A multi-scale calculation method and system for the magnetocaloric effect of two-dimensional magnets

Abstract

The application discloses a multi-scale calculation method and system for the magneto-caloric effect of a two-dimensional magnet, and the method combines density functional theory, atomic spin and thermodynamic knowledge related to the magneto-caloric effect, so that the step-by-step calculation of the two-dimensional magnet material is realized only according to the crystal structure of the two-dimensional magnet, and evaluation indexes of relevant magnetic properties and magneto-caloric properties are obtained after the step-by-step calculation at the electronic level, the atomic level and the macroscopic thermodynamic level, and finally, the prediction result is accurate and reliable.

Description

Technical Field

[0001] This invention relates to the field of magnetic refrigeration technology, and in particular to a multi-scale calculation method and system for the magnetocaloric effect of a two-dimensional magnet. Background Technology

[0002] Heat dissipation and cooling are crucial for the normal operation and performance of micro and nano devices. The heat generated by high-speed and high-density micro and nanoelectronic devices in confined spaces accumulates continuously, causing a sharp rise in device temperature, reducing reliability and speed, and even leading to failure. Magnetic refrigeration technology, due to its high efficiency, lack of pollution, and stable operation, holds promise as a potential replacement for traditional refrigeration technologies and an effective way to solve the increasingly serious cooling or heat dissipation problems of micro and nano devices.

[0003] Magnetic refrigeration technology differs from traditional refrigeration technology in that its main principle is based on the magnetocaloric effect of magnetic materials. Currently, typical bulk magnetocaloric materials such as rare earth compounds, perovskites, and lanthanum-iron-silicon have certain limitations: most selectable rare earth compounds exhibit excellent magnetocaloric performance in scientific research, but their large-scale application is limited by the criticality of rare earth resources; perovskite materials have advantages such as low price, high stability, and a wide phase transition temperature range, but their magnetocaloric effect is not prominent; lanthanum-iron-silicon compounds exhibit a large magnetic entropy change effect near room temperature due to their first-order phase transition, but the accompanying lattice thermal expansion and thermal hysteresis effects result in low material application efficiency. Furthermore, traditional magnetocaloric materials are mainly in bulk or thin film form, which is not suitable for the rapidly shrinking micro- and nano-sized devices.

[0004] Currently, limited by material preparation and measurement techniques, only a small number of two-dimensional magnets have been successfully obtained and proven to retain magnetism up to the monolayer limit. Research on the magnetocaloric effect of two-dimensional magnets remains very limited. Therefore, proposing multi-scale computational methods to predict the magnetocaloric effect of two-dimensional magnets is crucial for advancing research on this issue. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a multi-scale calculation method and system for the magnetocaloric effect of two-dimensional magnets. Based solely on the crystal structure of two-dimensional magnets, it enables step-by-step calculation of materials, thereby making the prediction results of the relevant magnetic properties and magnetocaloric performance of two-dimensional magnets accurate.

[0006] Technical solution: This invention provides a multi-scale calculation method for the magnetocaloric effect of a two-dimensional magnet, comprising the following steps:

[0007] Step 1: Establish the crystal structure of the two-dimensional magnet;

[0008] Step 2: Based on the crystal structure of the two-dimensional magnet, the crystal structure of the two-dimensional magnet is calculated using the software package VASP to obtain the atomic magnetic moments, magnetocrystalline anisotropy, and magnetic exchange coefficient.

[0009] Step 3: Combining atomic magnetic moments, magnetocrystalline anisotropy, and magnetic exchange coefficients, use the VAMPIRE software package to calculate the magnetization of a two-dimensional magnet as a function of magnetic field strength at a fixed temperature;

[0010] Step 4: By introducing the thermodynamic function of the magnetic field and Maxwell's relation, derive the evaluation index of the magnetocaloric effect, namely the isothermal magnetic entropy change and the adiabatic temperature change, and use the formula to calculate the values ​​of the isothermal magnetic entropy change and the adiabatic temperature change corresponding to the applied magnetic field.

[0011] Furthermore, in step 1, the range of two-dimensional magnets includes, but is not limited to, CrX3 (X = F, Cl, Br, I), CrAX (A = O, S, Se; X = F, Cl, Br, I), and VA2Z4 (A = Si, Ge; Z = N, P, As).

[0012] Furthermore, step 2 includes the following steps:

[0013] Step 2-1: Use the VASP software package to perform relaxation and self-consistent calculations on the crystal structure of the two-dimensional magnet to obtain the atomic magnetic moments;

[0014] Step 2-2: After optimization by self-consistent calculation, combined with spin-orbit coupling, the energy difference in different directions is obtained through non-collinear calculation to obtain the magnetocrystalline anisotropy.

[0015] Steps 2-3: Determine different magnetic configurations based on the spin direction of the outer electrons of the intracellular magnetic atoms, obtain the ground state energy and magnetic moment of the corresponding magnetic configuration through self-consistent calculation, and establish the relationship between energy and magnetic exchange coefficient based on the Hamiltonian equation of atomic spin. At the same time, combined with the ground state energy of the corresponding magnetic configuration, calculate the magnetic exchange coefficient of the two-dimensional magnet.

[0016] Furthermore, step 3 includes the following steps:

[0017] Step 3-1: Based on atomic magnetic moments, magnetocrystalline anisotropy, and magnetic exchange coefficients, use the VAMPIRE software package to create relevant files for a two-dimensional magnet;

[0018] Step 3-2: Based on the Monte Carlo algorithm, calculate the relationship between the magnetization intensity of the two-dimensional magnet and the temperature within a certain temperature range, and determine the Curie temperature of the two-dimensional magnet by taking its derivative.

[0019] Step 3-3: Calculate the relationship between magnetization and magnetic field strength of a two-dimensional magnet at a fixed temperature based on atomic spin dynamics.

[0020] Furthermore, step 4 includes the following steps:

[0021] Step 4-1: Based on the principle of energy conservation, introduce the magnetocaloric effect into the thermodynamic system and differentiate the Gibbs function;

[0022] Step 4-2: Obtain the expressions for entropy and magnetization through the differential expression of the Gibbs function, and obtain the Maxwell relations related to the magnetic parameters by taking the second derivatives of entropy and magnetization.

[0023] Step 4-3: Using Maxwell's relation, obtain the calculation formulas for isothermal magnetic entropy change and adiabatic temperature change. Based on the calculation formulas for isothermal magnetic entropy change and adiabatic temperature change, calculate the partial derivative of magnetization with respect to temperature under a fixed magnetic field strength, and integrate the obtained partial derivative with respect to magnetic field strength to obtain the numerical values ​​of isothermal magnetic entropy change and adiabatic temperature change under a given magnetic field strength.

[0024] This invention provides a multi-scale calculation system for the magnetocaloric effect of a two-dimensional magnet, comprising a crystal module, a VASP calculation module, a VAMPIRE calculation module, and a magnetocaloric effect calculation module;

[0025] The crystal module is used to establish the crystal structure of a two-dimensional magnet;

[0026] The VASP calculation module is used to calculate the crystal structure of a two-dimensional magnet. The VASP software package is used to calculate the crystal structure of a two-dimensional magnet to obtain atomic magnetic moments, magnetocrystalline anisotropy properties, and magnetic exchange coefficients.

[0027] The VAMPIRE calculation module combines atomic magnetic moments, magnetocrystalline anisotropy, and magnetic exchange coefficients to calculate the magnetization of a two-dimensional magnet as a function of magnetic field strength at a fixed temperature using the VAMPIRE software package.

[0028] The magnetocaloric effect calculation module is used to derive the evaluation index of the magnetocaloric effect, namely the isothermal magnetic entropy change and the adiabatic temperature change, by introducing the thermodynamic function of the magnetic field and Maxwell's relation. It then uses the formula to calculate the values ​​of the isothermal magnetic entropy change and the adiabatic temperature change corresponding to the applied magnetic field.

[0029] Furthermore, in the crystal module, the range of two-dimensional magnets includes, but is not limited to, CrX3 (X = F, Cl, Br, I), CrAX (A = O, S, Se; X = F, Cl, Br, I), and VA2Z4 (A = Si, Ge; Z = N, P, As).

[0030] Furthermore, the VASP calculation module includes atomic magnetic moment units, magnetocrystalline anisotropic property units, and magnetic exchange coefficient units;

[0031] The atomic magnetic moment unit is used to perform relaxation and self-consistent calculations on the crystal structure of two-dimensional magnets using the VASP software package to obtain atomic magnetic moments.

[0032] The magnetocrystalline anisotropic properties are obtained by optimizing the unit through self-consistent calculation, combining it with spin-orbit coupling, and obtaining the energy difference in different directions through non-collinear calculation.

[0033] The magnetic exchange coefficient unit is used to determine different magnetic configurations based on the spin direction of the outer electrons of the magnetic atoms in the cell. The ground state energy and magnetic moment of the corresponding magnetic configuration are obtained through self-consistent calculation. The relationship between energy and magnetic exchange coefficient is established based on the Hamiltonian equation of atomic spin. At the same time, the magnetic exchange coefficient of the two-dimensional magnet is calculated by combining the ground state energy of the corresponding magnetic configuration.

[0034] Furthermore, the VAMPIRE calculation module includes a file creation unit, a Curie temperature calculation unit, and a magnetization calculation unit;

[0035] Create file units to create two-dimensional magnet-related files based on atomic magnetic moments, magnetocrystalline anisotropy, and magnetic exchange coefficients using the VAMPIRE software package;

[0036] The Curie temperature calculation unit is used to calculate the relationship between the magnetization intensity of a two-dimensional magnet and temperature within a certain temperature range based on the Monte Carlo algorithm, and to determine the Curie temperature of the two-dimensional magnet by taking its derivative.

[0037] The magnetization calculation unit is used to calculate the relationship between the magnetization of a two-dimensional magnet and the magnetic field strength at a fixed temperature, based on atomic spin dynamics.

[0038] Furthermore, the magnetocaloric effect calculation module includes a thermodynamic unit, an entropy and magnetization intensity acquisition unit, and an isothermal magnetic entropy change and adiabatic temperature change calculation unit.

[0039] A thermodynamic unit is introduced to incorporate the magnetocaloric effect into the thermodynamic system through the magnetic work done during magnetization, and the Gibbs function is differentiated.

[0040] The entropy and magnetization acquisition unit is used to obtain the expressions for entropy and magnetization through the differential expression of the Gibbs function, and to obtain the Maxwell relations related to the magnetic parameters by taking the second derivatives of entropy and magnetization.

[0041] The isothermal magnetic entropy change and adiabatic temperature change calculation unit is used to obtain the calculation formulas for isothermal magnetic entropy change and adiabatic temperature change using Maxwell's relations. Based on the formulas for isothermal magnetic entropy change and adiabatic temperature change, the partial derivative of magnetization with respect to temperature is calculated under a fixed magnetic field strength, and the obtained partial derivative with respect to magnetic field strength is integrated to obtain the numerical values ​​of isothermal magnetic entropy change and adiabatic temperature change under a given magnetic field strength.

[0042] Beneficial effects: Compared with the prior art, the significant feature of this invention is that by combining density functional theory, atomic spin and thermodynamic knowledge related to magnetocaloric effect, it enables the step-by-step calculation of two-dimensional magnet materials based solely on the crystal structure of two-dimensional magnets. After step-by-step calculations at the electronic, atomic and macroscopic thermodynamic levels, the evaluation indicators of relevant magnetic and magnetocaloric properties are obtained, and the final prediction results are accurate and reliable. Attached Figure Description

[0043] Figure 1 This is a flowchart illustrating the present invention;

[0044] Figure 2 This is a schematic diagram of the two-dimensional CrI3 magnetization intensity versus temperature curve in this invention;

[0045] Figure 3 This is a schematic diagram of the curve of the two-dimensional CrI3 magnetization intensity as a function of the applied magnetic field in this invention;

[0046] Figure 4 This is a two-dimensional isothermal magnetic entropy change curve of CrI3 in this invention;

[0047] Figure 5 This is a two-dimensional CrI3 adiabatic temperature change curve diagram in this invention;

[0048] Figure 6 This is a comparison diagram of the maximum isothermal magnetic entropy change of a two-dimensional magnet under a 2T external magnetic field in this invention and a classical bulk magnetocaloric material;

[0049] Figure 7 This is a comparison diagram of the maximum adiabatic temperature change of a two-dimensional magnet under a 2T external magnetic field in this invention and a classic bulk magnetocaloric material;

[0050] Figure 8 This is a schematic diagram of the refrigeration cycle of the magnetocaloric effect of the two-dimensional magnet in this invention. Detailed Implementation

[0051] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0052] Example 1

[0053] This invention provides a multi-scale calculation method for the magnetocaloric effect of a two-dimensional magnet. The calculation of the magnetocaloric effect of the two-dimensional magnet involves the computational software package VASP developed by the Hafner group at the University of Vienna, Austria, and the open-source software package VAMPIRE developed by Richard FLEvans of the Department of Physics at the University of York. VASP is a commonly used computational software based on density functional theory, employing periodic boundary conditions to handle atomic models, and can calculate material structural parameters, electronic structure, and mechanical, magnetic, electrical, and optical properties. VAMPIRE can rapidly construct magnetic systems, and its built-in simulation types can meet the needs of most atomic spin simulation calculations. It can also generate a large amount of simulation data, facilitating detailed analysis of the calculation results. This invention uses the VASP and VAMPIRE software packages to calculate the intrinsic magnetic properties and temperature- and magnetic field-related magnetic properties of the two-dimensional magnet, serving as the data source for subsequent calculations of the magnetocaloric effect. In the crystal module, the range of two-dimensional magnets includes, but is not limited to, CrX3 (X = F, Cl, Br, I), CrAX (A = O, S, Se; X = F, Cl, Br, I), and VA2Z4 (A = Si, Ge; Z = N, P, As). Please refer to [link / reference needed]. Figure 1 As shown, the specific steps include:

[0054] Step 1: Establish the crystal structure of the two-dimensional magnet. In this embodiment, two-dimensional CrI3 is used as the specific application.

[0055] Step 1-1: Obtain the crystal structure of the magnetic material bulk CrI3.

[0056] Steps 1-2: Separate the atomic structure of monolayer CrI3 from the corresponding bulk structure and adjust the position of the atomic layer in the vacuum layer to avoid the interaction of adjacent cells.

[0057] Step 2: Based on the crystal structure of the two-dimensional magnet, the crystal structure of the two-dimensional magnet is calculated using the software package VASP to obtain the atomic magnetic moments, magnetocrystalline anisotropy properties, and magnetic exchange coefficients.

[0058] Step 2-1: For the two-dimensional CrI3 crystal structure, the VASP software package is used to perform relaxation and self-consistent calculations on the crystal structure of the two-dimensional magnet at the electronic level to obtain the magnetic moments of Cr atoms.

[0059] Step 2-2: After optimization by self-consistent calculation, combined with spin-orbit coupling, read the CHG and CHGCAR files from the previous self-consistent calculation and perform noncollinearity calculation. Specifically, the spin quantum axes are arranged along different crystal axis directions, and the energy difference in different directions is calculated to obtain the magnetocrystalline anisotropy properties.

[0060] Steps 2-3: Expand the monolayer CrI3 unit cell and determine the different magnetic configurations based on the spin direction of the outer electrons of the Cr magnetic atoms in the cell, i.e., the four magnetic configurations of the monolayer CrI3 supercell. Perform self-consistent calculations on the supercell to obtain the ground state energy and magnetic moment of the Cr atom corresponding to the four magnetic configurations. Establish the relationship between energy and magnetic exchange coefficient based on the Hamiltonian equation of atomic spin. At the same time, combine the ground state energy of the corresponding magnetic configuration to calculate the magnetic exchange coefficient of the two-dimensional magnet.

[0061] The relationship between energy and magnetic exchange coefficient is expressed as follows:

[0062]

[0063] Where E0 is the total energy excluding spin interactions, J1 is the nearest-neighbor magnetic exchange coefficient, J2 is the second-nearest-neighbor magnetic exchange coefficient, J3 is the second-second-nearest-neighbor magnetic exchange coefficient, and S... i S j Both represent unit vectors indicating the direction of atomic magnetic moments.

[0064] Step 3: Combining atomic magnetic moments, magnetocrystalline anisotropy, and magnetic exchange coefficients, use the VAMPIRE software package to calculate the magnetization of a two-dimensional magnet as a function of magnetic field strength at a fixed temperature.

[0065] Step 3-1: Based on atomic magnetic moments, magnetocrystalline anisotropy, and magnetic exchange coefficients, use the VAMPIRE software package to create two-dimensional CrI3 related input files cri3.mat and cri3.ucf ​​at the atomic level.

[0066] Step 3-2: Based on the Monte Carlo algorithm, refine the input file for atomic spin simulation, and calculate the relationship between magnetization and temperature in two-dimensional CrI3 in the temperature range of 0K to 80K, with a temperature increment of 1K. Figure 2 As shown, the temperature derivative of the magnetization is calculated with respect to temperature, and the Curie temperature of the two-dimensional CrI3 is determined by the maximum and minimum values ​​of the derivative.

[0067] Step 3-3: Based on atomic spin dynamics, change the input file (input) to apply varying magnetic fields along the (1,0,0) and (0,0,1) directions to two-dimensional CrI3. Calculate the relationship between the magnetization of two-dimensional CrI3 and the magnetic field strength at a fixed temperature, as follows: Figure 3 As shown.

[0068] Step 4: By introducing the thermodynamic function of the magnetic field and Maxwell's relation, derive the evaluation index of the magnetocaloric effect, namely the isothermal magnetic entropy change and the adiabatic temperature change, and use the formula to calculate the values ​​of the isothermal magnetic entropy change and the adiabatic temperature change corresponding to the applied magnetic field.

[0069] Step 4-1: Based on the principle of energy conservation, the magnetocaloric effect is introduced into the thermodynamic system, and the Gibbs free energy G is expressed as:

[0070] G(T,p,H)=U-TS+pV-μ0MH

[0071] Where T is temperature, p is pressure, H is magnetic field, U is internal energy, S is entropy, V is volume, μ0 is vacuum permeability, and M is magnetization.

[0072] For a two-dimensional magnet, neglecting thermal expansion and assuming constant pressure, the Gibbs function is differentiated as follows:

[0073] dG=Vdp-SdT-μ0MdH

[0074] The expressions for obtaining entropy and magnetization are:

[0075]

[0076]

[0077] Step 4-2: Obtain the expressions for entropy and magnetization through the differential expression of the Gibbs function, and take the second derivatives of entropy and magnetization to obtain the Maxwell relations related to the magnetic parameters, as shown in the following formulas:

[0078]

[0079] Step 4-3: Using Maxwell's relations, obtain the calculation formulas for isothermal magnetic entropy change and adiabatic temperature change:

[0080]

[0081]

[0082] Based on the calculation formulas for isothermal magnetic entropy change and adiabatic temperature change, the partial derivative of magnetization with respect to temperature under a fixed magnetic field strength is calculated. Integrating the obtained partial derivative with respect to magnetic field strength yields the numerical values ​​of the isothermal magnetic entropy change and adiabatic temperature change for a given magnetic field strength. Figure 4 and Figure 5 As shown.

[0083] The isothermal magnetic entropy change and adiabatic temperature change of two-dimensional CrI3 obtained by the above system calculation are in good agreement with the measurement results of the corresponding bulk CrI3 (Liu, et al. Phys. Rev. B, 2018, 97, 174418), verifying the accuracy and reliability of the calculation method. This embodiment extends the research scale of magnetocaloric materials from the micrometer (μm) to the angstrom (Å) level. This approach promises to reduce the volume and weight of magnets required in magnetic refrigeration, facilitating the application of magnetic refrigeration technology in confined spaces. Furthermore, the calculated magnetocaloric effects of representative two-dimensional magnets obtained through the above method can be theoretically compared with the measured magnetocaloric effects of typical magnetocaloric materials, such as... Figure 6 and Figure 7 As shown in the figure. The calculation results show that the magnetocaloric effect predicted by the two-dimensional magnet exhibits excellent performance in the low and medium temperature ranges. For example, magnetocaloric materials using CrF3 even surpass the magnetocaloric properties of most traditional first-order, second-order, and reversible first-order phase change materials. The working principle of the magnetic refrigeration cycle based on the magnetocaloric effect of the two-dimensional magnet is as follows: Figure 8 As shown, the entropy decrease and temperature rise that accompany the magnetization process require the absorption of heat from the external environment, and the reverse process is achieved during the demagnetization process. Therefore, the magnetic refrigeration cycle based on two-dimensional magnets provides the possibility for magnetic refrigeration at the nanoscale.

[0084] Example 2

[0085] Corresponding to the multi-scale calculation method for the magnetocaloric effect of a two-dimensional magnet provided in Embodiment 1, this embodiment provides a multi-scale calculation system for the thermal effect of a two-dimensional magnet. The calculation of the magnetocaloric effect of a two-dimensional magnet in this invention involves the computational software package VASP developed by the Hafner group at the University of Vienna, Austria, and the open-source software package VAMPIRE developed by Richard FLEvans of the Department of Physics at the University of York. VASP is a commonly used computational software based on density functional theory, employing periodic boundary conditions to handle atomic models, and can calculate material structural parameters, electronic structure, and mechanical, magnetic, electrical, and optical properties. VAMPIRE can rapidly construct magnetic systems, and its built-in simulation types can satisfy most atomic spin simulation calculations. It can also generate a large amount of simulation data, facilitating detailed analysis of the calculation results. This invention uses the VASP and VAMPIRE software packages to calculate the intrinsic magnetic properties and temperature- and magnetic field-related magnetic properties of the two-dimensional magnet, serving as the data source for subsequent calculations of the magnetocaloric effect. In the crystal module, the range of two-dimensional magnets includes, but is not limited to, CrX3 (X = F, Cl, Br, I), CrAX (A = O, S, Se; X = F, Cl, Br, I), and VA2Z4 (A = Si, Ge; Z = N, P, As). Please refer to [link / reference needed]. Figure 1 As shown, it specifically includes a crystal module, a VASP calculation module, a VAMPIRE calculation module, and a magnetocaloric effect calculation module.

[0086] The crystal module is used to establish the crystal structure of a two-dimensional magnet. In this embodiment, two-dimensional CrI3 is used as a specific application.

[0087] First, the crystal structure of the bulk magnetic material CrI3 was obtained. Second, the atomic structure of the monolayer CrI3 was separated from the corresponding bulk structure, and the position of the atomic layer in the vacuum layer was adjusted to avoid the interaction of adjacent cells.

[0088] The VASP calculation module is used to calculate the crystal structure of a two-dimensional magnet. The VASP software package is used to calculate the crystal structure of a two-dimensional magnet to obtain atomic magnetic moments, magnetocrystalline anisotropy, and magnetic exchange coefficients.

[0089] The VASP calculation module includes atomic magnetic moment units, magnetocrystalline anisotropic property units, and magnetic exchange coefficient units;

[0090] The atomic magnetic moment unit is used for the two-dimensional CrI3 crystal structure. At the electronic level, the VASP software package is used to perform relaxation and self-consistent calculations on the crystal structure of the two-dimensional magnet to obtain the Cr atomic magnetic moment.

[0091] The magnetocrystalline anisotropic property unit is used to perform noncollinearity calculations after optimization by self-consistent calculations, combined with spin-orbit coupling, by reading the CHG and CHGCAR files from the previous self-consistent calculation. Specifically, the spin quantum axes are arranged along different crystal axis directions, and the energy difference in different directions is calculated to obtain the magnetocrystalline anisotropic property.

[0092] The magnetic exchange coefficient unit is used to expand the monolayer CrI3 unit cell. Different magnetic configurations are determined according to the spin direction of the outer electrons of the Cr magnetic atoms in the cell, namely the four magnetic configurations of the monolayer CrI3 supercell. Self-consistent calculations are performed on the supercell to obtain the ground state energy and magnetic moment of the Cr atom corresponding to the four magnetic configurations. The relationship between energy and magnetic exchange coefficient is established according to the Hamiltonian equation of atomic spin. At the same time, combined with the ground state energy of the corresponding magnetic configuration, the magnetic exchange coefficient of the two-dimensional magnet is calculated.

[0093] The relationship between energy and magnetic exchange coefficient is expressed as follows:

[0094]

[0095] Where E0 is the total energy excluding spin interactions, J1 is the nearest-neighbor magnetic exchange coefficient, J2 is the second-nearest-neighbor magnetic exchange coefficient, J3 is the second-second-nearest-neighbor magnetic exchange coefficient, and S... i S j Both represent unit vectors indicating the direction of atomic magnetic moments.

[0096] The VAMPIRE calculation module combines atomic magnetic moments, magnetocrystalline anisotropy, and magnetic exchange coefficients to calculate the magnetization of a two-dimensional magnet at a fixed temperature as a function of magnetic field strength using the VAMPIRE software package.

[0097] The VAMPIRE calculation module includes a file creation unit, a Curie temperature calculation unit, and a magnetization calculation unit.

[0098] File units are created to generate two-dimensional CrI3-related input files cri3.mat and cri3.ucf ​​at the atomic level using the VAMPIRE software package, based on atomic magnetic moments, magnetocrystalline anisotropy, and magnetic exchange coefficients.

[0099] The Curie temperature calculation unit is used to refine the input file for atomic spin simulation based on the Monte Carlo algorithm, calculating the relationship between magnetization and temperature in two-dimensional CrI3 in the temperature range of 0K to 80K, with a temperature increment of 1K. Figure 2 As shown; and the temperature derivative of the magnetization is calculated with respect to temperature, and the Curie temperature of the two-dimensional CrI3 is determined by the maximum and minimum values ​​of the derivative.

[0100] The magnetization calculation unit is used to calculate the relationship between the magnetization of two-dimensional CrI3 and the magnetic field strength at a fixed temperature by applying varying magnetic fields along the (1,0,0) and (0,0,1) directions to the input file, based on atomic spin dynamics. Figure 3 As shown.

[0101] The magnetocaloric effect calculation module is used to derive the evaluation index of the magnetocaloric effect, namely the isothermal magnetic entropy change and the adiabatic temperature change, by introducing the thermodynamic function of the magnetic field and Maxwell's relation. It then uses the formula to calculate the values ​​of the isothermal magnetic entropy change and the adiabatic temperature change corresponding to the applied magnetic field.

[0102] The magnetocaloric effect calculation module includes a thermodynamic unit, an entropy and magnetization acquisition unit, and an isothermal magnetic entropy change and adiabatic temperature change calculation unit.

[0103] A thermodynamic unit is introduced to incorporate the magnetocaloric effect into the thermodynamic system based on the principle of energy conservation, and the Gibbs free energy G is expressed as follows:

[0104] G(T,p,H)=U-TS+pV-μ0MH

[0105] Where T is temperature, p is pressure, H is magnetic field, U is internal energy, S is entropy, V is volume, μ0 is vacuum permeability, and M is magnetization.

[0106] For a two-dimensional magnet, neglecting thermal expansion and assuming constant pressure, the Gibbs function is differentiated as follows:

[0107] dG=Vdp-SdT-μ0MdH

[0108] The expressions for obtaining entropy and magnetization are:

[0109]

[0110]

[0111] The entropy and magnetization acquisition unit is used to obtain the expressions for entropy and magnetization through the differential expression of the Gibbs function, and to obtain the Maxwell relations related to the magnetic parameters by taking the second derivatives of entropy and magnetization, as shown in the following formulas:

[0112]

[0113] The isothermal magnetic entropy change and adiabatic temperature change calculation unit is used to obtain the calculation formulas for isothermal magnetic entropy change and adiabatic temperature change using Maxwell's relations:

[0114]

[0115]

[0116] Based on the calculation formulas for isothermal magnetic entropy change and adiabatic temperature change, the partial derivative of magnetization with respect to temperature under a fixed magnetic field strength is calculated. Integrating the obtained partial derivative with respect to magnetic field strength yields the numerical values ​​of the isothermal magnetic entropy change and adiabatic temperature change for a given magnetic field strength. Figure 4 and Figure 5 As shown.

[0117] The isothermal magnetic entropy change and adiabatic temperature change of two-dimensional CrI3 obtained by the above system calculation are in good agreement with the measurement results of the corresponding bulk CrI3 (Liu, et al. Phys. Rev. B, 2018, 97, 174418), verifying the accuracy and reliability of the calculation method. This embodiment extends the research scale of magnetocaloric materials from the micrometer (μm) to the angstrom (Å) level. This approach promises to reduce the volume and weight of magnets required in magnetic refrigeration, facilitating the application of magnetic refrigeration technology in confined spaces. Furthermore, the calculated magnetocaloric effects of representative two-dimensional magnets obtained through the above method can be theoretically compared with the measured magnetocaloric effects of typical magnetocaloric materials, such as... Figure 6 and Figure 7 As shown in the figure. The calculation results show that the magnetocaloric effect predicted by the two-dimensional magnet exhibits excellent performance in the low and medium temperature ranges. For example, magnetocaloric materials using CrF3 even surpass the magnetocaloric properties of most traditional first-order, second-order, and reversible first-order phase change materials. The working principle of the magnetic refrigeration cycle based on the magnetocaloric effect of the two-dimensional magnet is as follows: Figure 8 As shown, the entropy decrease and temperature rise that accompany the magnetization process require the absorption of heat from the external environment, and the reverse process is achieved during the demagnetization process. Therefore, the magnetic refrigeration cycle based on two-dimensional magnets provides the possibility for magnetic refrigeration at the nanoscale.

Claims

1. A multi-scale calculation method for the magnetocaloric effect of a two-dimensional magnet, characterized in that, Includes the following steps: Step 1: Establish the crystal structure of the two-dimensional magnet; Step 2: Based on the crystal structure of the two-dimensional magnet, the crystal structure of the two-dimensional magnet is calculated using the software package VASP to obtain the atomic magnetic moments, magnetocrystalline anisotropy, and magnetic exchange coefficient. Step 3: Combining atomic magnetic moments, magnetocrystalline anisotropy, and magnetic exchange coefficients, use the VAMPIRE software package to calculate the magnetization of a two-dimensional magnet as a function of magnetic field strength at a fixed temperature; Step 4: By introducing the thermodynamic functions of the magnetic field and Maxwell's relations, derive the evaluation indices for the magnetocaloric effect, namely the isothermal magnetic entropy change and the adiabatic temperature change. Calculate the numerical values ​​of the isothermal magnetic entropy change and the adiabatic temperature change corresponding to the applied magnetic field using the formulas; this includes the following steps: Step 4-1: Based on the principle of energy conservation, introduce the magnetocaloric effect into the thermodynamic system and differentiate the Gibbs function; Step 4-2: Obtain the expressions for entropy and magnetization through the differential expression of the Gibbs function, and obtain the Maxwell relations related to the magnetic parameters by taking the second derivatives of entropy and magnetization. Step 4-3: Using Maxwell's relation, obtain the calculation formulas for isothermal magnetic entropy change and adiabatic temperature change. Based on the calculation formulas for isothermal magnetic entropy change and adiabatic temperature change, calculate the partial derivative of magnetization with respect to temperature under a fixed magnetic field strength, and integrate the obtained partial derivative with respect to magnetic field strength to obtain the numerical values ​​of isothermal magnetic entropy change and adiabatic temperature change under a given magnetic field strength.

2. The multi-scale calculation method for the magnetocaloric effect of a two-dimensional magnet according to claim 1, characterized in that, In step 1, the range of two-dimensional magnets includes, but is not limited to, CrX3 (X=F, Cl, Br, I), CrAX (A=O, S, Se; X=F, Cl, Br, I), and VA2Z4 (A=Si, Ge; Z=N, P, As).

3. The multi-scale calculation method for the magnetocaloric effect of a two-dimensional magnet according to claim 1, characterized in that, Step 2 includes the following steps: Step 2-1: Use the VASP software package to perform relaxation and self-consistent calculations on the crystal structure of the two-dimensional magnet to obtain the atomic magnetic moments; Step 2-2: After optimization by self-consistent calculation, combined with spin-orbit coupling, the energy difference in different directions is obtained through non-collinear calculation to obtain the magnetocrystalline anisotropy. Steps 2-3: Determine different magnetic configurations based on the spin direction of the outer electrons of the intracellular magnetic atoms, obtain the ground state energy and magnetic moment of the corresponding magnetic configuration through self-consistent calculation, and establish the relationship between energy and magnetic exchange coefficient based on the Hamiltonian equation of atomic spin. At the same time, combined with the ground state energy of the corresponding magnetic configuration, calculate the magnetic exchange coefficient of the two-dimensional magnet.

4. The multi-scale calculation method for the magnetocaloric effect of a two-dimensional magnet according to claim 1, characterized in that, Step 3 includes the following steps: Step 3-1: Based on atomic magnetic moments, magnetocrystalline anisotropy, and magnetic exchange coefficients, use the VAMPIRE software package to create relevant files for a two-dimensional magnet; Step 3-2: Based on the Monte Carlo algorithm, calculate the relationship between the magnetization intensity of the two-dimensional magnet and the temperature within a certain temperature range, and determine the Curie temperature of the two-dimensional magnet by taking its derivative. Steps 3-4: Calculate the relationship between magnetization and magnetic field strength of a two-dimensional magnet at a fixed temperature based on atomic spin dynamics.

5. A multi-scale calculation system for the magnetocaloric effect of a two-dimensional magnet, characterized in that, It includes a crystal module, a VASP calculation module, a VAMPIRE calculation module, and a magnetocaloric effect calculation module; The crystal module is used to establish the crystal structure of a two-dimensional magnet; The VASP calculation module is used to calculate the crystal structure of a two-dimensional magnet. The VASP software package is used to calculate the crystal structure of a two-dimensional magnet to obtain atomic magnetic moments, magnetocrystalline anisotropy properties, and magnetic exchange coefficients. The VAMPIRE calculation module combines atomic magnetic moments, magnetocrystalline anisotropy, and magnetic exchange coefficients to calculate the magnetization of a two-dimensional magnet as a function of magnetic field strength at a fixed temperature using the VAMPIRE software package. The magnetocaloric effect calculation module is used to derive the evaluation index of the magnetocaloric effect, namely the isothermal magnetic entropy change and the adiabatic temperature change, by introducing the thermodynamic function of the magnetic field and Maxwell's relation. It uses the formula to calculate the values ​​of the isothermal magnetic entropy change and the adiabatic temperature change corresponding to the applied magnetic field. The magnetocaloric effect calculation module includes a thermodynamic unit, an entropy and magnetization intensity acquisition unit, and an isothermal magnetic entropy change and adiabatic temperature change calculation unit. A thermodynamic unit is introduced to incorporate the magnetocaloric effect into the thermodynamic system through the magnetic work done during magnetization, and the Gibbs function is differentiated. The entropy and magnetization acquisition unit is used to obtain the expressions for entropy and magnetization through the differential expression of the Gibbs function, and to obtain the Maxwell relations related to the magnetic parameters by taking the second derivatives of entropy and magnetization. The isothermal magnetic entropy change and adiabatic temperature change calculation unit is used to obtain the calculation formulas for isothermal magnetic entropy change and adiabatic temperature change using Maxwell's relations. Based on the formulas for isothermal magnetic entropy change and adiabatic temperature change, the partial derivative of magnetization with respect to temperature is calculated under a fixed magnetic field strength, and the obtained partial derivative with respect to magnetic field strength is integrated to obtain the numerical values ​​of isothermal magnetic entropy change and adiabatic temperature change under a given magnetic field strength.

6. The multi-scale calculation system for the magnetocaloric effect of a two-dimensional magnet according to claim 5, characterized in that, In the crystal module, the range of two-dimensional magnets includes, but is not limited to, CrX3 (X=F, Cl, Br, I), CrAX (A=O, S, Se; X=F, Cl, Br, I), and VA2Z4 (A=Si, Ge; Z=N, P, As).

7. The multi-scale calculation system for the magnetocaloric effect of a two-dimensional magnet according to claim 5, characterized in that, The VASP calculation module includes atomic magnetic moment units, magnetocrystalline anisotropic property units, and magnetic exchange coefficient units; The atomic magnetic moment unit is used to perform relaxation and self-consistent calculations on the crystal structure of two-dimensional magnets using the VASP software package to obtain atomic magnetic moments. The magnetocrystalline anisotropic properties are obtained by optimizing the unit through self-consistent calculation, combining it with spin-orbit coupling, and obtaining the energy difference in different directions through non-collinear calculation. The magnetic exchange coefficient unit is used to determine different magnetic configurations based on the spin direction of the outer electrons of the magnetic atoms in the cell. The ground state energy and magnetic moment of the corresponding magnetic configuration are obtained through self-consistent calculation. The relationship between energy and magnetic exchange coefficient is established based on the Hamiltonian equation of atomic spin. At the same time, the magnetic exchange coefficient of the two-dimensional magnet is calculated by combining the ground state energy of the corresponding magnetic configuration.

8. The multi-scale calculation system for the magnetocaloric effect of a two-dimensional magnet according to claim 5, characterized in that, The VAMPIRE calculation module includes a file creation unit, a Curie temperature calculation unit, and a magnetization calculation unit. Create file units to create two-dimensional magnet-related files based on atomic magnetic moments, magnetocrystalline anisotropy, and magnetic exchange coefficients using the VAMPIRE software package; The Curie temperature calculation unit is used to calculate the relationship between the magnetization intensity of a two-dimensional magnet and temperature within a certain temperature range based on the Monte Carlo algorithm, and to determine the Curie temperature of the two-dimensional magnet by taking its derivative. The magnetization calculation unit is used to calculate the relationship between the magnetization of a two-dimensional magnet and the magnetic field strength at a fixed temperature, based on atomic spin dynamics.

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