Magnetic field simulation system based on first principle calculation

Abstract

The invention relates to a magnetic field simulation system based on first principle calculation, and belongs to the field of quantum information science. Comprising a superunit cell construction module used for constructing superunit cells, carrying out natural isotope replacement in the superunit cells, introducing defects and sending the defects to a structure optimization module; the structure optimization module is used for carrying out structure optimization on the super unit cell with introduced defects and sending the optimized structure to the spin magnetic moment acquisition module; the spinning magnetic moment acquisition module is used for acquiring magnetization density distribution data and spinning magnetic moment distribution of the supercell and sending the data to the magnetic field construction module; and the magnetic field construction module is used for screening the spinning magnetic moment according to the spinning magnetic moment distribution, and simulating the magnetic field induction intensity of any point in the supercell after structure optimization based on the screened spinning magnetic moment. According to the system, the spin magnetic moment is screened based on the preset boundary of the supercell, and the magnetic field calculation is carried out based on the screened spin magnetic moment, so that the calculation time is greatly shortened and the efficiency is improved while the calculation precision is met.

Description

Technical Field

[0001] The present invention relates to the field of quantum information science, and in particular to a magnetic field simulation system based on first-principles calculations. Background Art

[0002] Silicon carbide color centers are a type of quantum material for solid-state spin systems. They possess the advantages of long coherence time, high stability, and high integration density, and have attracted widespread attention in technologies such as quantum computing and quantum precision measurement. Silicon carbide color centers exist not only in ideal crystals but also within stacking faults within crystals. Stacking faults arise when the stacking order of a crystal is disrupted, and these disruptions can occur multiple times within a relatively small number of crystal layers. Stacking faults have numerous configurations, and these surface defects increase the complexity of the effects of the intracrystalline magnetic field on spins. The mechanism by which they affect the coherence time of solid-state spin systems remains largely unexplored.

[0003] Simulation studies are an effective method for exploring the coherence time of solid-state spin systems. However, existing methods fail to consider the intracrystalline magnetic field, making it difficult to reflect the impact of the magnetic field environment within the crystal caused by complex atomic defects. This, in turn, results in low spin coherence simulation accuracy using existing algorithms.

[0004] Therefore, constructing intracrystalline magnetic fields to study the spin coherence properties of materials with complex atomic defect color centers is of great significance for the exploration of quantum materials with long coherence times. However, simulating and solving intracrystalline magnetic fields is computationally intensive and inefficient. Finding a rapidly convergent solution region from spatially distributed magnetization density data is key to improving the efficiency and accuracy of intracrystalline magnetic field calculations. Therefore, a system that effectively screens spin magnetic moments and simulates intracrystalline magnetic fields is essential. Summary of the Invention

[0005] In view of the above analysis, the present invention aims to provide a magnetic field simulation system based on first-principles calculations to solve the problems of huge computational complexity and low efficiency when simulating and solving intracrystalline magnetic fields. The present invention provides a magnetic field simulation system based on first-principles calculations, the system comprising:

[0006] a supercell construction module for constructing a supercell, performing natural isotope substitution in the supercell, introducing defects, and sending the defect-introduced supercell to a structure optimization module;

[0007] A structure optimization module is used to optimize the structure of the supercell with defects based on first principles until the supercell has a stable configuration, and send the optimized supercell to the spin magnetic moment acquisition module;

[0008] A spin magnetic moment acquisition module is used to obtain magnetization density distribution data of the structurally optimized supercell, calculate the spin magnetic moment distribution of the structurally optimized supercell based on the magnetization density distribution data, and send the spin magnetic moment distribution to the magnetic field construction module;

[0009] The magnetic field construction module is used to screen the spin magnetic moment according to the spin magnetic moment distribution, and simulate the magnetic field induction intensity of any point in the supercell after structural optimization based on the screened spin magnetic moment.

[0010] Furthermore, the magnetic field construction module includes a spin magnetic moment screening module and a magnetic field simulation module;

[0011] The spin magnetic moment screening module is used to set a preset boundary of the supercell, screen the spin magnetic moment according to the spin magnetic moment distribution and the preset boundary of the supercell, and send the screened spin magnetic moment to the magnetic field simulation module;

[0012] The magnetic field simulation module is used to simulate the magnetic field induction intensity at any point in the structurally optimized supercell based on the screened spin magnetic moment and output the simulation results;

[0013] The predetermined boundary of the supercell is a limiting length that is proportional to the lattice constant of the supercell.

[0014] Furthermore, the screening of the spin magnetic moment according to the spin magnetic moment distribution and the preset boundary of the supercell includes:

[0015] Obtaining a calculation boundary based on the calculation point and the preset boundary of the supercell; the calculation boundary includes: a_min, a_max, b_min, b_max, c_min, c_max;

[0016] Performing virtual cell mapping according to the coordinates of the calculation boundary to obtain a calculation region;

[0017] According to the spin magnetic moment distribution, the corresponding spin magnetic moment in the calculation area is screened;

[0018] The calculation point refers to any point in the supercell where the magnetic field induction intensity is to be calculated.

[0019] Furthermore, performing virtual cell mapping according to the coordinates of the calculation boundary to obtain the calculation area includes:

[0020] Expanding the supercell with virtual cells according to the coordinates of the calculation boundary;

[0021] Within the scope of the virtual unit cell and supercell after cell expansion, a hexahedral region with the same angle as the basis vector is enclosed by the calculation boundary;

[0022] Mapping the area of ​​the hexahedral region that exceeds the supercell range to the corresponding area of ​​the supercell to obtain a first calculation area;

[0023] The area of ​​the hexahedral region that does not exceed the supercell range is used as the second calculation area;

[0024] The union of the first calculation area and the second calculation area is used as the calculation area.

[0025] Furthermore, the magnetic field induction intensity at any point in the supercell is the sum of the magnetic field induction intensities generated by the screened spin magnetic moments at that point.

[0026] Furthermore, the supercell construction module includes a supercell initialization module and a supercell deformation module;

[0027] The supercell initialization module is used to construct an initial cell, expand the initial cell into a supercell and send the supercell to the supercell deformation module;

[0028] The supercell deformation module is used to perform natural isotope substitution in the supercell, perform stacking faults on the supercell, remove corresponding atoms to introduce defects, and send the supercell with introduced defects to the structure optimization module;

[0029] The supercell deformation module performs stacking faults on the supercell and removes corresponding atomic introduced defects through the following steps:

[0030] S11, selecting a first position for a stacking fault in the supercell, and translating atomic coordinates at the first position to obtain a stacking fault;

[0031] S12. Select a second location for atomic removal in the supercell after the stacking fault, and remove corresponding atoms at the second location to introduce defects.

[0032] Furthermore, the structure optimization module includes a parameter setting module, a structure optimization algorithm module and a structure optimization output module;

[0033] The parameter setting module is used to set the optimization parameters and send them to the structure optimization algorithm module;

[0034] The structural optimization algorithm module is used to optimize the structure of the supercell with defects using first-principles calculation software according to the optimization parameters, and send the results to the structural optimization output module;

[0035] The structural optimization output module is used to determine whether the structurally optimized supercell has a stable configuration. If so, the structurally optimized supercell is sent to the magnetization density acquisition module; otherwise, the supercell deformation module is called to execute step S12 to change the second position, and then the structural optimization algorithm module is called until the structurally optimized supercell has a stable configuration.

[0036] Furthermore, the spin magnetic moment acquisition module calculates the spin magnetic moment distribution of the supercell after structural optimization using the following formula:

[0037]

[0038] Among them, g e is the electron g factor, which is approximately 2.002319; μ B is the Bohr magneton; m is the magnetization density distribution; V FFT is the total number of FFT grids; is the spin angular momentum vector.

[0039] Furthermore, the magnetic field simulation module calculates the magnetic field induction intensity at any point in the supercell after structural optimization using the following formula:

[0040]

[0041] Where μ0 is the vacuum permeability, is the screened spin magnetic moment, is the vector from the spin magnetic moment to any point in the supercell, and r is the distance from the spin magnetic moment to any point in the supercell.

[0042] Furthermore, the supercell deformation module performs natural isotope replacement in the supercell by the following steps:

[0043] determining naturally occurring isotopes of said atomic type and their concentrations;

[0044] Calculate the amount of isotopes of each type of atom based on the naturally occurring isotopes of the atom type and their concentrations;

[0045] The same number of corresponding atoms is randomly replaced in the supercell according to the isotope number of each type of atoms.

[0046] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0047] 1. The present invention introduces defects by performing stacking faults on the supercell and removing the corresponding atoms, taking into account the complexity of the influence of the intracrystalline magnetic field on the spin, and provides a basis for improving the accuracy of the calculation results of the intracrystalline magnetic field.

[0048] 2. The present invention provides an intracrystalline magnetic field simulation system based on first-principles calculations through a supercell construction module, a structure optimization module, a spin magnetic moment acquisition module, and a magnetic field construction module, which can efficiently simulate the magnetic field at any point in the crystal.

[0049] 3. The present invention obtains a calculation boundary based on a preset boundary of a supercell, and performs simulation calculations by screening the spin magnetic moments of electrons that are closer to the calculation point based on the calculation boundary. The calculation boundary is parallel to the unit cell basis vector and can be determined before iterating the magnetization density distribution data, thereby reducing the number of iterations. While meeting the calculation accuracy, it greatly reduces the calculation time and improves the calculation efficiency.

[0050] 4. The present invention performs virtual cell mapping according to the coordinates of the calculation boundary. When the calculation point is close to the edge of the supercell, the area beyond the supercell range in the hexahedral calculation area based on the basis vector is mapped to the corresponding area of ​​the supercell, thereby improving the accuracy of the calculation results of the intracrystalline magnetic field.

[0051] In the present invention, the above-mentioned technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of the present invention will be described in the following description, and some advantages will become apparent from the description or be learned through practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The accompanying drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like parts throughout the drawings.

[0053] Figure 1 A block diagram of a magnetic field simulation system based on first principles calculations provided by an embodiment of the present invention;

[0054] Figure 2 A schematic diagram of a silicon carbide stacking fault color center configuration used in simulations of an embodiment of the present invention;

[0055] Figure 3 Schematic diagram of the calculation boundary and calculation area of ​​a supercell according to an embodiment of the present invention;

[0056] Figure 4 Schematic diagram of the convergence of the magnetic field in a supercell calculated based on the spin magnetic moment in the calculation area of ​​the supercell according to an embodiment of the present invention. DETAILED DESCRIPTION

[0057] The preferred embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, and are not used to limit the scope of the present invention.

[0058] A specific embodiment of the present invention discloses a magnetic field simulation system based on first principles calculation. Figure 1 As shown, the system includes:

[0059] a supercell construction module for constructing a supercell, performing natural isotope substitution in the supercell, introducing defects, and sending the defect-introduced supercell to a structure optimization module;

[0060] A structure optimization module is used to optimize the structure of the supercell with defects based on first principles until the supercell has a stable configuration, and send the optimized supercell to the spin magnetic moment acquisition module;

[0061] A spin magnetic moment acquisition module is used to obtain magnetization density distribution data of the structurally optimized supercell, calculate the spin magnetic moment distribution of the structurally optimized supercell based on the magnetization density distribution data, and send the spin magnetic moment distribution to the magnetic field construction module;

[0062] The magnetic field construction module is used to screen the spin magnetic moment according to the spin magnetic moment distribution, and simulate the magnetic field induction intensity of any point in the supercell after structural optimization based on the screened spin magnetic moment.

[0063] Specifically, the supercell construction module includes a supercell initialization module and a supercell deformation module;

[0064] The supercell initialization module is used to construct an initial cell, expand the initial cell into a supercell and send the supercell to the supercell deformation module;

[0065] The supercell deformation module is used to perform natural isotope replacement in the supercell, perform stacking fault on the supercell, remove corresponding atoms to introduce defects, and send the supercell with introduced defects to the structure optimization module.

[0066] Specifically, the supercell initialization module constructs an initial cell and expands it into a supercell through the following steps:

[0067] Determining the atomic type of the crystal, setting the crystal lattice parameters and atomic coordinates based on the atomic type, and constructing an initial unit cell according to the crystal lattice parameters and atomic coordinates;

[0068] The initial unit cell is repeatedly expanded to obtain a supercell.

[0069] It should be noted that the crystal lattice parameters include the basis vectors of the unit cell and the angles between the crystal axes, which are used to describe the size and shape of a single unit cell; the basis vectors of the unit cell are the basic vectors that describe the crystal structure, usually expressed as three vectors They form the edges of the unit cell. Atomic coordinates are used to determine the positions of individual atoms within the unit cell. In simulation software, the size and shape of the initial unit cell are determined in three-dimensional space based on the set lattice parameters. Based on the atomic coordinates, the atoms are placed at corresponding positions within the initial unit cell to create the initial unit cell model. This initial unit cell is then repeatedly expanded to create a supercell model.

[0070] For example, assuming the crystal is cubic, use the variable The variables α, β, and γ represent the angles between the crystal axes b and c, a and c, and a and b, respectively. The angle between the crystal axes is set to α = β = γ = 90°. The atomic coordinates are expressed as fractional coordinates. Assuming that the fractional coordinates of an atom are (0.25, 0.25, 0.25), it means that the atom is located at a quarter position in all three coordinate axes of the unit cell.

[0071] Preferably, VESTA software is used for initial unit cell and supercell modeling.

[0072] Furthermore, the supercell deformation module performs natural isotope replacement in the supercell by the following steps:

[0073] determining naturally occurring isotopes of said atomic type and their concentrations;

[0074] Calculate the amount of isotopes of each type of atom based on the naturally occurring isotopes of the atom type and their concentrations;

[0075] The same number of corresponding atoms is randomly replaced in the supercell according to the isotope number of each type of atoms.

[0076] Specifically, the natural isotopes and concentrations of each atomic type are determined. For each atomic type, i.e., each class of atoms, the number of natural isotopes of each class of atoms is calculated by multiplying the number of atoms of that class in the supercell by the concentration of its natural isotope. Based on the number of natural isotopes of each class of atoms, the same number of atoms of that class in the supercell are randomly replaced with their natural isotopes.

[0077] For example, using VESTA simulation software, assuming that the crystal is silicon carbide 4H-SiC, its atomic types include carbon atoms C12 and silicon atoms Si28, and the crystal type is hexagonal. Set the basis vector of the initial unit cell to The angles between the crystal axes are set to α = β = 90°, γ = 120°, and the initial unit cell is Repeat the expansion in the direction 5, 5, and 5 times, respectively, to obtain a supercell; in which each carbon atom C12 and each silicon atom Si28 has its own number. The natural isotope of carbon atom C12 is determined to be C13, with a concentration of 1.1 at.%, and the natural isotope of silicon atom Si28 is determined to be Si29, with a concentration of 4.67 at.%. Assuming that the number of C12 and Si28 in the supercell is both 500, using 500*1.1 at.%, the number of C13 is approximately 6, and using 500*4.67 at.%, the number of Si29 is 23. Based on the number of C13, 6, Python is used to generate a first random number sequence with 6 elements, where each element has a value between 1 and 500 and each element has a different value. The value of the element represents the number of the carbon atom. In the supercell, replace the C12 with C13 for each element with the same number in the first random number sequence. Similarly, a second random number sequence with 23 elements is generated according to the number of Si29 (23), wherein the value range of each element is between 1 and 500 and the value of each element is different. In the supercell, Si28 with the same number corresponding to each element in the second random number sequence is replaced with Si29.

[0078] It should be noted that the unit at.% stands for atomic percentage, which represents the percentage of the number of atoms of this isotope to the total number of atoms of this type.

[0079] Furthermore, the supercell deformation module performs stacking faults on the supercell and removes corresponding atomic introduced defects through the following steps:

[0080] S11, selecting a first position for a stacking fault in the supercell, and translating atomic coordinates at the first position to obtain a stacking fault;

[0081] S12. Select a second location for atomic removal in the supercell after the stacking fault, and remove corresponding atoms at the second location to introduce defects.

[0082] For example, the silicon carbide stacking fault color center configuration used in the simulation of the embodiment of the present invention is as follows: Figure 2 As shown, in the supercell, the z coordinate (i.e., c coordinate) is greater than and less than The region where all atoms are located is taken as the first location for stacking fault. At this first location, the x coordinates (i.e., a coordinates) of all atoms are reduced by That is, translate to the left along the x-axis Then add the y coordinates (i.e. b coordinates) of all atoms That is, translate upward along the y-axis A stacking fault structure is obtained. In the supercell after the stacking fault, two locations with atomic coordinates of (3.08000, 7.11296, 13.21293) and (3.08000, 7.11296, 15.10500) in the absolute coordinate system are selected as the second locations for atomic removal. The corresponding atoms are removed at these second locations to form divacancy color centers, thereby introducing defects.

[0083] It can be understood that the present invention introduces defects by performing stacking faults on the supercell and removing corresponding atoms, taking into account the complexity of the influence of the intracrystalline magnetic field on the spin, and providing a basis for improving the accuracy of the calculation results of the intracrystalline magnetic field.

[0084] Specifically, the structure optimization module includes a parameter setting module, a structure optimization algorithm module and a structure optimization output module;

[0085] The parameter setting module is used to set the optimization parameters and send them to the structure optimization algorithm module;

[0086] The structural optimization algorithm module is used to optimize the structure of the supercell with defects using first-principles calculation software according to the optimization parameters, and send the results to the structural optimization output module;

[0087] The structural optimization output module is used to determine whether the structurally optimized supercell has a stable configuration. If so, the structurally optimized supercell is sent to the magnetization density acquisition module; otherwise, the supercell deformation module is called to execute step S12 to change the second position, and then the structural optimization algorithm module is called until the structurally optimized supercell has a stable configuration.

[0088] Preferably, the optimization parameters include the limited number of electron steps, the limited number of ion steps, the convergence accuracy of ion steps, and the convergence accuracy of electron steps.

[0089] It should be noted that, through the structural optimization, the position of atoms in space is adjusted, the atomic position distortion in the supercell is eliminated, and the total energy of the supercell is minimized, thereby obtaining a stable configuration. The electron density distribution and energy of the supercell are solved by the electron step. In each electron step, the wave function and energy of the electron are calculated according to the current position of the atomic nucleus. The movement of the atomic nucleus in the average potential field generated by the electron is obtained by the ion step. In each ion step, the force it receives is calculated according to the electronic structure at the current position of the atomic nucleus to update the speed of the atom, and the new position of the atom is calculated according to the speed of the updated atom. Therefore, it is necessary to set the maximum and minimum number of electron steps and ion steps. The ion step convergence accuracy and the electron step convergence accuracy refer to the criteria for judging whether the calculation results meet the convergence in the process of structural optimization. When the change in certain key calculation results (such as energy change, atomic displacement) is less than the corresponding convergence accuracy set, it is considered that the calculation results have converged.

[0090] Preferably, VASP software is used as the first-principles calculation software, and a corresponding input file is generated according to the optimization parameters, and the structure of the supercell with introduced defects is optimized through the input file.

[0091] Specifically, the input files include an INCAR file, a KPOINTS file, a POSCAR file, and a POTCAR file. The constructed defect-introduced supercell is exported to generate a first POSCAR file. The convergence accuracy is set to use a PBE pseudopotential, and the optimization parameters are written into the first INCAR file. A KPOINTS file containing k-points or only gamma points and a POTCAR pseudopotential file are generated. The defect-introduced supercell is structurally optimized using VASP software using these input files to generate a second POSCAR file.

[0092] It should be noted that the Brillouin zone refers to a periodically arranged region in reciprocal space. The Gamma point is the center of the Brillouin zone, and the k-point is the sampling point of the Brillouin zone. For crystal cells with high symmetry and relatively simple electronic structures, using only the Gamma point for relevant calculations can yield results that meet the required accuracy, greatly reducing the amount of computation and improving efficiency.

[0093] Preferably, whether the supercell after structural optimization has a stable configuration is determined by judging whether the absolute value of the energy difference between adjacent ion steps is less than the ion step convergence accuracy.

[0094] Specifically, the spin magnetic moment acquisition module includes an electronic structure calculation module, a magnetization density acquisition module, and a spin magnetic moment output module;

[0095] The electronic structure calculation module is used to converge the electronic structure of the supercell through static electronic structure calculation;

[0096] The magnetization density acquisition module is used to send the magnetization density distribution data corresponding to the electronic structure convergence of the supercell to the spin magnetic moment acquisition module;

[0097] The spin magnetic moment output module is used to calculate the spin magnetic moment distribution of the supercell after structural optimization based on the magnetization density distribution data, and send the spin magnetic moment distribution to the magnetic field construction module.

[0098] Specifically, the electronic structure calculation module converges the electronic structure of the supercell through the following steps:

[0099] Step S31: Keep the k-point setting and convergence accuracy unchanged, and set the spin-orbit coupling parameters;

[0100] Step S32: Set the number of ion steps to 0, use first-principles calculation software based on spin-orbit coupling parameters, and obtain the energy corresponding to the supercell through electron steps; iterate the electron steps until the electronic structure of the supercell converges.

[0101] Preferably, the spin-orbit coupling parameters include: LSORBIT=TRUE, LNONCOLLINEAR=TRUE, LORBMOM=TRUE, GGA_COMPAT=FALSE.

[0102] It should be noted that, in the electronic step, the electronic wave function and energy corresponding to the supercell are obtained by constructing an effective potential and solving the Kohn-Sham equation.

[0103] Specifically, the energy corresponding to the current electron step is compared with the energy corresponding to the electron step of the previous iteration. If the absolute value of the difference between the two is less than the electron step convergence accuracy, it is determined that the electronic structure of the supercell is converged.

[0104] It should be noted that the total energy corresponding to the electronic structure of the supercell is converged to a minimum value through iterative electronic steps.

[0105] For example, VASP software is used as the first-principles calculation software. The spin-orbit coupling parameters are written into the first INCAR file to obtain a second INCAR file. Static calculations are performed based on the second INCAR file, the second POSCAR file, the KPOINTS file, and the POTCAR file to obtain the CHGCAR file and WAVECAR file corresponding to the convergence of the electronic structure of the supercell. The WAVECAR file contains the electron wave function data corresponding to the supercell, and the CHGCAR file contains the charge density distribution data and magnetization density distribution data corresponding to the supercell.

[0106] Specifically, the spin magnetic moment acquisition module calculates the spin magnetic moment distribution of the supercell after structural optimization using the following formula:

[0107]

[0108] Among them, g e is the electron g factor, which is approximately 2.002319; μ B is the Bohr magneton; m is the magnetization density distribution; V FFT is the total number of FFT grids; is the spin angular momentum vector.

[0109] Preferably, the direction of the spin angular momentum vector relative to the Cartesian coordinate system is (0, 0, 1).

[0110] It should be noted that the FFT grid refers to the grid used to discretize the real space or reciprocal space during the Fast Fourier Transform (FFT). Data reconstruction is performed on the real space or reciprocal space FFT grid based on the magnetization density distribution data, and the magnetization density distribution data on the FFT grid is converted into the spin magnetic moment distribution on the FFT grid according to formula (1). The spin magnetic moment distribution on the FFT grid means that each FFT grid point has a spin magnetic moment value.

[0111] Specifically, the magnetic field construction module includes a spin magnetic moment screening module and a magnetic field simulation module;

[0112] The spin magnetic moment screening module is used to set a preset boundary of the supercell, screen the spin magnetic moment according to the spin magnetic moment distribution and the preset boundary of the supercell, and send the screened spin magnetic moment to the magnetic field simulation module;

[0113] The magnetic field simulation module is used to simulate the magnetic field induction intensity of any point in the supercell after structural optimization based on the screened spin magnetic moment, and output the simulation results.

[0114] Specifically, the preset boundary of the supercell is a limiting length proportional to the lattice constant of the supercell.

[0115] Specifically, the schematic diagram of the calculation boundary and calculation area of ​​the supercell according to the embodiment of the present invention is as follows: Figure 3 As shown in the figure, the solid line is the supercell boundary and the dotted line is the virtual cell. The screening of the spin magnetic moment according to the spin magnetic moment distribution and the preset boundary of the supercell includes:

[0116] Obtaining a calculation boundary based on the calculation point and the preset boundary of the supercell; the calculation boundary includes: a_min, a_max, b_min, b_max, c_min, c_max;

[0117] Performing virtual cell mapping according to the coordinates of the calculation boundary to obtain a calculation region;

[0118] According to the spin magnetic moment distribution, the corresponding spin magnetic moment in the calculation area is screened.

[0119] Specifically, performing virtual cell mapping according to the coordinates of the calculation boundary to obtain the calculation area includes:

[0120] Expanding the supercell with virtual cells according to the coordinates of the calculation boundary;

[0121] Within the scope of the virtual unit cell and supercell after cell expansion, a hexahedral region with the same angle as the basis vector is enclosed by the calculation boundary;

[0122] Mapping the area of ​​the hexahedral region that exceeds the supercell range to the corresponding area of ​​the supercell to obtain a first calculation area;

[0123] The area of ​​the hexahedral region that does not exceed the supercell range is used as the second calculation area;

[0124] The union of the first calculation area and the second calculation area is used as the calculation area.

[0125] For example, assuming that the area beyond the supercell in the hexahedral area falls on the lower left part of a virtual cell, the lower left part of the virtual cell is mapped to the corresponding area of ​​the supercell, that is, the lower left part of the supercell.

[0126] It should be noted that the calculation point refers to any point in the supercell where the magnetic field induction intensity is to be calculated. a_min and a_max are the minimum and maximum values ​​of the boundary corresponding to the a-axis direction, with the coordinates of the calculation point on the a-axis as the center and the preset boundary as the length; b_min and b_max are the minimum and maximum values ​​of the boundary corresponding to the b-axis direction, with the coordinates of the calculation point on the b-axis as the center and the preset boundary as the length; c_min and c_max are the minimum and maximum values ​​of the boundary corresponding to the c-axis direction, with the coordinates of the calculation point on the c-axis as the center and the preset boundary as the length. a_min should be less than the length of the lattice vector a, b_min should be less than the length of the lattice vector b, and c_min should be less than the length of the lattice vector c; a_max, b_max, and c_max should be greater than 0 and greater than a_min, b_min, and c_min, respectively.

[0127] Preferably, a_min, a_max, b_min, b_max, c_min, and c_max are coordinates of a coordinate system with lattice vectors as coordinate axes. When a_min>0, a_max<|a|, b_min>0, b_max<|b|, c_min>0, and c_max<|c|, virtual cell mapping is not required.

[0128] It can be understood that the present invention obtains a calculation boundary based on the preset boundary of the supercell, and performs simulation calculations based on the calculation boundary to screen the spin magnetic moment of electrons closer to the calculation point. The calculation boundary is parallel to the unit cell basis vector and can be determined before iterating the magnetization density distribution data, thereby reducing the number of iterations. While meeting the calculation accuracy, the calculation time is greatly reduced and the calculation efficiency is improved. The present invention performs virtual unit cell mapping based on the coordinates of the calculation boundary. When the calculation point is close to the edge of the supercell, the area outside the supercell range in the hexahedron calculation area based on the basis vector is mapped to the corresponding area of ​​the supercell, thereby improving the accuracy of the intracrystalline magnetic field calculation results.

[0129] Specifically, the magnetic field simulation module calculates the magnetic field induction intensity at any point in the supercell after structural optimization using the following formula:

[0130]

[0131] Where μ0 is the vacuum permeability, is the screened spin magnetic moment, is the vector from the spin magnetic moment to any point in the supercell, and r is the distance from the spin magnetic moment to any point in the supercell.

[0132] Specifically, the magnetic field induction intensity at any point in the supercell is the sum of the magnetic field induction intensities generated by the screened spin magnetic moments at that point.

[0133] For example, the embodiment of the present invention calculates the convergence of the magnetic field in the supercell based on the spin magnetic moment in the calculation area of ​​the supercell, such as Figure 4 As shown in the figure, the limit distance is the distance from the center point to all calculation boundaries, and the coordinates of the center point are (3.08000, 7.11296, 13.21293). From formula (2), we can see that the farther the magnetic moment is from the center point, the smaller its contribution to the magnetic field induction intensity at the center point. Figure 4 It can be seen that as the restriction distance increases, that is, the calculation range increases, the calculation results of the magnetic field induction intensity at the center point converge, indicating that the correct magnetic field calculation results can be obtained by the above-mentioned method of screening the spin magnetic moment based on the preset boundary of the supercell.

[0134] It can be understood that the present invention provides an intracrystalline magnetic field simulation system based on first-principles calculations through a supercell construction module, a structure optimization module, a spin magnetic moment acquisition module, and a magnetic field construction module, which can efficiently simulate the magnetic field at any point in the crystal.

[0135] Compared with the prior art, the magnetic field simulation system based on first-principles calculation provided by the present invention has the following beneficial effects:

[0136] 1. The present invention introduces defects by performing stacking faults on the supercell and removing the corresponding atoms, taking into account the complexity of the influence of the intracrystalline magnetic field on the spin, and provides a basis for improving the accuracy of the calculation results of the intracrystalline magnetic field.

[0137] 2. The present invention provides an intracrystalline magnetic field simulation system based on first-principles calculations through a supercell construction module, a structure optimization module, a spin magnetic moment acquisition module, and a magnetic field construction module, which can efficiently simulate the magnetic field at any point in the crystal.

[0138] 3. The present invention obtains a calculation boundary based on a preset boundary of a supercell, and performs simulation calculations on the spin magnetic moments of electrons that are closer to the calculation point based on the calculation boundary. The calculation boundary is parallel to the unit cell basis vector and can be determined before iterating the magnetization density distribution data, thereby reducing the number of iterations. While meeting the calculation accuracy, the calculation time is greatly reduced and the calculation efficiency is improved.

[0139] 4. The present invention performs virtual cell mapping according to the coordinates of the calculation boundary. When the calculation point is close to the edge of the supercell, the area beyond the supercell range in the hexahedral calculation area based on the basis vector is mapped to the corresponding area of ​​the supercell, thereby improving the accuracy of the calculation results of the intracrystalline magnetic field.

[0140] Those skilled in the art will appreciate that all or part of the process steps of the above-described embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, such as a magnetic disk, an optical disk, a read-only memory, or a random access memory.

[0141] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A magnetic field simulation system based on first principles calculation, characterized in that: The system comprises: a supercell construction module for constructing a supercell, performing natural isotope substitution in the supercell, introducing defects, and sending the defect-introduced supercell to a structure optimization module; A structure optimization module is used to optimize the structure of the supercell with defects based on first principles until the supercell has a stable configuration, and send the optimized supercell to the spin magnetic moment acquisition module; A spin magnetic moment acquisition module is used to obtain magnetization density distribution data of the structurally optimized supercell, calculate the spin magnetic moment distribution of the structurally optimized supercell based on the magnetization density distribution data, and send the spin magnetic moment distribution to the magnetic field construction module; The magnetic field construction module is used to screen the spin magnetic moment according to the spin magnetic moment distribution, and simulate the magnetic field induction intensity of any point in the supercell after structural optimization based on the screened spin magnetic moment.

2. A magnetic field simulation system based on first principles calculation according to claim 1, characterized in that: The magnetic field construction module includes a spin magnetic moment screening module and a magnetic field simulation module; The spin magnetic moment screening module is used to set a preset boundary of the supercell, screen the spin magnetic moment according to the spin magnetic moment distribution and the preset boundary of the supercell, and send the screened spin magnetic moment to the magnetic field simulation module; The magnetic field simulation module is used to simulate the magnetic field induction intensity at any point in the structurally optimized supercell based on the screened spin magnetic moment and output the simulation results; The predetermined boundary of the supercell is a limiting length that is proportional to the lattice constant of the supercell.

3. A magnetic field simulation system based on first principles calculation according to claim 2, characterized in that: The screening of the spin magnetic moment according to the spin magnetic moment distribution and the preset boundary of the supercell includes: Obtaining a calculation boundary based on the calculation point and the preset boundary of the supercell; the calculation boundary includes: a_min, a_max, b_min, b_max, c_min, c_max; Performing virtual cell mapping according to the coordinates of the calculation boundary to obtain a calculation region; According to the spin magnetic moment distribution, the corresponding spin magnetic moment in the calculation area is screened; The calculation point refers to any point in the supercell where the magnetic field induction intensity is to be calculated.

4. A magnetic field simulation system based on first principles calculation according to claim 3, characterized in that: The performing virtual cell mapping according to the coordinates of the calculation boundary to obtain the calculation area includes: Expanding the supercell with virtual cells according to the coordinates of the calculation boundary; Within the scope of the virtual unit cell and supercell after cell expansion, a hexahedral region with the same angle as the basis vector is enclosed by the calculation boundary; Mapping the area of ​​the hexahedral region that exceeds the supercell range to the corresponding area of ​​the supercell to obtain a first calculation area; The area of ​​the hexahedral region that does not exceed the supercell range is used as the second calculation area; The union of the first calculation area and the second calculation area is used as the calculation area.

5. The magnetic field simulation system based on first principles calculation according to claim 1, characterized in that: The magnetic field induction intensity at any point in the supercell is the sum of the magnetic field induction intensities generated by the screened spin magnetic moments at that point.

6. The magnetic field simulation system based on first principles calculation according to claim 1, characterized in that: The supercell construction module includes a supercell initialization module and a supercell deformation module; The supercell initialization module is used to construct an initial cell, expand the initial cell into a supercell and send the supercell to the supercell deformation module; The supercell deformation module is used to perform natural isotope substitution in the supercell, perform stacking faults on the supercell, remove corresponding atoms to introduce defects, and send the supercell with introduced defects to the structure optimization module; The supercell deformation module performs stacking faults on the supercell and removes corresponding atomic introduced defects through the following steps: S11, selecting a first position for a stacking fault in the supercell, and translating atomic coordinates at the first position to obtain a stacking fault; S12. Select a second location for atomic removal in the supercell after the stacking fault, and remove corresponding atoms at the second location to introduce defects.

7. A magnetic field simulation system based on first principles calculation according to claim 6, characterized in that: The structural optimization module includes a parameter setting module, a structural optimization algorithm module and a structural optimization output module; The parameter setting module is used to set the optimization parameters and send them to the structure optimization algorithm module; The structural optimization algorithm module is used to optimize the structure of the supercell with defects using first-principles calculation software according to the optimization parameters, and send the results to the structural optimization output module; The structural optimization output module is used to determine whether the structurally optimized supercell has a stable configuration. If so, the structurally optimized supercell is sent to the magnetization density acquisition module; otherwise, the supercell deformation module is called to execute step S12 to change the second position, and then the structural optimization algorithm module is called until the structurally optimized supercell has a stable configuration.

8. The magnetic field simulation system based on first principles calculation according to claim 1, characterized in that: The spin magnetic moment acquisition module calculates the spin magnetic moment distribution of the optimized supercell using the following formula: Among them, g e is the electron g factor, which is approximately 2.002319; μ B is the Bohr magneton; m is the magnetization density distribution; V FFT is the total number of FFT grids; is the spin angular momentum vector.

9. The magnetic field simulation system based on first principles calculation according to claim 2, characterized in that: The magnetic field simulation module calculates the magnetic field induction intensity at any point in the supercell after structural optimization using the following formula: Where μ0 is the vacuum permeability, is the screened spin magnetic moment, is the vector from the spin magnetic moment to any point in the supercell, and r is the distance from the spin magnetic moment to any point in the supercell.

10. The magnetic field simulation system based on first principles calculation according to claim 6, characterized in that: The supercell deformation module performs natural isotope substitution in the supercell by the following steps: determining naturally occurring isotopes of said atomic type and their concentrations; Calculate the amount of isotopes of each type of atom based on the naturally occurring isotopes of the atom type and their concentrations; The same number of corresponding atoms is randomly replaced in the supercell according to the isotope number of each type of atoms.

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