A method for constructing intracrystalline magnetic field of complex atomic defects

Abstract

The application relates to a method for constructing an intracrystalline magnetic field of a complex atomic defect, and belongs to the field of quantum information science. The method comprises the following steps: constructing an initial unit cell and expanding the initial unit cell into a supercell; performing natural isotope replacement in the supercell; performing a stacking fault on the supercell and removing corresponding atoms to introduce defects; performing structure optimization on the supercell with the introduced defects based on a first principle until the structure-optimized supercell has a stable configuration, so that a structure-optimized supercell is obtained; obtaining magnetic density distribution data of the structure-optimized supercell through static electronic structure calculation; calculating spin magnetic moment distribution of the structure-optimized supercell according to the magnetic density distribution data; and calculating the magnetic field induction intensity of any point in the structure-optimized supercell according to the spin magnetic moment distribution to construct a magnetic field. The method provides a basis for studying the spin coherence properties of a color center material with a complex atomic defect by constructing an intracrystalline magnetic field.

Description

Technical Field

[0001] This invention relates to the field of quantum information science, and in particular to a method for constructing an intracrystalline magnetic field for complex atomic defects. Background Technology

[0002] Solid-state spin systems possess advantages such as long coherence times, high stability, and high integrability, attracting widespread attention in technologies like quantum computing and quantum precision measurement. Silicon carbide color centers (SCCCs) are a type of solid-state spin quantum material. Recent research has discovered a high-performance color center at room temperature within silicon carbide stacking faults. Its uniform dephase time at room temperature reaches 40.6 μs, and its non-uniform dephase time (T2*) is 1.2 μs, breaking the 1 μs limit of other silicon carbide color centers at room temperature. Stacking faults arise from the disorder of the crystal stacking order, and multiple stacking order disorderes can occur within a small number of crystal layers. The diverse stacking fault configurations, particularly the planar defects, increase the complexity of the influence of intracrystalline magnetic fields on the spin, potentially leading to the existence of numerous undiscovered high-performance color centers. This explains why the coherence time limits of silicon carbide color centers and other solid-state spin systems remain unrevealed.

[0003] The study of coherent properties of solid-state spin systems generally employs cluster correlation expansion (CCE) theory. However, existing studies on color center materials typically do not consider complex atomic defects, resulting in existing cluster correlation expansion algorithms failing to account for the influence of intracrystalline magnetic fields on spin coherence.

[0004] Therefore, studying the spin coherence properties of materials with complex atomic defect color centers by constructing intracrystalline magnetic fields is of great significance for exploring quantum materials with long coherence times. Quantum materials with long coherence times can improve the sensitivity of quantum precision detection and have broad application prospects in quantum computing and quantum communication. Summary of the Invention

[0005] Based on the above analysis, this invention aims to provide a method for constructing an intracrystalline magnetic field with complex atomic defects, addressing the problem that existing studies on color center materials generally do not consider complex atomic defects in their configurations, resulting in low simulation accuracy due to the lack of consideration for the influence of complex atomic defects and intracrystalline magnetic fields on spin coherence in current spin coherence property simulations. This invention provides a method for constructing an intracrystalline magnetic field with complex atomic defects, the method comprising the following steps:

[0006] The atomic type of the crystal is determined, an initial unit cell is constructed based on the atomic type and expanded into a supercell; natural isotope substitution is performed in the supercell; stacking faults are removed from the supercell and corresponding atomic defects are eliminated;

[0007] Based on first principles, the structure of the supercell with introduced defects is optimized until the optimized supercell has a stable configuration, thus obtaining the optimized supercell.

[0008] The magnetization density distribution data of the optimized supercell was obtained through static electronic structure calculations.

[0009] The spin magnetic moment distribution of the optimized supercell was calculated based on the magnetization density distribution data.

[0010] Based on the spin magnetic moment distribution, the magnetic field induction intensity at any point within the optimized supercell is calculated, and a magnetic field is constructed.

[0011] Furthermore, the process of performing stacking fault treatment on the supercell and removing corresponding atomic-introduced defects includes:

[0012] S11. Select a first position for stacking faults in the supercell, and translate atomic coordinates at the first position to obtain a stacking fault;

[0013] S12. Select a second position for atom removal in the supercell after stacking faults, and remove the corresponding atom to introduce defects at the second position.

[0014] Furthermore, the structural optimization of the supercell with introduced defects based on first-principles calculations... ， Until the optimized supercell has a stable configuration, including:

[0015] S21. Set optimization parameters;

[0016] S22. Based on the optimization parameters, first-principles calculation software is used to optimize the structure of the supercell with introduced defects.

[0017] S23. Determine whether the structure-optimized supercell has a stable configuration. If so, obtain the structure-optimized supercell; otherwise, return to step S12 to change the second position and execute steps S22 and S23.

[0018] Furthermore, the optimization parameters include the limit number of electronic steps, the limit number of ion steps, the ion step convergence accuracy, and the electronic step convergence accuracy.

[0019] Furthermore, by determining whether the absolute value of the energy difference between adjacent ion steps is less than the ion step convergence accuracy, it can be determined whether the supercell after structural optimization has a stable configuration.

[0020] Furthermore, the magnetization density distribution data of the optimized supercell obtained through static electronic structure calculation includes:

[0021] Step S31: Keep the k-point setting and convergence accuracy unchanged, and set the spin-orbit coupling parameters;

[0022] Step S32: Set the number of ion steps to 0, and use first-principles calculation software based on the spin-orbit coupling parameters to obtain the energy corresponding to the supercell through electronic steps; iterate the electronic steps until the electronic structure of the supercell converges;

[0023] Step S33: Output the magnetization density distribution data corresponding to the convergence of the electronic structure of the supercell.

[0024] Furthermore, the energy corresponding to the current electronic step is compared with the energy corresponding to the electronic step of the previous iteration. If the absolute value of the difference between the two is less than the electronic step convergence accuracy, then the electronic structure of the supercell is determined to have converged.

[0025] Furthermore, the spin magnetic moment distribution of the structure-optimized supercell is calculated using the following formula:

[0026]

[0027] Among them, g e The electron g-factor is approximately 2.002319; μ B V is the Bohr magneton; m is the magnetization density distribution; V FFT This represents the total number of FFT grids. It is the spin angular momentum vector.

[0028] Furthermore, the magnetic field induction intensity at any point within the optimized supercell is calculated using the following formula:

[0029]

[0030] Where μ0 is the free permeability. The distribution is based on spin magnetic moment. Let be the vector from the spin magnetic moment to any point within the supercell, and r be the distance from the spin magnetic moment to any point within the supercell.

[0031] Furthermore, the construction of the initial unit cell based on the atomic type and its expansion into a supercell includes:

[0032] Based on the atom type, set the crystal lattice parameters and atomic coordinates, and construct the initial unit cell according to the crystal lattice parameters and atomic coordinates;

[0033] The initial unit cell is repeatedly expanded to obtain a supercell.

[0034] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0035] 1. This invention addresses the complexity of the influence of the intracrystalline magnetic field on spin by stacking faults in the supercell and removing defects introduced by corresponding atoms, thus providing a basis for improving the accuracy of intracrystalline magnetic field calculation results.

[0036] 2. This invention provides a foundation for improving the accuracy of simulating the spin coherence properties of materials with complex atomic defect color centers by constructing an intracrystalline magnetic field.

[0037] 3. This invention uses the preset boundary of the supercell to screen spin magnetic moments. When calculating the magnetic field induction intensity at any point in the supercell, the spin magnetic moments of electrons that are closer to that point are selected for calculation. This greatly reduces the calculation time and improves efficiency while meeting the calculation accuracy requirements.

[0038] 4. This invention performs virtual cell mapping based on the coordinates of the calculation boundary. When the calculation point is close to the edge of the supercell, the region in the hexahedral region that exceeds the range of the supercell is mapped to the corresponding region of the supercell, thereby improving the accuracy of the calculation results of the magnetic field within the crystal.

[0039] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0040] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0041] Figure 1 A flowchart illustrating a method for constructing an intracrystalline magnetic field for complex atomic defects, as provided in an embodiment of the present invention.

[0042] Figure 2 This is a schematic diagram of the silicon carbide stacked layer misalignment color center configuration used in the simulation of this embodiment of the invention;

[0043] Figure 3 This is a schematic diagram of the computational boundary and computational region of the supercell in an embodiment of the present invention;

[0044] Figure 4 This is a schematic diagram illustrating the convergence of the calculation of the magnetic field within the supercell based on the spin magnetic moment within the calculation region of the supercell, according to an embodiment of the present invention. Detailed Implementation

[0045] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0046] One specific embodiment of the present invention discloses a method for constructing an intracrystalline magnetic field for complex atomic defects. For example... Figure 1 As shown, the method includes the following steps:

[0047] Step S1: Determine the atomic type of the crystal, construct an initial unit cell based on the atomic type and expand it into a supercell; perform natural isotope substitution in the supercell; perform stacking fault treatment on the supercell and remove corresponding atomic-introduced defects;

[0048] Step S2: Optimize the structure of the supercell with introduced defects based on first principles until the optimized supercell has a stable configuration, thus obtaining the optimized supercell.

[0049] Step S3: Obtain the magnetization density distribution data of the optimized supercell through static electronic structure calculation;

[0050] Step S4: Calculate the spin magnetic moment distribution of the optimized supercell based on the magnetization density distribution data;

[0051] Step S5: Based on the spin magnetic moment distribution, calculate the magnetic field induction intensity at any point within the optimized supercell and construct the magnetic field.

[0052] Specifically, in step S1, constructing an initial unit cell based on the atom type and expanding it into a supercell includes:

[0053] Based on the atom type, set the crystal lattice parameters and atomic coordinates, and construct the initial unit cell according to the crystal lattice parameters and atomic coordinates;

[0054] The initial unit cell is repeatedly expanded to obtain a supercell.

[0055] It should be noted that crystal lattice parameters include the basis vectors of the unit cell and the angles between the crystal axes, used to describe the size and shape of a single unit cell; the basis vectors of the unit cell are the fundamental vectors describing the crystal structure, usually represented as three vectors. These form the edges of the unit cell. Atomic coordinates are used to determine the position of each atom within the unit cell. In simulation software, based on the set lattice parameters, the size and shape of the initial unit cell are determined in three-dimensional space. Using the atomic coordinates, each atom is placed at its corresponding position within the initial unit cell to perform initial unit cell modeling. The initial unit cell is then repeatedly expanded to perform supercell modeling.

[0056] For example, assuming the crystal is cubic, use variables... Let represent the basis vectors of its unit cell, and let variables α, β, and γ represent the angles between crystal axes b and c, a and c, and a and b, respectively. Let its basis vectors be... The angles between the crystal axes are set to α = β = γ = 90°. The atomic coordinates are represented by fractional coordinates. For example, if 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.

[0057] Preferably, VESTA software is used for initial cell and supercell modeling.

[0058] Furthermore, the substitution of natural isotopes in the supercell includes:

[0059] Determine the natural isotopes of the aforementioned atom type and their concentrations;

[0060] Calculate the number of isotopes for each type of atom based on their natural isotopes and concentrations.

[0061] The same number of corresponding atoms are randomly replaced in the supercell according to the isotopic quantity of each type of atom.

[0062] Specifically, the natural isotopes and their concentrations for each atomic type are determined. For each atomic type, i.e., each class of atoms, the number of natural isotopes for that class of atoms is calculated by multiplying the number of atoms of that class in the supercell by the concentration of their natural isotopes; based on the number of natural isotopes for that class of atoms, the same number of atoms of that class are randomly replaced with their natural isotopes in the supercell.

[0063] For example, using VESTA simulation software, assume the crystal is silicon carbide 4H-SiC, with atomic types including carbon atoms (C12) and silicon atoms (Si28), and the crystal system is hexagonal. Set the basis vectors of the initial unit cell as follows: Set the included angles between its crystal axes to α = β = 90° and γ = 120°, and for the initial unit cell in... A supercell was obtained by repeating the expansion 5, 5, 5 times in each direction; each carbon atom (C12) and each silicon atom (Si28) had its own number. The natural isotope of carbon atom C12 was determined to be C13, with a concentration of 1.1 at.%; the natural isotope of silicon atom Si28 was 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, the number of C13 is approximately 6 when calculated by multiplying 500 by 1.1 at.%, and the number of Si29 is approximately 23 when calculated by multiplying 500 by 4.67 at.%. Based on the number of C13 (6), a first random number sequence with 6 elements was generated using Python, where each element has a value between 1 and 500 and each element's value is unique. The element value represents the number of the carbon atom. In the supercell, each C12 atom with the same number corresponding to each element in the first random number sequence was replaced with C13. Similarly, based on the quantity 23 of Si29, a second random number sequence with 23 elements is generated, where the value of each element is between 1 and 500 and the values ​​of each element are different. In the supercell, the Si28 with the same number corresponding to each element in the second random number sequence is replaced with Si29.

[0064] It should be noted that the unit at.% represents the atomic percentage, which is the percentage of the number of atoms of that isotope out of the total number of atoms of that type.

[0065] Furthermore, the process of performing stacking fault treatment on the supercell and removing corresponding atomic-introduced defects includes:

[0066] S11. Select a first position for stacking faults in the supercell, and translate atomic coordinates at the first position to obtain a stacking fault;

[0067] S12. Select a second position for atom removal in the supercell after stacking faults, and remove the corresponding atom to introduce defects at the second position.

[0068] For example, the silicon carbide stacking fault color center configuration used in the simulation of the embodiments of the present invention is as follows: Figure 2 As shown, in the supercell, the z-coordinate (i.e., the c-coordinate) in the absolute coordinate system is greater than... and less than The region containing all atoms is designated as the first location for stacking faults. At this first location, the x-coordinates (i.e., a-coordinates) of all atoms are subtracted. 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 upwards along the y-axis A stacking fault structure is obtained. In the supercell after stacking faults, two positions with atomic coordinates (3.08000, 7.11296, 13.21293) and (3.08000, 7.11296, 15.10500) in the absolute coordinate system are selected as the second positions for atomic removal. The corresponding atoms are removed at the second positions to form double vacancy color centers, thereby introducing defects.

[0069] Understandably, this invention addresses the complexity of the influence of intracrystalline magnetic fields on spin by stacking faults in supercells and removing defects introduced by corresponding atoms, thus providing a foundation for improving the accuracy of intracrystalline magnetic field calculations.

[0070] Specifically, in step S2, the structure optimization of the supercell with introduced defects is performed based on first-principles calculations. ， Until the optimized supercell has a stable configuration, including:

[0071] S21. Set optimization parameters;

[0072] S22. Based on the optimization parameters, first-principles calculation software is used to optimize the structure of the supercell with introduced defects.

[0073] S23. Determine whether the structure-optimized supercell has a stable configuration. If so, obtain the structure-optimized supercell; otherwise, return to step S12 to change the second position and execute steps S22 and S23.

[0074] Preferably, the optimization parameters include the limit number of electronic steps, the limit number of ion steps, the ion step convergence accuracy, and the electronic step convergence accuracy.

[0075] It should be noted that through the aforementioned structural optimization, the positions of atoms in space are adjusted, eliminating atomic position distortions in the supercell and minimizing the total energy of the supercell, thereby obtaining a stable configuration. The electron density distribution and energy of the supercell are solved through the electronic steps. In each electronic step, the wave function and energy of the electron are calculated based on the current nucleus position. The motion of the nucleus in the average potential field generated by the electrons is obtained through ion steps. In each ion step, the force acting on the nucleus is calculated based on the electronic structure at the current nucleus position to update the atom's velocity, and the new position of the atom is calculated based on the updated atom's velocity. Therefore, it is necessary to set the maximum and minimum number of electronic and ion steps. The convergence accuracy of ion steps and electronic steps refers to whether the calculation results have reached the convergence standard during the structural optimization process. When the change in certain key calculation results (such as energy change and atomic displacement) is less than the set corresponding convergence accuracy, the calculation results are considered to have converged.

[0076] Preferably, VASP software is used as the first-principles calculation software to generate corresponding input files based on the optimization parameters, and the supercell with introduced defects is structurally optimized using the input files.

[0077] Specifically, the input files include INCAR, KPOINTS, POSCAR, and POTCAR files. The constructed defect-introduced supercell is exported to generate the first POSCAR file. The convergence accuracy is set to PBE pseudopotential, and the optimization parameters are written into the first INCAR file to generate a KPOINTS file containing k points or only containing Gamma points, and a POTCAR pseudopotential file. Using the above input files, the defect-introduced supercell is structurally optimized using VASP software to obtain the second POSCAR file.

[0078] It should be noted that the Brillouin zone refers to a periodically arranged region in reciprocal lattice 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, results that meet the accuracy requirements can be obtained by using only the Gamma point for related calculations, thereby greatly reducing the amount of computation and improving computational efficiency.

[0079] Preferably, the stability of the supercell after structural optimization is determined by judging whether the absolute value of the energy difference between adjacent ion steps is less than the ion step convergence accuracy.

[0080] Specifically, in step S3, obtaining the magnetization density distribution data of the optimized supercell through static electronic structure calculation includes:

[0081] Step S31: Keep the k-point setting and convergence accuracy unchanged, and set the spin-orbit coupling parameters;

[0082] Step S32: Set the number of ion steps to 0, and use first-principles calculation software based on the spin-orbit coupling parameters to obtain the energy corresponding to the supercell through electronic steps; iterate the electronic steps until the electronic structure of the supercell converges;

[0083] Step S33: Output the magnetization density distribution data corresponding to the convergence of the electronic structure of the supercell.

[0084] Preferably, the spin-orbit coupling parameters include: LSORBIT = TRUE, LNONCOLLINEAR = TRUE, LORBMOM = TRUE, and GGA_COMPAT = FALSE.

[0085] 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.

[0086] Specifically, the energy corresponding to the current electronic step is compared with the energy corresponding to the electronic step in the previous iteration. If the absolute value of the difference between the two is less than the electronic step convergence accuracy, then the electronic structure of the supercell is determined to have converged.

[0087] It should be noted that by iterating the electronic steps, the total energy corresponding to the electronic structure of the supercell is brought to a minimum.

[0088] For example, VASP software is used as the first-principles calculation software. The spin-orbit coupling parameters are written into a 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 electronic wavefunction data corresponding to the supercell, and the CHGCAR file contains the charge density distribution data and magnetization density distribution data corresponding to the supercell.

[0089] Specifically, in step S4, the spin magnetic moment distribution of the structure-optimized supercell is calculated using the following formula:

[0090]

[0091] Among them, g e The electron g-factor is approximately 2.002319; μ B V is the Bohr magneton; m is the magnetization density distribution; V FFT This represents the total number of FFT grids. It is the spin angular momentum vector.

[0092] Preferably, the direction of the spin angular momentum vector relative to the Cartesian coordinate system is (0, 0, 1).

[0093] 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. Based on the magnetization density distribution data, data reconstruction is performed on the real space or reciprocal space FFT grid, and the magnetization density distribution data of the FFT grid distribution is converted into the spin magnetic moment distribution of the FFT grid distribution according to formula (1). The spin magnetic moment of the FFT grid distribution refers to the fact that each FFT grid point has a spin magnetic moment value.

[0094] Specifically, in step S5, the magnetic field induction intensity at any point within the optimized supercell is calculated using the following formula:

[0095]

[0096] Where μ0 is the free permeability. The distribution is based on spin magnetic moment. Let be the vector from the spin magnetic moment to any point within the supercell, and r be the distance from the spin magnetic moment to any point within the supercell.

[0097] Preferably, the magnetic field induction intensity at any point within the supercell is the sum of the magnetic field induction intensities generated at that point by the selected spin magnetic moments.

[0098] Preferably, a preset boundary is set for the supercell, and the spin magnetic moment is screened based on the spin magnetic moment distribution and the preset boundary of the supercell; the preset boundary of the supercell is a limiting length that is proportional to the lattice constant of the supercell.

[0099] Preferably, a schematic diagram of the computational boundary and computational region of the supercell in an embodiment of the present invention is shown below. Figure 3 As shown in the figure, the solid lines represent supercell boundaries, and the dashed lines represent virtual units. The supercell-based preset boundary screening of spin magnetic moments includes:

[0100] The calculation boundary is obtained 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;

[0101] The computational region is obtained by performing virtual cell mapping based on the coordinates of the computational boundary;

[0102] Based on the spin magnetic moment distribution, the corresponding spin magnetic moments within the calculation region are selected.

[0103] Specifically, the virtual cell mapping based on the coordinates of the computational boundary to obtain the computational region includes:

[0104] Based on the coordinates of the calculated boundary, expand the supercell using a virtual cell;

[0105] Within the virtual unit cell and supercell after cell expansion, a hexahedral region is enclosed by the calculated boundary, which is consistent with the angle between the basis vectors.

[0106] The regions in the hexahedral region that extend beyond the supercell are mapped to the corresponding regions of the supercell to obtain the first computational region;

[0107] The region within the hexahedral region that does not exceed the supercell range is taken as the second calculation region;

[0108] The union of the first and second computation regions is taken as the computation region.

[0109] For example, assuming that the region of the hexahedral region that extends beyond the supercell falls in the lower left part of a certain virtual cell, then the lower left part of the virtual cell is mapped to the corresponding region of the supercell, that is, the lower left part of the supercell.

[0110] It should be noted that the calculation point refers to any point within the supercell where the magnetic field induction intensity is to be calculated. a_min and a_max are the minimum and maximum values ​​along the a-axis direction, centered on the coordinates of the calculation point along the a-axis and with a preset boundary as the length; b_min and b_max are the minimum and maximum values ​​along the b-axis direction, centered on the coordinates of the calculation point along the b-axis and with a preset boundary as the length; c_min and c_max are the minimum and maximum values ​​along the c-axis direction, centered on the coordinates of the calculation point along the c-axis and with a 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. Formula (2) is used to obtain the magnetic field induction intensity generated at the center point by the magnetic moments at all FFT grid points within the calculation region.

[0111] Preferably, a_min, a_max, b_min, b_max, c_min, and c_max are coordinates in 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.

[0112] Understandably, this invention uses a preset boundary of the supercell to screen spin magnetic moments. When calculating the magnetic field induction intensity at any point within the supercell, it selects the spin magnetic moments of electrons closest to that point for calculation. This significantly reduces computation time and improves efficiency while maintaining computational accuracy. Furthermore, this invention performs virtual cell mapping based on the coordinates of the calculation boundary. When the calculation point is close to the edge of the supercell, it maps regions in the hexahedral region that extend beyond the supercell to the corresponding regions within the supercell, thus improving the accuracy of the calculated intracrystalline magnetic field.

[0113] For example, in embodiments of the present invention, the convergence of the magnetic field within the supercell is calculated based on the spin magnetic moment within the computational region of the supercell, such as... Figure 4 As shown in the figure, the limiting distance is the distance from the center point to all calculated boundaries, and the coordinates of the center point are (3.08000, 7.11296, 13.21293). From formula (2), it can be seen 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 4It can be seen that as the limiting distance increases, i.e. the calculation range increases, the calculation result of the magnetic field induction intensity at the center point converges, indicating that the above method of screening spin magnetic moments based on the preset boundary of the supercell can obtain the correct magnetic field calculation result.

[0114] Understandably, this invention provides a foundation for improving the accuracy of simulating the spin coherence properties of materials with complex atomic defect color centers by constructing an intracrystalline magnetic field.

[0115] Compared with existing technologies, the beneficial effects of the method for constructing intracrystalline magnetic fields for complex atomic defects provided by this invention are as follows:

[0116] 1. This invention addresses the complexity of the influence of the intracrystalline magnetic field on spin by stacking faults in the supercell and removing defects introduced by corresponding atoms, thus providing a basis for improving the accuracy of intracrystalline magnetic field calculation results.

[0117] 2. This invention provides a foundation for improving the accuracy of simulating the spin coherence properties of materials with complex atomic defect color centers by constructing an intracrystalline magnetic field.

[0118] 3. This invention uses the preset boundary of the supercell to screen spin magnetic moments. When calculating the magnetic field induction intensity at any point in the supercell, the spin magnetic moments of electrons that are closer to that point are selected for calculation. This greatly reduces the calculation time and improves efficiency while meeting the calculation accuracy requirements.

[0119] 4. This invention performs virtual cell mapping based on the coordinates of the calculation boundary. When the calculation point is close to the edge of the supercell, the region in the hexahedral region that exceeds the range of the supercell is mapped to the corresponding region of the supercell, thereby improving the accuracy of the calculation results of the magnetic field within the crystal.

[0120] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0121] The above description is only a preferred 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 conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for constructing an intracrystalline magnetic field for complex atomic defects, characterized in that, The method includes the following steps: The atomic type of the crystal is determined, an initial unit cell is constructed based on the atomic type and expanded into a supercell; natural isotope substitution is performed in the supercell; stacking faults are removed from the supercell and corresponding atomic defects are eliminated; Based on first principles, the structure of the supercell with introduced defects is optimized until the optimized supercell has a stable configuration, thus obtaining the optimized supercell. The magnetization density distribution data of the optimized supercell was obtained through static electronic structure calculations. The spin magnetic moment distribution of the optimized supercell was calculated based on the magnetization density distribution data. Based on the spin magnetic moment distribution, the magnetic field induction intensity at any point within the optimized supercell is calculated, and a magnetic field is constructed. The process of stacking faults in the supercell and removing corresponding atomic-introduced defects includes: S11. Select a first position for stacking faults in the supercell, and translate atomic coordinates at the first position to obtain a stacking fault; S12. Select a second position for atom removal in the supercell after stacking faults, and remove the corresponding atom at the second position to introduce defects; The method of optimizing the structure of a supercell with introduced defects based on first-principles calculations until the optimized supercell has a stable configuration includes: S21. Set optimization parameters; S22. Based on the optimization parameters, first-principles calculation software is used to optimize the structure of the supercell with introduced defects. S23. Determine whether the structure-optimized supercell has a stable configuration. If so, obtain the structure-optimized supercell; otherwise, return to step S12 to change the second position and execute steps S22 and S23. The spin magnetic moment distribution of the optimized supercell is calculated using the following formula: ，（1） in, The electron g-factor is approximately 2.002319; For Bohr magneton; The magnetization density distribution; This represents the total number of FFT grids. It is the spin angular momentum vector; The magnetic field strength at any point within the optimized supercell is calculated using the following formula: ，（2） in, The permeability of free space, The distribution is based on spin magnetic moment. Let be the vector from the spin magnetic moment to any point within the supercell. denoted as , where is the distance from the spin magnetic moment to any point within the supercell.

2. The method for constructing an intracrystalline magnetic field for complex atomic defects according to claim 1, characterized in that, The optimization parameters include the limit on the number of electronic steps, the limit on the number of ion steps, the convergence accuracy of the ion steps, and the convergence accuracy of the electronic steps.

3. The method for constructing an intracrystalline magnetic field for complex atomic defects according to claim 2, characterized in that, By determining whether the absolute value of the energy difference between adjacent ion steps is less than the ion step convergence accuracy, it can be determined whether the supercell after structure optimization has a stable configuration.

4. The method for constructing an intracrystalline magnetic field for complex atomic defects according to claim 2, characterized in that, The magnetization density distribution data of the optimized supercell obtained through static electronic structure calculations includes: Step S31: Keep the k-point setting and convergence accuracy unchanged, and set the spin-orbit coupling parameters; Step S32: Set the number of ion steps to 0, and use first-principles calculation software based on the spin-orbit coupling parameters to obtain the energy corresponding to the supercell through electronic steps; iterate the electronic steps until the electronic structure of the supercell converges; Step S33: Output the magnetization density distribution data corresponding to the convergence of the electronic structure of the supercell.

5. The method for constructing an intracrystalline magnetic field for complex atomic defects according to claim 4, characterized in that, The energy corresponding to the current electronic step is compared with the energy corresponding to the electronic step of the previous iteration. If the absolute value of the difference between the two is less than the electronic step convergence accuracy, then the electronic structure of the supercell is determined to be converged.

6. The method for constructing an intracrystalline magnetic field for complex atomic defects according to claim 1, characterized in that, The process of constructing an initial unit cell based on the atomic type and expanding it into a supercell includes: Based on the atom type, set the crystal lattice parameters and atomic coordinates, and construct the initial unit cell according to the crystal lattice parameters and atomic coordinates; The initial unit cell is repeatedly expanded to obtain a supercell.

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