermined temperature exchange strategy; In the scanning iterations, a simulated annealing algorithm is performed using the data set of the spin configuration and the model parameter values ​​at the temperature, and the Hamiltonian parameter values ​​at the temperature are updated in each scanning iteration.

4. The method according to claim 3, characterized in that The step of solving the optimal Hamiltonian parameters of the magnetic system according to the replica exchange simulated annealing algorithm, combining the data sets of the multiple spin configurations and the magnetic Hamiltonian model, comprises: Defining the order required for the spin exchange interaction parameter, the Landau self-energy parameter and the biquadratic exchange interaction parameter; Determining a neighbor relationship according to the distance between the spins, selecting a spin configuration from the data set of the plurality of spin configurations according to the neighbor relationship, and inputting the spin configuration into the magnetic Hamiltonian model; Using the magnetic Hamiltonian model, respectively calculating the total energy of the system corresponding to each set of Hamiltonian parameter values ​​under the spin configuration and order, wherein each set of Hamiltonian parameter values ​​includes a spin exchange interaction parameter value, an anisotropy parameter value, a Landau self-energy parameter value, and a biquadratic exchange interaction parameter value; The weighted energy difference calculation formula is used as the loss function of the simulated annealing algorithm: Solve for the energy difference of the magnetic system; where f i W represents the weight factor of the i-th spin configuration, represents the total system energy calculated by the magnetic Hamiltonian model, represents the total energy of the system calculated using first-principles density functional theory, and N represents the total number of spin configurations; When the energy difference is minimized, the Hamiltonian parameter value corresponding to the minimized energy difference is selected as the optimal Hamiltonian parameter of the magnetic system.

5. The method according to claim 4, characterized in that The step of determining a neighbor relationship according to the distance between spins, selecting a spin configuration from the data set of the plurality of spin configurations according to the neighbor relationship, and inputting the spin configuration into the magnetic Hamiltonian model comprises: defining a spin center of the data set, and selecting a central spin configuration from the spin center; According to a predetermined search distance, searching for other spin configurations that are close to the central spin configuration in all directions; Inputting the central spin configuration and other spin configurations of the neighbors into the magnetic Hamiltonian model to solve the total energy of the system; After the total energy of the system is solved, the other spin configurations are taken as the central spin configuration, and the steps of searching for other spin configurations that are close to the central spin configuration in all directions according to the predetermined search distance and subsequent steps are re-executed until the data set of the spin configuration is traversed.

6. A model building and parameter optimization device for a magnetic system, characterized in that: The device comprises: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program is configured to implement the steps of the model building and parameter optimization method for a magnetic system according to any one of claims 1 to 5.

7. A storage medium, characterized in that: The storage medium is a computer-readable storage medium, and a computer program is stored on the storage medium. When the computer program is executed by a processor, the steps of the model building and parameter optimization method of the magnetic system according to any one of claims 1 to 5 are implemented.

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