A design method of a multiferroic based on vanadium-doped two-dimensional ferroelectrics and the multiferroic

Abstract

The application belongs to the technical field of multiferroic materials, and relates to a design method of a multiferroic material based on a vanadium-doped two-dimensional ferroelectric body and the multiferroic material. Single-layer NbOI2 primitive cells are expanded in different directions to obtain supercells of different sizes. Vanadium is used as a doping element to dope the supercells of different sizes, and the doping configurations of each supercell under different doping concentrations are obtained. The doping configuration with the lowest total energy of the ferromagnetic state and the antiferromagnetic state under each doping concentration is used as the ground state configuration of the doping concentration. The band gap Eg and the spontaneous ferroelectric polarization intensity along the b-axis of the ground state configuration under different doping concentrations are calculated. A double-Y-axis curve graph is drawn with the doping concentration as the horizontal coordinate and the spontaneous ferroelectric polarization intensity and the band gap Eg as the vertical coordinate, and the multiferroic phase region and the magnetic semimetal phase region are divided. The doping concentration-physical property evolution phase diagram is obtained, so that the corresponding doping concentration value range of the ground state configuration with the multiferroic phase of ferroelectricity and antiferromagnetism is obtained to design the multiferroic material.

Description

Technical Field

[0001] This invention relates to the field of multiferroic materials technology, and in particular to a design method and a multiferroic body based on vanadium-doped two-dimensional ferroelectrics. Background Technology

[0002] In recent years, two-dimensional multiferroic materials have shown great application potential in next-generation spintronic devices, magnetoelectric sensors, and multi-state storage due to their unique properties, such as atomic-level thickness and the coexistence of ferroelectric and magnetic order. However, their development faces a fundamental challenge: ferroelectricity and magnetism are inherently conflicting in electronic structure, and ferroelectricity typically requires cations to be... Configuration, while magnetism depends on partially filled d orbitals (such as...) (n≠0), which makes intrinsic two-dimensional multiferroic materials extremely rare.

[0003] To address these challenges, current research focuses on introducing magnetism into non-magnetic two-dimensional systems and achieving coexistence and coupling of the two through external field or structural engineering methods such as doping, heterostructure construction, and strain modulation. For example, the multiferroic properties of BiFeO3-based nanomaterials are optimized, magnetoelectric coupling mechanisms are explored in FeI2 / In2Se3 heterojunctions and strain-modulated ZnIn2S4 systems, and magnetic superlattices are constructed through intercalation-cation exchange strategies. This demonstrates that through reasonable material design and property control, the synergistic design and functional integration of ferroelectricity, magnetism, and magnetoelectric coupling can be achieved in the two-dimensional limit, providing a rich material platform and physical basis for novel low-power, highly integrated information devices.

[0004] Specifically, monolayer NbOI2 is a two-dimensional material in the NbOX2 family that exhibits robust room-temperature ferroelectricity. From a microscopic perspective, its ferroelectricity originates from Nb. 4+ Synergistic effect of ionic electronic configuration and crystal structure distortion: Nb 4d 1 Electron half-occupancy Track, such as Figure 1 As shown in (a) and (b), an Nb-Nb dimer structure is formed along the a-axis, while along the b-axis... The orbitals remain empty, and the electronic structure is simulated. The configuration satisfies the ferroelectricity requirement, and the dimerization of the a-axis leads to adjacent The overlap of orbits forms local electron pairs, quenching the magnetic moment and making the system nonmagnetic. To address the challenge of achieving intrinsic multiferroic properties in two-dimensional ferroelectric materials due to the mutual repulsion between ferroelectricity and magnetic electrons, mainstream existing strategies include constructing van der Waals heterojunctions and applying epitaxial strain. For example, heterojunctions can be built by stacking FeI2 and In2Se3 to induce magnetoelectric coupling at the interface, or biaxial tensile strain can be used to modulate the flat band structure of ZnIn2S4 to excite itinerant ferromagnetism. However, these methods suffer from complex processes, unstable interfaces, weak coupling strength, or difficulty in integration. Furthermore, these approaches cannot resolve the fundamental conflict between the electronic structures of ferroelectricity and magnetism, and the material still struggles to exhibit an intrinsic multiferroic phase. In addition, while applying epitaxial strain can modulate the electronic structure and magnetic order of the material, it usually requires an external loading device in practical devices, making it difficult to achieve static, uniform, and integrable continuous strain. Excessive strain can also induce lattice distortion or even fracture, especially for NbOI2 monolayers with fine structural features such as Peierls dimerization, where small structural perturbations may disrupt the origin of ferroelectricity and inhibit functional performance.

[0005] In summary, existing design methods for two-dimensional multiferroic materials suffer from problems such as complex processes, unstable interfaces, weak coupling strength, difficulty in integration, inability to make the material exhibit intrinsic multiferroic properties, and even damage to the material structure. Summary of the Invention

[0006] Therefore, the technical problem to be solved by the present invention is to overcome the problems of complex process, unstable interface, weak coupling strength, difficulty in integration, inability to make the material exhibit intrinsic multiferroicity, and even damage to the material structure in the design methods of two-dimensional multiferroic materials in the prior art.

[0007] To address the aforementioned technical problems, this invention provides a design method for multiferroic materials based on vanadium-doped two-dimensional ferroelectric materials, comprising:

[0008] A monolayer of NbOI2 was obtained as the primitive cell, and the primitive cell was expanded in different directions to obtain supercells of different sizes; vanadium was used as the doping element to dope supercells of different sizes to obtain the doping configuration of each supercell under different doping concentrations.

[0009] Calculate the total energy of the ferromagnetic and antiferromagnetic states for each doping configuration at each doping concentration, and take the doping configuration with the lowest total energy of the ferromagnetic and antiferromagnetic states at each doping concentration as the ground state configuration for that doping concentration.

[0010] Calculate the band gap Eg and spontaneous ferroelectric polarization intensity along the b-axis for ground state configurations with different doping concentrations, and plot a double Y-axis curve with doping concentration as the abscissa and spontaneous ferroelectric polarization intensity and band gap Eg as the ordinates; divide the multiferroic phase region and magnetic half-metal phase region in the double Y-axis curve to obtain the doping concentration-property evolution phase diagram.

[0011] Based on the doping concentration-property evolution phase diagram, the range of doping concentration values ​​corresponding to the multiferroic phase with ferroelectricity and antiferromagnetism in the ground state configuration is obtained, so as to design the multiferroic body.

[0012] Preferably, a monolayer of NbOI2 is obtained as the primitive cell, and the primitive cell is expanded in different directions to obtain supercells of different sizes; vanadium is used as the doping element to dope the supercells of different sizes to obtain the doping configurations of each supercell at different doping concentrations, including:

[0013] Extending along the lattice a-axis of the primitive cell yields a supercell of the first size; extending along the lattice b-axis of the primitive cell yields a supercell of the second size; extending along both the lattice a-axis and b-axis of the primitive cell simultaneously yields a supercell of the third size.

[0014] Multiple doping concentrations with equal spacing are obtained. For each doping concentration, Nb atoms are replaced with vanadium atoms in supercells of different sizes to obtain the doping configurations corresponding to supercells of different sizes at that doping concentration.

[0015] Preferably, the total energy of the ferromagnetic and antiferromagnetic states for each doping configuration at each doping concentration is calculated, including:

[0016] Structural relaxation is performed on each doped configuration at each doping concentration to obtain the stable configuration of that doped configuration;

[0017] Static self-consistent calculations were performed on the steady-state configuration of the doped configuration to obtain the total energy of the ferromagnetic and antiferromagnetic states of the doped configuration.

[0018] Preferably, structural relaxation is performed on each doped configuration at each doping concentration to obtain a stable configuration of that doped configuration, including:

[0019] Input the crystal structure file, parameter control file, k-point mesh file, pseudopotential file, and runtime control file for each doping configuration at each doping concentration into the magnetic state calculation directory;

[0020] After setting the maximum number of ion step iterations to 30 in the parameter control file, start the VASP relaxation calculation.

[0021] When the ion step iteration reaches the point where the maximum atomic force is <0.01eV / Å, relaxation ends, and a stable configuration file for this doped configuration is generated.

[0022] Preferably, a static self-consistent calculation is performed on the steady-state configuration of the doped configuration to obtain the total energy of the ferromagnetic and antiferromagnetic states of the doped configuration, including:

[0023] Use the stable configuration file of the doped configuration as the crystal structure file of the doped configuration, and start the self-consistent calculation after setting the maximum number of ion steps in the parameter control file to 0.

[0024] Based on the 1F energy value in the output file after the self-consistent calculation, the total energy of the ferromagnetic and antiferromagnetic states of this doped configuration is obtained.

[0025] Preferably, the calculation of the band gap Eg and spontaneous ferroelectric polarization along the b-axis for ground state configurations with different doping concentrations includes:

[0026] Using the centrosymmetric phase corresponding to each ground state configuration as a reference phase, multiple intermediate transition phases are obtained based on the reference phase when the atomic displacement changes from 100% to 10%.

[0027] Structural relaxation and self-consistency calculations were performed for each intermediate transition phase to obtain the polarization displacement correlation value and the reference polarization displacement reference value for each intermediate transition phase.

[0028] Based on the polarization displacement correlation value of each intermediate transition phase, the polarization displacement reference value of the reference phase, and the lattice parameters of the ground state configuration along the a-axis and b-axis, the spontaneous ferroelectric polarization intensity of each intermediate transition phase along the b-axis is calculated, thereby obtaining the spontaneous ferroelectric polarization intensity of the ground state configuration along the b-axis.

[0029] Structural relaxation and self-consistency calculations are performed on each ground state configuration to obtain the stable configuration;

[0030] Based on the crystal structure file, parameter control file, k-point grid file, pseudopotential file, operation control file, and stable configuration file of the ground state configuration, spin polarization band calculation is performed to obtain the band data of the ground state configuration, and then the band gap Eg of the ground state configuration is calculated based on the band data.

[0031] Preferably, the doping concentration-property evolution phase diagram is obtained by dividing the dual Y-axis curve into a multiferroic phase region and a magnetic half-metallic phase region, including: dividing the dual Y-axis curve into a multiferroic phase region and a magnetic half-metallic phase region based on the band gap Eg of the multiferroic phase region being greater than a preset threshold and the band gap Eg of the magnetic half-metallic phase region being less than a preset threshold; wherein, the preset threshold is less than or equal to 0.01 eV.

[0032] Preferably, the doping concentration ranges from 0.125 to 0.625 when the ground state configuration is a multiferroic phase with ferroelectricity and antiferromagnetism.

[0033] The doping concentration ranges from 0.75 to 0.875 when the ground state configuration is a half-metallic phase.

[0034] When the doping concentration is 1, the ground state configuration is a ferromagnetic metallic phase.

[0035] Preferably, the multiferroic body is designed based on the range of doping concentration values, including:

[0036] Based on the range of doping concentrations, vanadium ions are used to dop NbOI2 with equivalent cations, thereby disrupting the atomic dimerization structure of NbOI2 and activating the local magnetic moment to prepare a multiferroic body.

[0037] The present invention also provides a multiferroic body, which is designed by the above-described design method for multiferroic bodies based on vanadium-doped two-dimensional ferroelectric bodies.

[0038] The multiferroic body design method based on vanadium-doped two-dimensional ferroelectrics provided in this application has the following advantages:

[0039] By expanding the monolayer NbOI2 primitive cell in different directions, supercells of different sizes were obtained. Vanadium was then used as the dopant element to dope these supercells, resulting in doping configurations for each supercell at different doping concentrations. The doping configuration with the lowest total energy of the ferromagnetic and antiferromagnetic states at each doping concentration was selected as the ground state configuration for that concentration. The band gap Eg and spontaneous ferroelectric polarization along the b-axis were calculated for the ground state configurations at different doping concentrations. A dual Y-axis curve was plotted with doping concentration on the x-axis and spontaneous ferroelectric polarization and band gap Eg on the y-axis. The dual Y-axis curve was used to divide the region into a multiferroic phase region and a magnetic half-metal phase region, resulting in a doping concentration-property evolution phase diagram. This allowed the determination that the ground state configuration exhibits ferroelectricity. The application proposes and verifies a novel control pathway based on equivalent cation doping (vanadium ions replacing niobium ions). By breaking down dimerization and inducing local magnetic moments through vanadium doping, stable magnetic order is introduced while preserving the intrinsic ferroelectric polarization of NbOI2, allowing ferroelectricity and magnetism to coexist. This approach eliminates the need for multilayer stacking, interface assembly, and epitaxial strain processes, thus avoiding problems such as interface diffusion, weak lattice fit and coupling strength, and lattice distortion caused by epitaxial strain. The application achieves intrinsic multiferroic properties without compromising the material structure. Attached Figure Description

[0040] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein:

[0041] Figure 1 This is a schematic diagram of the NbOI2 crystal structure and orbital energy splitting provided in this application; wherein, Figure 1 (a) in the diagram is a schematic diagram of the crystal structure of a single-layer NbOI2. Figure 1 (b) in the diagram shows the local aggregate structure of NbOI2 and the Nb-d orbital energy splitting.

[0042] Figure 2 A flowchart of the design method for multiferroic materials based on vanadium-doped two-dimensional ferroelectrics provided in this application;

[0043] Figure 3 This is a schematic diagram of the doping configuration of each supercell when the doping concentration is 0.375, as provided in this application; wherein, Figure 3 (a) in the diagram is a schematic diagram of the doping configuration of the first-sized supercell extending along the a-axis of the lattice when the doping concentration is 0.375. Figure 3 (b) in the diagram is a schematic diagram of the doping configuration of the second-sized supercell extending along the b-axis of the lattice when the doping concentration is 0.375. Figure 3 (c) is a schematic diagram of the doping configuration of the third-size supercell that extends along both the a-axis and b-axis of the lattice when the doping concentration is 0.375.

[0044] Figure 4 This is a schematic diagram of the doping configuration of each supercell when the doping concentration is 0.5, as provided in this application; wherein, Figure 4 (a) in the diagram is a schematic diagram of the doping configuration of the first-sized supercell extending along the a-axis of the lattice when the doping concentration is 0.5. Figure 4 (b) is a schematic diagram of the doping configuration of the second-sized supercell extending along the b-axis of the lattice when the doping concentration is 0.5.

[0045] Figure 5 The doping concentration-property evolution phase diagram provided in this application;

[0046] Figure 6 The present application provides the structure and ferroelectric properties of NbOI2 and its vanadium-doped system; wherein, Figure 6 (a) in the figure is a side view of NbOI2 along the b-axis of the crystal lattice. Figure 6 (b) in the diagram is a schematic diagram of the ferropolarization direction of NbOI2. Figure 6 (c) in the figure is the ferroelectric double well potential energy diagram of the NbOI2 vanadium doped system under different doping concentrations;

[0047] Figure 7 This application provides schematic diagrams of the projected density of states for Nb, V, and O at different doping concentrations; wherein, Figure 7 In the figure, (a) represents the projected density of states of Nb, V, and O when the doping concentration x=0. Figure 7 In the diagram, (b) represents the projected density of states of Nb, V, and O when the doping concentration x = 0.125. Figure 7In the diagram, (c) represents the projected density of states of Nb, V, and O when the doping concentration x = 0.25. Figure 7 In the figure, (d) represents the projected density of states of Nb, V, and O when the doping concentration x = 0.375. Figure 7 In this context, (e) represents the projected density of states of Nb, V, and O when the doping concentration x = 0.5. Figure 7 In the figure, (f) represents the projected density of states of Nb, V, and O when the doping concentration x = 0.625;

[0048] Figure 8 This is a schematic diagram of the lattice structure and charge density distribution of NbOI2 and its vanadium-doped system provided in this application; wherein, Figure 8 (a) in the diagram is a schematic diagram of the crystal lattice structure of NbOI2. Figure 8 (b) in the middle is (Nb) 0.875 V 0.125 A schematic diagram of the crystal structure of OI2. Figure 8 (c) in the diagram is a schematic diagram of the charge density distribution at the top of the valence band of NbOI2. Figure 8 (d) in (Nb) 0.875 V 0.125 )Schematic diagram of charge density distribution at the top of the OI2 valence band. Figure 8 (e) in (Nb) 0.875 V 0.125 A front view of the charge density distribution of Nb, I, and V atoms in OI2. Figure 8 (f) in (Nb) 0.875 V 0.125 Top view of the charge density distribution of Nb, I, and V atoms in OI2;

[0049] Figure 9 Provided for this application A schematic diagram illustrating the electronic phase transition and magnetoelectric coupling behavior of the system at high doping concentrations; where... Figure 9 (a) in the diagram is a schematic diagram of the projected density of states of the Vd orbitals when the doping concentration x = 0.625. Figure 9 (b) in the diagram is a schematic diagram of the projected density of states of the Vd orbitals when the doping concentration x = 0.75. Figure 9 (c) in (Nb) 0.375 V 0.625 The graph shows the variation trend of the average magnetic moment and polarization intensity of the OI2 system. Figure 9 (d) represents the condition of fixed V atom positions, (Nb) 0.375 V 0.625 The ferroelectric polarization electron contribution of OI2 varies with the local magnetic moment of V. Figure 9 (e) in the equation represents the atomic position modulation condition, where (Nb) 0.375 V 0.625 The ferroelectric polarization (P) of the OI2 system varies with the local magnetic moment of V. Figure 9 (f) in the equation is based on (Nb) 0.375 V 0.625 A schematic diagram of a high-sensitivity magnetoelectric sensor based on the OI2 system. Detailed Implementation

[0050] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0051] Please see Figure 2 , Figure 2 The diagram shows a flowchart of the design method for multiferroic materials based on vanadium-doped two-dimensional ferroelectrics provided in this application. The design method specifically includes steps S10 to S40:

[0052] S10: Obtain a monolayer of NbOI2 as the primitive cell, expand the primitive cell in different directions to obtain supercells of different sizes; use vanadium as the doping element to dope supercells of different sizes to obtain the doping configuration of each supercell under different doping concentrations.

[0053] S20: Calculate the total energy of the ferromagnetic and antiferromagnetic states for each doping configuration at each doping concentration, and take the doping configuration with the lowest total energy of the ferromagnetic and antiferromagnetic states at each doping concentration as the ground state configuration for that doping concentration.

[0054] S30: Calculate the band gap Eg and spontaneous ferroelectric polarization intensity along the b-axis for ground state configurations with different doping concentrations, and plot a double Y-axis curve with doping concentration as the abscissa and spontaneous ferroelectric polarization intensity and band gap Eg as the ordinate; divide the multiferroic phase region and magnetic half-metal phase region in the double Y-axis curve to obtain the doping concentration-property evolution phase diagram.

[0055] S40: Based on the doping concentration-property evolution phase diagram, the range of doping concentration values ​​corresponding to the multiferroic phase with ferroelectricity and antiferromagnetism in the ground state configuration is obtained, so as to design the multiferroic body.

[0056] Furthermore, considering the arrangement characteristics of Nb atoms in NbOI2, this application constructs supercells by extending along the a-axis, b-axis, a-axis, and b-axis of the lattice, respectively. Then, based on the doping concentration, Nb atoms are systematically replaced with vanadium (V) atoms in the corresponding expanded lattice structure files, thereby generating doped configurations with different spatial arrangements. This method can examine the stability differences of V atoms under different local environments and eliminate modeling randomness by comparing the lowest energy configurations in different directions, thus more reliably determining the ground-state electronic structure and phase evolution behavior of the system.

[0057] Specifically, step S10 includes S100~S101:

[0058] S100: Extend along the lattice a-axis of the primitive cell to obtain a supercell of the first size; extend along the lattice b-axis of the primitive cell to obtain a supercell of the second size; extend simultaneously along both the lattice a-axis and the lattice b-axis of the primitive cell to obtain a supercell of the third size.

[0059] S101: Obtain multiple doping concentrations with equal spacing, and replace Nb atoms with vanadium atoms in supercells of different sizes with each doping concentration as the target to obtain the doping configurations corresponding to supercells of different sizes at that doping concentration.

[0060] like Figure 3 The diagram shows the doping configuration of each supercell when the doping concentration is 0.375, as provided in this application; where, Figure 3 (a) in the diagram is a schematic diagram of the doping configuration of the first-sized supercell extending along the a-axis of the lattice when the doping concentration is 0.375. Figure 3 (b) in the diagram is a schematic diagram of the doping configuration of the second-sized supercell extending along the b-axis of the lattice when the doping concentration is 0.375. Figure 3 (c) is a schematic diagram of the doping configuration of the third-size supercell that extends along both the a-axis and b-axis of the lattice when the doping concentration is 0.375.

[0061] like Figure 4 The diagram shows the doping configuration of each supercell when the doping concentration is 0.5, as provided in this application; where, Figure 4 (a) in the diagram is a schematic diagram of the doping configuration of the first-sized supercell extending along the a-axis of the lattice when the doping concentration is 0.5. Figure 4 (b) is a schematic diagram of the doping configuration of the second-sized supercell extending along the b-axis of the lattice when the doping concentration is 0.5.

[0062] Furthermore, after obtaining the doping configurations at various doping concentrations, this application uses VASP (containing five basic files: crystal structure file (POSCAR), parameter control file (INCAR), k-point mesh file (KPOINTS), pseudopotential file (POTCAR), and run control file (job.sh)) to complete the calculation in two steps. Specifically, it calculates the total energy of the ferromagnetic and antiferromagnetic states for each doping configuration at each doping concentration, including S200~S201:

[0063] S200: Perform structural relaxation on each doped configuration at each doping concentration to obtain the stable configuration of that doped configuration.

[0064] S201: Perform static self-consistent calculations on the steady-state configuration of the doped configuration to obtain the total energy of the ferromagnetic and antiferromagnetic states of the doped configuration.

[0065] In some embodiments, step S200 includes S200-1 to S200-3:

[0066] S200-1: Input the crystal structure file, parameter control file, k-point mesh file, pseudopotential file, and runtime control file for each doping configuration at each doping concentration into the magnetic state calculation directory.

[0067] S200-2: Set the maximum number of ion step iterations in the parameter control file to 30 and then start the VASP relaxation calculation.

[0068] S200-3: Relaxation ends when the ion step iteration reaches the point where the maximum atomic force is <0.01eV / Å, generating a stable configuration file for this doped configuration.

[0069] Step S201 includes S201-1 to S201-2:

[0070] S201-1: Use the stable configuration file of the doped configuration as the crystal structure file of the doped configuration, set the maximum number of ion steps in the parameter control file to 0, and then start the self-consistent calculation.

[0071] S201-2: Based on the 1F energy value in the output file after the self-consistent calculation, obtain the total energy of the ferromagnetic and antiferromagnetic states of this doped configuration.

[0072] It should be noted that, because the doped configuration may exhibit magnetism, this application considers both ferromagnetic and antiferromagnetic states when determining the stable configuration of the doped configuration. The initial atomic magnetic moments in the magnetic moment part of the parameter control file have been modified. Specifically, the ferromagnetic state is arranged in the same direction as "1 1 1", while the antiferromagnetic state is changed to an alternating arrangement of "1 1 -1-1" or "1 -1 1 -1" depending on the configuration. Self-consistent calculations are then performed to avoid falling into a metastable state with high energy due to improper initial magnetic moment settings, and to ensure that the calculation can converge to the true ground state with the lowest global energy.

[0073] Furthermore, step S30 involves calculating the band gap Eg and spontaneous ferroelectric polarization along the b-axis for ground-state configurations with different doping concentrations, including steps S300 to S304:

[0074] S300: Using the centrosymmetric phase corresponding to each ground state configuration as a reference phase, obtain multiple intermediate transition phases corresponding to atomic displacements ranging from 100% to 10%. For example, obtain multiple intermediate transition phases corresponding to atomic displacements of 100%, 90%, 80%, ... 10% based on the reference phase.

[0075] S301: Perform structural relaxation and self-consistency calculations for each intermediate transition phase to obtain the polarization displacement correlation value and the polarization displacement reference value of the reference phase for each intermediate transition phase.

[0076] S302: Based on the polarization displacement correlation value of each intermediate transition phase, the polarization displacement reference value of the reference phase, and the lattice parameters of the ground state configuration along the a-axis and b-axis, the spontaneous ferroelectric polarization intensity of each intermediate transition phase along the b-axis is calculated, thereby obtaining the spontaneous ferroelectric polarization intensity of the ground state configuration along the b-axis.

[0077] Specifically, the formula for calculating the spontaneous ferroelectric polarization intensity P along the b-axis in the intermediate transition phase is as follows: Where Dipx represents the polarization shift correlation value of the intermediate transition phase, Dip0 represents the polarization shift reference value of the reference phase, and a and b represent the lattice parameters of the ground state configuration along the a-axis and b-axis, respectively. The spontaneous ferroelectric polarization intensity of the intermediate transition phase along the b-axis corresponding to an atomic displacement of 100% is the same as the spontaneous ferroelectric polarization intensity of the ground state configuration along the b-axis.

[0078] S303: Perform structural relaxation and self-consistency calculations on each ground state configuration to obtain a stable configuration.

[0079] S304: Based on the crystal structure file, parameter control file, k-point grid file, pseudopotential file, operation control file, and stable configuration file of the ground state configuration, spin polarization band calculation is performed to obtain the band data of the ground state configuration, and then the band gap Eg of the ground state configuration is calculated based on the band data.

[0080] Optionally, in some embodiments, the method further includes extracting orbit-resolved projected density of states data of the ground state configuration and plotting the projected density of states distribution map to analyze the orbital occupancy characteristics of the ground state configuration. Specifically, based on the self-consistent calculation results of the ground state configuration, the charge density reading mode is set to 11 and the k-point grid is densified (e.g., the grid in the k-point grid file is multiplied), static density of states calculation is performed, and then the orbit-resolved projected density of states data is extracted after post-processing.

[0081] Specifically, the doping concentration-property evolution phase diagram is obtained by dividing the dual Y-axis curve into a multiferroic phase region and a magnetic half-metallic phase region, including: dividing the dual Y-axis curve into a multiferroic phase region and a magnetic half-metallic phase region based on the band gap Eg of the multiferroic phase region being greater than a preset threshold and the band gap Eg of the magnetic half-metallic phase region being less than a preset threshold; wherein, the preset threshold is less than or equal to 0.01eV.

[0082] For example, such as Figure 5 The diagram shown is a doping concentration-property evolution phase diagram provided in this application. The horizontal axis represents the doping concentration x, the left vertical axis represents the polarization intensity P in pC / m, the right vertical axis represents the band gap Eg in eV, the multiferroic phase region is the part where Eg > 0, and the magnetic half-metal phase region is the part where Eg → 0.

[0083] from Figure 5As can be seen, the doping concentration ranges from 0.125 to 0.625 when the ground state configuration is a multiferroic phase with ferroelectricity and antiferromagnetism; the doping concentration ranges from 0.75 to 0.875 when the ground state configuration is a half-metallic phase; and when the doping concentration is 1, the ground state configuration is a ferromagnetic metallic phase.

[0084] like Figure 6 The diagram shows the structure and ferroelectric properties of NbOI2 and its vanadium-doped system provided in this application; wherein, Figure 6 (a) in the figure is a side view of NbOI2 along the b-axis of the crystal lattice. Figure 6 (b) in the diagram is a schematic diagram of the ferropolarization direction of NbOI2. Figure 6 (c) in the figure is the potential energy diagram of the ferroelectric double well of the NbOI2 vanadium doped system under different doping concentrations.

[0085] from Figure 6 As can be seen in (a) of NbOI₂, there are two unequal Nb-O bond lengths (1.83 Å and 2.10 Å) along the polarization direction, resulting in an off-center displacement of approximately 0.14 Å for the Nb ion, which constitutes the structural basis for ferroelectricity. Figure 6 As can be seen from (c) in the figure, the system can still maintain a stable ferroelectric phase after vanadium doping.

[0086] like Figure 7 The diagram shown is a schematic representation of the projected density of states of Nb, V, and O at different doping concentrations provided in this application; wherein, Figure 7 In the figure, (a) represents the projected density of states of Nb, V, and O when the doping concentration x=0. Figure 7 In the diagram, (b) represents the projected density of states of Nb, V, and O when the doping concentration x = 0.125. Figure 7 In the diagram, (c) represents the projected density of states of Nb, V, and O when the doping concentration x = 0.25. Figure 7 In the figure, (d) represents the projected density of states of Nb, V, and O when the doping concentration x = 0.375. Figure 7 In this context, (e) represents the projected density of states of Nb, V, and O when the doping concentration x = 0.5. Figure 7 In the equation (f), the projected density of states of Nb, V and O is given by doping concentration x = 0.625.

[0087] from Figure 7 As can be seen from the data, with the increase of V doping concentration, the doped system always maintains significant Nb / Vd and Op orbital hybridization characteristics in the energy region from -2eV to 0eV, and the Vd / Op hybridization intensity gradually increases with doping, indicating that ferroelectric polarization is driven by the synergistic hybridization of transition metal d orbitals and Op orbitals.

[0088] like Figure 8The diagram shows the lattice structure and charge density distribution of NbOI2 and its vanadium-doped system provided in this application; wherein, Figure 8 (a) in the diagram is a schematic diagram of the crystal lattice structure of NbOI2. Figure 8 (b) in the middle is (Nb) 0.875 V 0.125 A schematic diagram of the crystal structure of OI2. Figure 8 (c) in the diagram is a schematic diagram of the charge density distribution at the top of the valence band of NbOI2. Figure 8 (d) in (Nb) 0.875 V 0.125 )Schematic diagram of charge density distribution at the top of the OI2 valence band. Figure 8 (e) in (Nb) 0.875 V 0.125 A front view of the charge density distribution of Nb, I, and V atoms in OI2. Figure 8 (f) in (Nb) 0.875 V 0.125 A top view of the charge density distribution of Nb, I, and V atoms in OI2.

[0089] from Figure 8 As can be seen in (a) of the image, NbOI2 exhibits Nb-Nb dimerization (bond lengths of 3.15 Å and 4.42 Å, respectively). Figure 8 As shown in (b), with low doping (doping concentration x = 0.125), the bond lengths in the doped region increase significantly (bond lengths are 3.92 Å and 4.07 Å, respectively), and dimerization is disrupted. Figure 8 As can be seen in (c), the top charge distribution of the NbOI2 valence band shows... Orbital overlap forms localized electron pairs, resulting in a nonmagnetic ground state. Figure 8 (d) shows that after high doping (doping concentration x=0.625), adjacent The orbital overlap completely disappeared, thus magnetism appeared. Figure 8 The charge density distributions in (e) and (f) further demonstrate the formation of a continuous orbital network between Nb / V and I atoms, facilitating the passage of Nb... 4+ –I - –V 4+ Superswitching enables long-range antiferromagnetic order to provide electron channels.

[0090] like Figure 9 The image shown is provided by this application. A schematic diagram illustrating the electronic phase transition and magnetoelectric coupling behavior of the system at high doping concentrations; where... Figure 9 (a) in the diagram is a schematic diagram of the projected density of states of the Vd orbitals when the doping concentration x = 0.625. Figure 9 (b) in the diagram is a schematic diagram of the projected density of states of the Vd orbitals when the doping concentration x = 0.75. Figure 9(c) in (Nb) 0.375 V 0.625 The graph shows the variation trend of the average magnetic moment and polarization intensity of the OI2 system. Figure 9 (d) represents the condition of fixed V atom positions, (Nb) 0.375 V 0.625 The ferroelectric polarization electron contribution of OI2 varies with the local magnetic moment of V. Figure 9 (e) in the equation represents the atomic position modulation condition, where (Nb) 0.375 V 0.625 The ferroelectric polarization (P) of the OI2 system varies with the local magnetic moment of V. Figure 9 (f) in the equation is based on (Nb) 0.375 V 0.625 A schematic diagram of a high-sensitivity magnetoelectric sensor based on the OI2 system.

[0091] from Figure 9 As can be seen from (a) and (b) in the figure, when the doping concentration increases from 0.625 to 0.75, V- / The orbitals shift towards the Fermi level and broaden significantly, causing the spin-down channel bandgap to close, and the system transitions from a multiferroic semiconductor to a half-metallic state; from Figure 9 As can be seen in (c), when the doping concentration is 0.625%, the system exhibits magnetoelectric coupling characteristics with opposite signs between the Nb and V sites. Enhanced polarization increases the Nb magnetic moment (negative coupling) while decreasing the V magnetic moment (positive coupling). This relationship between the magnetic moment and polarization intensity is obtained from the Landau level. It is known that only when and Only when the signs are opposite can it be expressed. Figure 9 The magnetoelectric response shown in (c) is as follows, where, Represents the square of the magnetic moment; Indicates polarization intensity; Indicates the system temperature; This represents the Nell temperature at zero polarization; Represents the polarization-magnetic moment coupling coefficient of the Nb component; Represents the polarization-magnetic moment coupling coefficient of the V component; This represents the coefficient of the temperature term in the Landau free energy expansion; Let represent the coefficients of the fourth-order terms in the Landau free energy expansion. From Figure 9 As can be seen from (d) and (e) in the figure, Nb exhibits a conventional negative coupling coefficient, while V exhibits an anomalous positive coupling coefficient. This coupling mainly originates from polarization-driven lattice displacement rather than electron cloud rearrangement. Based on this magnetoelectric response mechanism, a low-power, high-sensitivity magnetoelectric sensor based on this two-dimensional system can also be designed, such as... Figure 9As shown in (f), when an external magnetic field acts on a multiferroic body based on a vanadium-doped two-dimensional ferroelectric material, the anomalous positive magnetoelectric coupling effect of vanadium ions can cause the multiferroic body to undergo lattice displacement-type ferroelectric polarization reversal or change. Conversely, when an external electric field modulates the ferroelectric polarization of the multiferroic body, the lattice distortion caused by polarization will inversely regulate the local magnetic moment and magnetic order state of the system through magnetoelectric coupling. Therefore, this magnetoelectric sensor utilizes the anomalous positive magnetoelectric coupling generated by polarization-driven lattice displacement in the multiferroic body obtained from the vanadium-doped two-dimensional ferroelectric material to achieve direct conversion of magnetic field-lattice polarization-electric signal, thereby achieving high-sensitivity and low-power detection of magnetic field by detecting changes in polarization intensity or magnetic moment under the action of an external field.

[0092] Furthermore, based on the above analysis results, a multiferroic body was designed based on the range of doping concentration values, including: using vanadium ions to dope NbOI2 with equivalent cations based on the range of doping concentration values, thereby destroying the atomic dimerization structure of NbOI2 to activate the local magnetic moment and prepare a multiferroic body.

[0093] This application also provides a multiferroic body, which is designed by the above-described design method for multiferroic bodies based on vanadium-doped two-dimensional ferroelectric bodies.

[0094] Furthermore, based on the above experimental data and analysis results, it can be seen that when the doping concentration x = 0.625, (Nb 0.375 V 0.625 OI2 exhibits a unique magnetoelectric response: polarization changes enhance the magnetic moment of Nb while suppressing the magnetic moment of V, forming a new two-state magnetoelectric coupling effect. This characteristic can be applied to high-sensitivity magnetoelectric devices.

[0095] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0096] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0097] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0098] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0099] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A design method for multiferroic materials based on vanadium-doped two-dimensional ferroelectrics, characterized in that, include: A monolayer of NbOI2 was obtained as the primitive cell, and the primitive cell was expanded in different directions to obtain supercells of different sizes; vanadium was used as the doping element to dope supercells of different sizes to obtain the doping configuration of each supercell under different doping concentrations. Calculate the total energy of the ferromagnetic and antiferromagnetic states for each doping configuration at each doping concentration, and take the doping configuration with the lowest total energy of the ferromagnetic and antiferromagnetic states at each doping concentration as the ground state configuration for that doping concentration. Calculate the band gap Eg and spontaneous ferroelectric polarization intensity along the b-axis for ground state configurations with different doping concentrations, and plot a double Y-axis curve with doping concentration as the abscissa and spontaneous ferroelectric polarization intensity and band gap Eg as the ordinates; divide the multiferroic phase region and magnetic half-metal phase region in the double Y-axis curve to obtain the doping concentration-property evolution phase diagram. Based on the doping concentration-property evolution phase diagram, the range of doping concentration values ​​corresponding to the ground state configuration of a multiferroic phase with ferroelectricity and antiferromagnetism is obtained, thereby designing a multiferroic body. Among them, the design of a multiferroic body based on the doping concentration range includes: using vanadium ions to dope NbOI2 with equivalent cations based on the doping concentration range, thereby destroying the atomic dimerization structure of NbOI2, activating the local magnetic moment, and preparing a multiferroic body.

2. The design method for multiferroic materials based on vanadium-doped two-dimensional ferroelectric materials according to claim 1, characterized in that, A monolayer of NbOI2 was obtained as the primitive cell, and the primitive cell was expanded in different directions to obtain supercells of different sizes. Vanadium was used as the dopant element to dope the supercells of different sizes, resulting in doping configurations of each supercell at different doping concentrations, including: Extending along the lattice a-axis of the primitive cell yields a supercell of the first size; extending along the lattice b-axis of the primitive cell yields a supercell of the second size; extending along both the lattice a-axis and b-axis of the primitive cell simultaneously yields a supercell of the third size. Multiple doping concentrations with equal spacing are obtained. For each doping concentration, Nb atoms are replaced with vanadium atoms in supercells of different sizes to obtain the doping configurations corresponding to supercells of different sizes at that doping concentration.

3. The design method for multiferroic materials based on vanadium-doped two-dimensional ferroelectric materials according to claim 1, characterized in that, Calculate the total energy of the ferromagnetic and antiferromagnetic states for each doping configuration at each doping concentration, including: Structural relaxation is performed on each doped configuration at each doping concentration to obtain the stable configuration of that doped configuration; Static self-consistent calculations were performed on the steady-state configuration of the doped configuration to obtain the total energy of the ferromagnetic and antiferromagnetic states of the doped configuration.

4. The design method for multiferroic materials based on vanadium-doped two-dimensional ferroelectric materials according to claim 3, characterized in that, Structural relaxation is performed on each doped configuration at each doping concentration to obtain the stable configuration of that doped configuration, including: Input the crystal structure file, parameter control file, k-point mesh file, pseudopotential file, and runtime control file for each doping configuration at each doping concentration into the magnetic state calculation directory; After setting the maximum number of ion step iterations to 30 in the parameter control file, start the VASP relaxation calculation. When the ion step iteration reaches the point where the maximum atomic force is <0.01eV / Å, relaxation ends, and a stable configuration file for this doped configuration is generated.

5. The design method for multiferroic materials based on vanadium-doped two-dimensional ferroelectric materials according to claim 4, characterized in that, Static self-consistent calculations were performed on the steady-state configuration of the doped structure to obtain the total energy of the ferromagnetic and antiferromagnetic states, including: Use the stable configuration file of the doped configuration as the crystal structure file of the doped configuration, and start the self-consistent calculation after setting the maximum number of ion steps in the parameter control file to 0. Based on the 1F energy value in the output file after the self-consistent calculation, the total energy of the ferromagnetic and antiferromagnetic states of this doped configuration is obtained.

6. The design method for multiferroic materials based on vanadium-doped two-dimensional ferroelectric materials according to claim 1, characterized in that, Calculate the band gap Eg and spontaneous ferroelectric polarization along the b-axis for ground-state configurations with different doping concentrations, including: Using the centrosymmetric phase corresponding to each ground state configuration as a reference phase, multiple intermediate transition phases are obtained based on the reference phase when the atomic displacement changes from 100% to 10%. Structural relaxation and self-consistency calculations were performed for each intermediate transition phase to obtain the polarization displacement correlation value and the reference polarization displacement reference value for each intermediate transition phase. Based on the polarization displacement correlation value of each intermediate transition phase, the polarization displacement reference value of the reference phase, and the lattice parameters of the ground state configuration along the a-axis and b-axis, the spontaneous ferroelectric polarization intensity of each intermediate transition phase along the b-axis is calculated, thereby obtaining the spontaneous ferroelectric polarization intensity of the ground state configuration along the b-axis. Structural relaxation and self-consistency calculations are performed on each ground state configuration to obtain the stable configuration; Based on the crystal structure file, parameter control file, k-point grid file, pseudopotential file, operation control file, and stable configuration file of the ground state configuration, spin polarization band calculation is performed to obtain the band data of the ground state configuration, and then the band gap Eg of the ground state configuration is calculated based on the band data.

7. The design method for multiferroic materials based on vanadium-doped two-dimensional ferroelectric materials according to claim 1, characterized in that, The doping concentration-property evolution phase diagram is obtained by dividing the multiferroic phase region and the magnetic half-metal phase region in the dual Y-axis curve diagram. The division is based on the band gap Eg of the multiferroic phase region being greater than a preset threshold and the band gap Eg of the magnetic half-metal phase region being less than a preset threshold. The preset threshold is less than or equal to 0.01 eV.

8. The design method for multiferroic materials based on vanadium-doped two-dimensional ferroelectric materials according to claim 1, characterized in that, The doping concentration ranges from 0.125 to 0.625 when the ground state configuration is a multiferroic phase with both ferroelectricity and antiferromagnetism. The doping concentration ranges from 0.75 to 0.875 when the ground state configuration is a half-metallic phase. When the doping concentration is 1, the ground state configuration is a ferromagnetic metallic phase.

9. A multiferroic material, characterized in that, The multiferroic body is designed using the multiferroic body design method based on vanadium-doped two-dimensional ferroelectrics as described in any one of claims 1 to 8.

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