Phase field method for multi-topological domain cycling transition of lead titanate (pto) ferroelectric thin film and multi-state storage application thereof

Abstract

This invention discloses a phase-field method for multi-topological domain cyclic transformation in lead titanate (PTO) ferroelectric thin films. A computational model of the PTO ferroelectric thin film is established, defining polarization, potential, displacement, and oxygen vacancy concentration as field variables. Based on Ginzburg-Landau theory, a total free energy expression for the PTO ferroelectric thin film is established, incorporating oxygen vacancy transport processes and the coupling between oxygen vacancies and the electrostatic field. Combining time-correlated Ginzburg-Landau kinetic equations, mechanical equilibrium equations, electrostatic equilibrium equations, and Nernst-Planck equations, a phase-field model of the PTO ferroelectric thin film coupled with multiple physics fields is established. A stable initial skyrmion domain structure is constructed, and a preset uniform electric field sequence is applied to simulate the cyclic transformation process between skyrmions and flux-closed domains and / or stripe domains. This method can analyze the evolution path, transformation threshold, oxygen vacancy distribution, and cyclic stability of topological domains in PTO ferroelectric thin films under the synergistic effect of an applied electric field and oxygen vacancies, providing a theoretical basis for the design of ferroelectric topological domain multi-state storage devices.

Description

Technical Field

[0001] This invention relates to the field of ferroelectric thin film simulation analysis and multi-state storage technology, and particularly to a phase field method for multi-topological domain cyclic conversion of PTO ferroelectric thin films. Background Technology

[0002] Ferroelectric materials possess spontaneous polarization and polarization reversibility, making them important for applications in non-volatile memories, sensors, actuators, and micro / nanoelectronic devices. Traditional ferroelectric memory primarily relies on two polarization states in opposite directions to represent binary information, resulting in a limited number of stored states.

[0003] With the development of thin film fabrication and micro / nano characterization techniques, complex topological domain structures such as flux-closed domains, vortex domains, bubble domains, and skyrmion domains have been discovered in ferroelectric thin films. Different topological domain structures have different polarization vector distributions, domain wall morphologies, and external field response behaviors, which can provide a new physical basis for multi-state memory and reconfigurable devices.

[0004] PbTiO3 (PTO) is a typical perovskite ferroelectric material, exhibiting stable spontaneous polarization and clear ferroelectric phase transition characteristics, making it an important model system for studying ferroelectric topological domain structures. Under specific electrical boundary conditions, mechanical boundary conditions, and mismatch strain, stable skyrmion domain structures can be formed in PTO ferroelectric thin films.

[0005] Oxygen vacancies are common charged defects in oxide ferroelectric thin films. Under the influence of an applied electric field and a local electric field, oxygen vacancies migrate, altering the local space charge, potential distribution, and built-in electric field. Oxygen vacancies also tend to accumulate near domain walls, probe interaction regions, and topological domain cores, thus affecting the domain structure evolution path and stability. Therefore, when analyzing the topological domain cyclic transformation of PTO ferroelectric thin films, it is necessary to consider oxygen vacancy transport and its coupling relationship with electrostatic and polarization fields.

[0006] Phase-field methods can describe the formation, evolution, and external field response of ferroelectric domain structures within a continuous dielectric framework, making them suitable for studying the dynamic evolution of multi-topological domain structures. Existing methods are mostly used to analyze conventional ferroelectric domain flipping or single-topological domain evolution behavior, and a phase-field analysis method for multi-topological domain cyclic transformation in PTO ferroelectric thin films that simultaneously considers oxygen vacancy transport and electrical coupling is still lacking. Summary of the Invention

[0007] (I) Purpose of the Invention

[0008] The purpose of this invention is to provide a phase-field analysis method for the cyclic conversion and multi-state storage of multiple topological domains in PTO ferroelectric thin films. By establishing a phase-field model that couples polarization field, electric field, elastic field and oxygen vacancy concentration, the cyclic conversion process of multiple topological domain structures in PTO ferroelectric thin films under the synergistic effect of an applied uniform electric field and oxygen vacancies is simulated, providing a theoretical basis for the design of ferroelectric topological domain multi-state storage devices.

[0009] (II) Technical Solution

[0010] To achieve the above objectives, the present invention provides a phase field method for PTO ferroelectric thin films based on multi-topological domain cyclic conversion, comprising the following steps.

[0011] Step (1): Establish a calculation model for PTO ferroelectric thin films.

[0012] The PTO ferroelectric thin film model is a three-dimensional model, which determines the polarization P and the potential. Displacement u and oxygen vacancy concentration As field variables, the polarization vector P=(P1,P2,P3) is used as the ferroelectric sequence parameter, where P1, P2, and P3 represent the polarization components along the x, y, and z directions, respectively; simultaneously, an electric potential is introduced. Displacement component u i and oxygen vacancy concentration As a coupling variable.

[0013] Step (2), establish the expression for the total free energy of PTO ferroelectric thin films based on Ginzburg-Landau theory:

[0014]

[0015] Among them, f lan For the Landau energy density, f elas f is the elastic energy density. grad f is the gradient energy density. ele Let σ be the electrostatic energy density. 0 ·ε is the coupling term between applied stress and strain, E 0 • P represents the coupling term between the applied electric field and polarization.

[0016] Step (3) introduces the oxygen vacancy transport process and couples the oxygen vacancy with the electrostatic field to establish the coupling relationship between the oxygen vacancy, the electric field and the polarization field, so as to achieve coordinated control of the electric field and the oxygen vacancy.

[0017] Oxygen vacancies, as charged defects, migrate under the combined influence of concentration gradient and local electric field. The oxygen vacancy flux is described by the Nernst-Planck equation:

[0018]

[0019] in, Where is the oxygen vacancy concentration, and E is the electric field strength. and These are the oxygen vacancy diffusion coefficient and mobility, respectively.

[0020] The oxygen vacancy diffusion coefficient and mobility satisfy the Einstein relation:

[0021]

[0022] Where, k B δ is the Boltzmann constant, T is the temperature, δ is the effective charge of vacancies, and q0 is the unit charge.

[0023] According to the law of conservation of mass, the evolution of oxygen vacancy concentration distribution over time satisfies:

[0024]

[0025] The space charge density of oxygen vacancies is expressed as:

[0026]

[0027] And introduce it into the electrostatic equilibrium equation:

[0028]

[0029] Where D is the electric displacement vector. This establishes the coupling relationship between oxygen vacancies, electric field, and polarization field, enabling coordinated control of the electric field and oxygen vacancies.

[0030] Step (4) combines the time-dependent Ginzburg-Landau kinetic equation, mechanical equilibrium equation, electrostatic equilibrium equation and Nernst-Planck equation to establish a phase-field model of PTO ferroelectric thin film coupled with oxygen vacancies and multiple physical fields.

[0031] The polarization field satisfies the time-dependent Ginzburg-Landau dynamic equations:

[0032]

[0033] Where r(x1,x2,x3) are spatial coordinates, t is time, L is the kinetic coefficient, and F is the total free energy of the system.

[0034] The elastic field satisfies the mechanical equilibrium equations:

[0035]

[0036] Where, σ ij Let be the stress tensor.

[0037] The time step for the oxygen vacancy concentration distribution is 0.001≤Δt1≤0.005, and the time step for the polarization distribution is 0.005≤Δt2≤0.02, where Δt1 is the time step for the oxygen vacancy concentration distribution and Δt2 is the time step for the polarization distribution.

[0038] Therefore, a phase-field model of PTO ferroelectric thin films with mutual coupling of polarization field, electric field, elastic field and oxygen vacancy concentration is established.

[0039] Step (5) involves constructing a stable initial skyrmion domain structure in the PTO ferroelectric thin film phase-field model. The specific construction method of the initial skyrmion domain structure Sky1 includes: establishing a three-dimensional computational model of the PTO ferroelectric thin film and discretizing the PTO three-dimensional computational model; setting the mechanical boundary conditions as free on the upper surface of the thin film and fixed on the lower surface of the thin film, setting the electrical boundary conditions as ideal open circuit conditions in the thickness direction, and introducing biaxial compressive mismatch strain e1= e2=-1% in the in-plane direction of the thin film; under the combined action of the mechanical boundary conditions, electrical boundary conditions and in-plane biaxial compressive mismatch strain, the PTO ferroelectric thin film system first forms regular 90° domains, and further applies temperature and electric field control on the basis of the regular 90° domains, eventually evolving into a periodically distributed skyrmion array.

[0040] More specifically, a three-dimensional computational model of a PTO ferroelectric thin film with dimensions of approximately 100×100×10 nm was established and discretized into 200×200×50 mesh elements. The mechanical boundary conditions were set as follows: the upper surface of the film was free, and the lower surface was fixed. The electrical boundary conditions were set as an ideal open circuit condition in the thickness direction, and biaxial compressive mismatch strains e1= e2=-1% were introduced in the in-plane direction of the film. Under the combined action of the above boundary conditions and mismatch strains, the PTO ferroelectric thin film system first formed regular 90° domains. Then, under the conditions of temperature T=277 K and electric field strength E=3.8 MV / cm, the striped domains were induced to evolve into a periodically distributed skyrmion array, thus obtaining a stable initial skyrmion domain structure. The stable initial skyrmion domain structure obtained through phase-field evolution is denoted as Sky1.

[0041] An oxygen vacancy concentration of 4 × 10⁻⁶ was introduced into the initial Skyming subdomain structure Sky1. 20 ~8×10 20 cm -3 .

[0042] Step (6) involves applying a preset uniform electric field sequence to achieve fine control of the electric field, driving the domain structure in the PTO ferroelectric thin film to cyclically switch between skyrmions and flux-closed domains and / or stripe domains.

[0043] An oxygen vacancy concentration is introduced into the initial skyrmion domain structure, and a preset uniform electric field sequence is applied along the thickness direction of the PTO ferroelectric thin film. The preset uniform electric field sequence is a segmented cyclic electric field sequence, including a negative electric field loading segment, a positive electric field loading segment, and a repeated cyclic loading segment.

[0044] When the oxygen vacancy concentration introduced into the initial Skyming subdomain structure Sky1 is 4 × 10 20 -7×10 20 cm -3 In step (6), the preset uniform electric field sequence drives the topological domain structure in the PTO ferroelectric thin film to complete one cycle ① according to the following path: When the oxygen vacancy concentration introduced into the initial skymin subdomain structure Sky1 is 7 × 10⁻⁶ 20 -8×10 20 cm -3 In step (6), the preset uniform electric field sequence drives the topological domain structure in the PTO ferroelectric thin film to complete one cycle ② according to the following path: Sky1 is the initial skymin subdomain structure, Flux1 is the first type of flux-closed domain, L is the stripe domain, Sky2 is the flipped skymin subdomain structure, and Flux2 is the second type of flux-closed domain. When the preset uniform electric field sequence is repeatedly applied, the recovered initial skymin subdomain structure Sky1 serves as the starting state of the next cycle, causing the topological domain structure in the PTO ferroelectric thin film to undergo repeated cyclic transformations along the above-mentioned cycle ① or ②.

[0045] The repeated cyclic loading segment refers to repeatedly applying an external electric field in the order of the negative electric field loading segment and the positive electric field loading segment, thereby realizing the continuous cyclic conversion of the multi-topological domain structure in the PTO ferroelectric thin film.

[0046] Within a segmented cyclic electric field cycle, the topological domain structures in PTO ferroelectric thin films under different electric field conditions correspond to the following relationships: where the introduced oxygen vacancy concentration is 7 × 10⁻⁶. 20 -8×10 20 cm -3 At that time, the absolute value of the adjustment step size of the applied electric field is 0.01 MV / cm, which specifically includes the following process:

[0047] In the first stage, the negative electric field loading section is gradually adjusted from 0 MV / cm to -0.35 MV / cm, with an electric field step size of -0.01 MV / cm. During this stage, the domain structure in the PTO ferroelectric thin film evolves from the initial skyminton domain structure Sky1 to the first flux-closed domain Flux1, and the first flux-closed domain Flux1 is formed in the range of -0.25 MV / cm to -0.35 MV / cm.

[0048] In the second stage, the applied electric field is adjusted negatively from -0.35MV / cm to -0.40MV / cm, with a step size of -0.01MV / cm. In this stage, the first flux closed domain Flux1 is transformed into a striped domain L, and striped domain L is formed in the range of -0.35MV / cm to -0.40MV / cm.

[0049] In the third stage, the applied electric field is adjusted negatively from -0.40MV / cm to -0.50MV / cm, with a step size of -0.01MV / cm. In this stage, the stripe domain L evolves into the skymin subdomain structure Sky2, and the skymin subdomain structure Sky2 is formed in the range of -0.45MV / cm to -0.50MV / cm.

[0050] In the fourth stage, the direction of the applied electric field changes from negative to positive and is gradually adjusted from -0.50MV / cm to +0.35MV / cm, with a field step size of +0.01MV / cm. In this stage, the Skymin domain structure Sky2 evolves into the second flux-closed domain Flux2 and forms the second flux-closed domain Flux2 in the range of +0.25MV / cm to +0.35MV / cm.

[0051] In the fifth stage, the applied electric field is further adjusted in the positive direction from +0.35 MV / cm to +0.50 MV / cm, with a field step size of +0.01 MV / cm. In this stage, the second type of flux-closed domain... The original skymin subdomain structure Sky1 was restored, and the restored original skymin subdomain structure Sky1 was formed in the range of +0.45MV / cm to +0.50MV / cm;

[0052] The first to fifth stages constitute a complete cycle. The segmented cyclic electric field sequence is repeatedly applied to complete a complete cycle, causing the topological domain structure in the PTO ferroelectric thin film to undergo repeated cyclic transformations in the order of Sky1, Flux1, L, Sky2, Flux2 and Sky1.

[0053] When the introduced oxygen vacancy concentration is 4 × 10 20 -7×10 20 cm -3 At that time, the absolute value of the adjustment step size of the applied electric field is 0.01 MV / cm, which specifically includes the following process:

[0054] In the first stage, the negative electric field loading section is gradually adjusted from 0 MV / cm to -0.35 MV / cm, with an electric field step size of -0.01 MV / cm. During this stage, the domain structure in the PTO ferroelectric thin film evolves from the initial skyminton domain structure Sky1 to the first flux-closed domain Flux1, and the first flux-closed domain Flux1 is formed in the range of -0.25 MV / cm to -0.35 MV / cm.

[0055] In the second stage, the applied electric field is adjusted negatively from -0.35MV / cm to -0.50MV / cm, with a field step size of -0.01MV / cm. In this stage, the first flux closed domain Flux1 evolves into the skymin subdomain structure Sky2, and the skymin subdomain structure Sky2 is formed in the range of -0.45MV / cm to -0.50MV / cm.

[0056] In the third stage, the direction of the applied electric field changes from negative to positive and is gradually adjusted from -0.50MV / cm to +0.35MV / cm, with a field step size of +0.01MV / cm. During this stage, the Skymin domain structure Sky2 evolves into the second flux-closed domain Flux2 and forms the second flux-closed domain Flux2 in the range of +0.25MV / cm to +0.35MV / cm.

[0057] In the fourth stage, the applied electric field is further adjusted in the positive direction from +0.35 MV / cm to +0.50 MV / cm, with a field step size of +0.01 MV / cm. In this stage, the second type of flux-closed domain... The original skymin subdomain structure Sky1 was restored, and the restored original skymin subdomain structure Sky1 was formed in the range of +0.45MV / cm to +0.50MV / cm;

[0058] The first to fourth stages constitute a complete cycle. The segmented cyclic electric field sequence is repeatedly applied to complete a complete cycle, causing the topological domain structure in the PTO ferroelectric thin film to undergo repeated cyclic transformations in the order of Sky1, Flux1, Sky2, Flux2 and Sky1.

[0059] Furthermore, the method also includes an oxygen-vacancy-free control analysis step. Specifically, under conditions where no oxygen vacancy concentration is introduced or the oxygen vacancy concentration is set to zero, the domain structure evolution process under oxygen-vacancy-free conditions is solved while keeping the geometry, boundary conditions, mismatch strain, and applied electric field sequence of the PTO ferroelectric thin film unchanged. The results show that under oxygen-vacancy-free conditions, the domain structure in the PTO ferroelectric thin film mainly exhibits a reversible switching between the initial skyrmion domain structure Sky1 and the flipped skyrmion domain structure Sky2; while after introducing oxygen vacancies, the system can further undergo intermediate topological domain states such as the first flux-closed domain Flux1, the stripe domain L, and the second flux-closed domain Flux2, forming a multi-topological domain cyclic conversion path. This control result indicates that oxygen vacancies can regulate the local electric field and space charge distribution, thereby enriching the topological domain conversion path of the PTO ferroelectric thin film.

[0060] The domain structure cyclic evolution results include the polarization vector distribution, oxygen vacancy concentration distribution, electric field distribution, domain structure type, electric field interval, number of cycles, and cyclic transition path of skyrmions, flux-closed domains, striped domains, and flipped skyrmions under different electric field conditions. These results are used to determine the distinguishability, repeatability, and stability of different topological domain structures as information states.

[0061] The domain structure cyclic evolution results are obtained through the following steps:

[0062] The total free energy expression, material parameters, polarization field control equation, elastic field control equation, electrostatic equilibrium equation, and oxygen vacancy concentration evolution equation are numerically discretized, and a phase field calculation program coupling oxygen vacancy with multiple physics fields is established.

[0063] Set the initial values, boundary conditions, applied electric field sequence, mesh size, and time step for each physical field in the PTO ferroelectric thin film;

[0064] The polarization field, electric field, elastic field, and oxygen vacancy concentration are solved iteratively to obtain field variable data under different electric field conditions and different number of cycles;

[0065] Export the obtained polarization vector field, electric field, elastic field and oxygen vacancy concentration data as text files, data table files or formats that can be read by visualization software;

[0066] The polarization vector field, oxygen vacancy concentration, and domain structure evolution process are visualized in three dimensions. The domain structure type, electric field range, number of cycles, and field variable variation curves under different electric field conditions are plotted to obtain the visualized field variable results.

[0067] (III) Beneficial Effects

[0068] The present invention has the following beneficial effects:

[0069] 1. Compared with traditional phase-field methods that only analyze ferroelectric domain flipping or single topological domain evolution, this invention takes skyminton domain structure in PTO ferroelectric thin films as the research object and considers the coupling effect between polarization field, electric field, elastic field and oxygen vacancy concentration, which can more completely simulate the dynamic evolution process of topological domain structure under the participation of oxygen vacancy.

[0070] 2. This invention couples the oxygen vacancy transport equation with the electrostatic equilibrium equation, enabling changes in oxygen vacancy concentration to be fed back into the space charge distribution and local electric field distribution. This allows for the analysis of the impact of oxygen vacancy migration on polarization reversal, domain wall movement, and topological domain transition threshold, providing a basis for revealing the mechanism by which defects regulate topological domain evolution.

[0071] 3. This invention achieves precise control of the electric field by applying a preset uniform electric field sequence, driving the domain structure in the PTO ferroelectric thin film to undergo cyclic transformations between skyrmions and flux-closed domains and / or stripe domains, resulting in Sky1→Flux1→L→Sky2→Flux2→Sky1 or The topological domain cyclic transformation path enriches the analytical methods for the evolution behavior of multiple topological domains in PTO ferroelectric thin films.

[0072] 4. This invention can obtain the electric field range corresponding to different topological domain structures by performing multiple consecutive electric field cycle calculations, and verify the repeatability of the electric field range and domain structure conversion path under different cycle numbers, thereby evaluating the stability and retention capability of multi-topological domain cyclic conversion in PTO ferroelectric thin films.

[0073] 5. This invention can study the effects of different parameters on the conversion path, conversion threshold and cycle stability of PTO ferroelectric thin film topological domain structure by changing the applied electric field sequence, oxygen vacancy concentration, boundary conditions and mismatch strain conditions. This provides theoretical guidance for the experimental control of ferroelectric topological domain structure and reduces experimental trial and error costs.

[0074] 6. The basic phase field calculation program of this invention obtains field variable data such as polarization, electric field, displacement and oxygen vacancy concentration, and obtains visualized field variable results. It can intuitively display the multi-topological domain cyclic conversion process, oxygen vacancy distribution characteristics and electric field interval variation law, and provide a reference for the design of ferroelectric topological domain multi-state storage devices. Attached Figure Description

[0075] Figure 1 This is a flowchart of the multi-state storage phase field analysis method for PTO ferroelectric thin films based on multi-topological domain cyclic conversion provided by the present invention.

[0076] Figure 2 This is a flowchart of the construction and visualization process of the PTO ferroelectric thin film phase field model provided by the present invention.

[0077] Figure 3This is the initial skymin subdomain structure polarization vector distribution diagram provided by the present invention.

[0078] Figure 4 This is an oxygen vacancy concentration distribution diagram provided by the present invention.

[0079] Figure 5 This is a diagram of skyrmion reversible switching under anaerobic vacancy conditions, presented in a comparative manner.

[0080] Figure 6 The oxygen vacancy concentration introduced in Examples 1-5 and 9-10 is 7 × 10⁻⁶. 20 cm -3 -8×10 20 cm -3 Multi-topology domain cyclic transformation path diagram.

[0081] Figure 7 This is a multi-topological domain cyclic electric field interval diagram provided by the present invention.

[0082] Figure 8 The oxygen vacancy concentration introduced in Examples 6-8 is 4 × 10⁻⁶. 20 cm -3 -7×10 20 cm -3 Multi-topology domain cyclic transformation path diagram. Detailed Implementation

[0083] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. It should be understood that the following embodiments are only for illustrating the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention. Equivalent substitutions or improvements made to model dimensions, boundary conditions, material parameters, applied electric field sequences, oxygen vacancy concentrations, and visualization processing methods without departing from the technical concept of the present invention should all be included within the scope of protection of the present invention.

[0084] Example 1:

[0085] This invention provides a multi-state storage phase-field analysis method for PTO ferroelectric thin films based on multi-topological domain cyclic transformation, the overall process of which is as follows: Figure 1 As shown, the specific steps include the following.

[0086] Step (1): Establish a calculation model for PTO ferroelectric thin films.

[0087] A three-dimensional computational model of a PTO ferroelectric thin film is established, with the in-plane directions of the film represented by the x and y axes, and the thickness direction by the z axis. The polarization vector is used as the ferroelectric order parameter.

[0088]

[0089] Where P1, P2, and P3 represent the polarization components along the x, y, and z directions, respectively.

[0090] Simultaneously introducing electric potential Displacement component u i and oxygen vacancy concentration As coupling variables, the electric field is determined by both the electric potential gradient and the applied electric field.

[0091]

[0092] Among them, E i For local electric field components, E is the electric potential. i 0 This represents the component of the applied electric field.

[0093] The strain tensor is expressed as:

[0094]

[0095] Among them, u i For the displacement component, u i,j Represents the displacement component u i For spatial coordinates x j The partial derivative of .

[0096] In the PTO ferroelectric thin film model, periodic boundary conditions are applied in the in-plane direction, and open-circuit electrical boundary conditions are applied in the thickness direction. The upper surface of the film is set as a free boundary, and the lower surface is set as a fixed boundary. Mismatch strain conditions are introduced in the in-plane direction. This computational model is used to describe the coupling evolution relationship between the polarization field, electric field, elastic field, and oxygen vacancy concentration in the PTO ferroelectric thin film.

[0097] Step (2) Establish the expression for the total free energy of PTO ferroelectric thin films.

[0098] Based on the Ginzburg-Landau theory, the total free energy of the system can be expressed as the sum of the Landau energy, elastic energy, gradient energy, electrostatic energy, applied stress coupling term, and applied electric field coupling term:

[0099]

[0100] Among them, f lan f is the Landau energy density, used to describe the ferroelectric polarization behavior of PTO thin films; elas f is the elastic energy density, used to describe the coupling effect between polarization and strain; grad f is the gradient energy density, used to describe the polarization space variation and domain wall energy; ele σ is the electrostatic energy density, used to describe the coupling effect between polarization and the electric field; 0 ·ε represents the coupling term between applied stress and strain; E 0 • P represents the coupling term between the applied electric field and polarization.

[0101]

[0102] Wherein, α1, α 11 α 12 α 111 α 112 and α 123 is the Landau expansion coefficient for PTO material.

[0103] The gradient energy density is used to describe the polarization vector space variation and domain wall energy, and its expression is:

[0104]

[0105] Among them, G ijkl P is the gradient energy coefficient. i,j Represents the polarization component P i Along x j Spatial gradient of direction.

[0106] The elastic energy density is used to describe the energy contribution between elastic strain and intrinsic strain, and its expression is:

[0107]

[0108] Among them, c ijkl ε is the elastic stiffness coefficient. ij For the total strain, ε ij 0 For intrinsic response.

[0109] The intrinsic strain includes electrostrictive strain, mismatch strain, and chemical strain caused by oxygen vacancies, and can be expressed as:

[0110]

[0111] Among them, Q ijkl ε is the electrostriction coefficient. ij m For in-plane mismatch strain, β ij The coefficient of chemical expansion, This represents the initial oxygen vacancy concentration.

[0112] The electrostatic energy density is used to describe the coupling effect between polarization and electric field, and its expression is:

[0113]

[0114] Where ε0 is the vacuum permittivity, κ b E is the background dielectric constant. i This represents the local electric field component.

[0115] Step (3) introduces oxygen vacancy transport and couples the oxygen vacancy with the electrostatic field.

[0116] Oxygen vacancies, as charged defects, migrate under the combined influence of concentration gradient and local electric field. The oxygen vacancy flux is expressed as: ,in, Where is the vacancy concentration, and E is the electric field strength. and Let be the oxygen vacancy diffusion coefficient and mobility, respectively. The first term on the right-hand side of the equation represents the diffusion flux caused by the concentration gradient, and the second term represents the drift flux driven by the electric field.

[0117] The oxygen vacancy diffusion coefficient and mobility satisfy the Einstein relation: ,

[0118] Where, k B δ is the Boltzmann constant, T is the temperature, δ is the effective charge of vacancies, and q0 is the unit charge.

[0119] According to the law of conservation of mass, the evolution of oxygen vacancy concentration over time satisfies:

[0120]

[0121] The space charge density contributed by oxygen vacancies is expressed as:

[0122]

[0123] And introduce it into the electrostatic equilibrium equation:

[0124] Where D is the electric displacement vector, satisfying:

[0125] This establishes the coupling relationship between oxygen vacancy concentration and electrostatic field.

[0126] Step (4) Establish a phase-field model of PTO ferroelectric thin film coupled with oxygen vacancies and multiple physical fields.

[0127] The polarization field satisfies the time-dependent Ginzburg-Landau dynamic equations:

[0128]

[0129] Where r(x1,x2,x3) are spatial coordinates, t is time, L is the kinetic coefficient, and F is the total free energy of the system.

[0130] Taking the variational factor of the total free energy with respect to the polarization components yields the driving force of polarization evolution:

[0131]

[0132] Among them, P i,j Represents the polarization component P i For spatial coordinates x j The partial derivative of .

[0133] Therefore, the polarization field evolution equation can be written as:

[0134]

[0135] The elastic field satisfies the mechanical equilibrium equations: The stress tensor is expressed as: ;

[0136] The strain tensor is expressed as:

[0137] The electrostatic field satisfies the electrostatic equilibrium equation after introducing the space charge of oxygen vacancies:

[0138] Right now:

[0139]

[0140] Combination:

[0141]

[0142] The oxygen vacancy concentration satisfies the Nernst-Planck transport equation.

[0143]

[0144] The time step for the oxygen vacancy concentration distribution is set to Δt1=0.002, and the time step for the polarization distribution is set to Δt2=0.01.

[0145] Where Δt1 is the time step for updating the oxygen vacancy concentration, and Δt2 is the time step for updating the polarization field. Through the coupling of the above equations, a phase-field model of the PTO ferroelectric thin film interacting with the polarization field, electric field, elastic field, and oxygen vacancy concentration is established.

[0146] The model construction and post-processing process is as follows: Figure 2 As shown, the process includes establishing the total free energy expression and determining material parameters, establishing the governing equations for each physical field, setting initial and boundary conditions, writing a phase field calculation program and solving iteratively, and exporting field variable data and obtaining visualized field variable results.

[0147] Step (5) constructs a stable initial skymin subdomain structure.

[0148] In this embodiment, a three-dimensional computational model of the PTO ferroelectric thin film is established, with a computational region size of approximately 100×100×10nm. The in-plane directions of the film are the x-axis and y-axis, and the thickness direction is the z-axis. To ensure spatial resolution in the phase-field simulation, the three-dimensional computational model of the PTO ferroelectric thin film is discretized into 200×200×50 pixels in the x, y, and z directions, respectively.

[0149] Regarding boundary condition settings, the mechanical boundary conditions are set as follows: the upper surface of the film is free, and the lower surface is fixed. The electrical boundary conditions employ an ideal open-circuit condition to preserve the influence of the depolarization field within the film on the evolution of the polarization structure. Simultaneously, biaxial compressive mismatch strain is introduced in the in-plane direction of the film.

[0150] The in-plane biaxial compressive mismatch strain is used to simulate the epitaxial constraint effect of the substrate on the PTO ferroelectric thin film and to provide an elastic energy background for the formation and stabilization of polarization texture.

[0151] Under the combined effects of the aforementioned mechanical boundary conditions, electrical boundary conditions, and in-plane biaxial compressive mismatch strain, the PTO ferroelectric thin film system first forms regular 90° stripe domains. These regular 90° stripe domains exhibit a periodic domain sequence under confined thin film conditions, with the polarization directions distributed in a segmented orientation, providing the initial polarization basis for the subsequent formation of skyrmion domain structures.

[0152] Based on the existing regular 90° striped domains, further temperature and electric field manipulations are applied. The temperature is set to T = 277 K, and the electric field strength is set to E = 3.8 MV / cm. Under the combined influence of these temperature and electric fields, the polarization distribution within the regular 90° striped domains gradually evolves, changing from segmented orientation to a locally continuous rotating distribution, ultimately forming a periodically distributed skyrmion array. The resulting skyrmion array exhibits a regular lattice morphology, with each skyrmion unit possessing a clear core region, transition region, and ring-shaped boundary, indicating that the system has evolved to a stable ideal skyrmion state, denoted as Sky1.

[0153] The stable initial skymin subdomain structure serves as the initial state for subsequent multi-topological domain cyclic transformations driven by an applied uniform electric field sequence.

[0154] Simultaneously, an oxygen vacancy concentration of 7.2 × 10⁻⁶ was introduced. 20 cm -3 And calculate its spatial distribution. For example... Figure 4 As shown, the oxygen vacancy concentration reflects the non-uniform distribution of oxygen vacancies in PTO ferroelectric thin films. Oxygen vacancies migrate under the combined influence of an applied electric field and a local electric field, further affecting the local potential distribution and polarization evolution process through the space charge effect.

[0155] Step (6) involves applying a preset uniform electric field sequence to achieve multi-topological domain cyclic conversion.

[0156] Oxygen vacancy concentration is introduced into the initial skyrmion domain structure, and a preset uniform electric field sequence is applied along the film thickness direction. The preset uniform electric field sequence is a segmented cyclic electric field sequence applied along the thickness direction of the PTO ferroelectric film, including a negative electric field loading segment, a positive electric field loading segment, and a repeated cyclic loading segment.

[0157] The negative electric field loading segment refers to starting from the electric field interval where the initial skyrmion Sky1 is located, and gradually adjusting the intensity of the applied electric field in the negative direction, so that the domain structure in the PTO ferroelectric thin film is transformed sequentially from the initial skyrmion Sky1 into the first flux-closed domain Flux1, the stripe domain L, and the flipped skyrmion Sky2.

[0158] The forward electric field loading segment refers to changing the direction of the applied electric field after the skymion Sky2 is formed, gradually adjusting the intensity of the applied electric field in the forward direction, so that the domain structure changes from the skymion Sky2 to the second flux closed domain Flux2, and further restores it to the initial skymion Sky1.

[0159] The repeated cyclic loading segment refers to repeatedly applying an external electric field in the order of the negative electric field loading segment and the positive electric field loading segment, thereby realizing the continuous cyclic conversion of the multi-topological domain structure in the PTO ferroelectric thin film.

[0160] Within a segmented cyclic electric field period, the topological domain structures in PTO ferroelectric thin films under different electric field conditions include the following correspondences:

[0161] When the applied electric field is near zero, the PTO ferroelectric thin film retains the initial skyrmion domain structure Sky1. When the applied electric field is adjusted negatively to -0.28 MV / cm, the initial skyrmion domain structure Sky1 transforms into the first flux-closed domain Flux1. When the applied electric field is further adjusted to approximately -0.39 MV / cm, the first flux-closed domain Flux1 transforms into a striped domain L. When the applied electric field is further adjusted negatively to approximately -0.46 MV / cm, the striped domain L transforms into a flipped skyrmion Sky2. When the applied electric field direction changes from negative to positive and is adjusted to approximately +0.28 MV / cm, the flipped skyrmion Sky2 transforms into the second flux-closed domain Flux2. When the applied electric field is further adjusted positively to approximately +0.45 MV / cm, the second flux-closed domain Flux2 reverts to the initial skyrmion domain structure Sky1.

[0162] Within one complete cycle, the preset uniform electric field sequence drives the topological domain structure in the PTO ferroelectric thin film to complete the cyclic transformation according to the following path:

[0163]

[0164] Wherein, Sky1 is the initial skyrmion, Flux1 is the first type of flux-closed domain, L is the stripe domain, Sky2 is the flipped skyrmion, and Flux2 is the second type of flux-closed domain. When the preset uniform electric field sequence is repeatedly applied, the recovered initial skyrmion Sky1 serves as the starting state for the next cycle, causing the topological domain structure in the PTO ferroelectric thin film to undergo repeated cyclic transformations along the aforementioned path.

[0165] The total free energy expression, material parameters, polarization field control equation, elastic field control equation, electrostatic equilibrium equation, and oxygen vacancy concentration evolution equation are numerically discretized to establish a phase field calculation program that couples oxygen vacancies with multiple physics fields.

[0166] The initial values, boundary conditions, applied electric field sequence, grid size, and time step of each physical field in the PTO ferroelectric thin film are set, and a program is written to iteratively solve the polarization field, electric field, elastic field, and oxygen vacancy concentration to obtain field variable data under different electric field conditions and different number of cycles.

[0167] Export the obtained polarization vector field, electric field, elastic field, and oxygen vacancy concentration data as text files, data table files, or other formats readable by visualization software. Perform three-dimensional visualization of the polarization vector field, oxygen vacancy concentration, and multi-topological domain structure evolution process; plot the domain structure type, electric field range, cycle number, and field variable variation curves under different electric field conditions to obtain visualized field variable results.

[0168] Multi-topological domain cycle conversion pathways under oxygen-vacancy conditions, such as Figure 6 As shown, during the aforementioned cycling process, oxygen vacancies migrate under the influence of an applied electric field and a local electric field, altering the space charge distribution and local electric field distribution within the thin film. This redistribution of oxygen vacancies further influences the formation of domain wall migration and flux closure structures after polarization reversal, thereby regulating the transition threshold and cycling stability between different topological domain structures.

[0169] By statistically analyzing three consecutive cyclic processes, the electric field ranges corresponding to different topological domain structures can be obtained. For example... Figure 7 As shown, the data points in the first, second, and third cycles largely overlap within their respective topological domain intervals, indicating that the cyclic transformation process exhibits good repeatability and stability. The electric field intervals corresponding to different topological domain structures can be used to analyze the distinguishability and maintainability of domain structures as information states, providing a theoretical basis for multi-state storage based on ferroelectric topological domains.

[0170] Example 2:

[0171] The time step for oxygen vacancy concentration distribution was set to Δt1=0.005, and the time step for polarization distribution was set to Δt2=0.001. Other parameters were the same as in Example 1.

[0172] Example 3:

[0173] The time step for oxygen vacancy concentration distribution was set to Δt1=0.005, and the time step for polarization distribution was set to Δt2=0.02. Other parameters were the same as in Example 1.

[0174] Example 4:

[0175] The magnitude of the electric field varies in the PTO thin film when a preset uniform electric field sequence is applied along the thickness direction, while other parameters are the same as in Example 2.

[0176] When the applied electric field is near zero, the PTO ferroelectric thin film retains the initial skyrmion domain structure Sky1. When the applied electric field is adjusted negatively to -0.30 MV / cm, the initial skyrmion domain structure Sky1 transforms into the first flux-closed domain Flux1. When the applied electric field is further adjusted to approximately -0.38 MV / cm, the first flux-closed domain Flux1 transforms into a striped domain L. When the applied electric field is further adjusted negatively to approximately -0.48 MV / cm, the striped domain L transforms into a flipped skyrmion Sky2. When the applied electric field direction changes from negative to positive and is adjusted to approximately +0.30 MV / cm, the flipped skyrmion Sky2 transforms into the second flux-closed domain Flux2. When the applied electric field is further adjusted positively to approximately +0.47 MV / cm, the second flux-closed domain Flux2 reverts to the initial skyrmion domain structure Sky1.

[0177] Example 5:

[0178] The magnitude of the electric field varies in the PTO thin film when a preset uniform electric field sequence is applied along the thickness direction, while other parameters are the same as in Example 3.

[0179] When the applied electric field is near zero, the PTO ferroelectric thin film retains the initial skyrmion domain structure Sky1. When the applied electric field is adjusted negatively to -0.25 MV / cm, the initial skyrmion domain structure Sky1 transforms into the first flux-closed domain Flux1. When the applied electric field is further adjusted to approximately -0.36 MV / cm, the first flux-closed domain Flux1 transforms into a striped domain L. When the applied electric field is further adjusted negatively to approximately -0.45 MV / cm, the striped domain L transforms into a flipped skyrmion Sky2. When the applied electric field direction changes from negative to positive and is adjusted to approximately +0.26 MV / cm, the flipped skyrmion Sky2 transforms into the second flux-closed domain Flux2. When the applied electric field is further adjusted positively to approximately +0.46 MV / cm, the second flux-closed domain Flux2 reverts to the initial skyrmion domain structure Sky1.

[0180] Example 6:

[0181] The oxygen vacancy concentration was set at 4.8 × 10⁻⁶. 20 cm -3 Other parameters are the same as in Example 1.

[0182] like Figure 8 As shown, at an oxygen vacancy concentration of 4.8 × 10⁻⁶ 20 cm -3 Under certain conditions, when the applied electric field is near zero, the PTO ferroelectric thin film retains its initial skyrmion domain structure Sky1. When the applied electric field is adjusted negatively to -0.26 MV / cm, the initial skyrmion domain structure Sky1 transforms into the first flux-closed domain Flux1. Subsequent adjustments to the applied electric field do not result in L-domains. When the applied electric field is further adjusted negatively to approximately -0.46 MV / cm, the first flux-closed domain Flux1 transforms into a flipped skyrmion Sky2. When the applied electric field direction changes from negative to positive and is adjusted to approximately +0.27 MV / cm, the flipped skyrmion Sky2 transforms into the second flux-closed domain Flux2. When the applied electric field continues to be adjusted positively to approximately +0.45 MV / cm, the second flux-closed domain Flux2 reverts to the initial skyrmion domain structure Sky1. This can achieve... The four topological domain structures can be cyclically transformed, which can be used for four-state information storage applications.

[0183] Example 7:

[0184] The oxygen vacancy concentration was set at 5.6 × 10⁻⁶. 20 cm -3 The magnitude of the electric field varies in the preset uniform electric field sequence applied along the thickness direction of the PTO thin film, while other parameters are the same as in Example 1.

[0185] When the applied electric field is near zero, the PTO ferroelectric thin film retains the initial skyrmion domain structure Sky1. When the applied electric field is adjusted negatively to -0.27 MV / cm, the initial skyrmion domain structure Sky1 transforms into the first flux-closed domain Flux1. When the applied electric field is further adjusted negatively to approximately -0.49 MV / cm, the first flux-closed domain Flux1 transforms into the flipped skyrmion Sky2. When the applied electric field direction changes from negative to positive and is adjusted to approximately +0.30 MV / cm, the flipped skyrmion Sky2 transforms into the second flux-closed domain Flux2. When the applied electric field continues to be adjusted positively to approximately +0.47 MV / cm, the second flux-closed domain Flux2 reverts to the initial skyrmion domain structure Sky1.

[0186] Example 8:

[0187] The oxygen vacancy concentration was set at 6.4 × 10⁻⁶. 20 cm -3 The magnitude of the electric field varies in the preset uniform electric field sequence applied along the thickness direction of the PTO thin film, while other parameters are the same as in Example 1.

[0188] When the applied electric field is near zero, the PTO ferroelectric thin film retains the initial skyrmion domain structure Sky1. When the applied electric field is adjusted negatively to -0.28 MV / cm, the initial skyrmion domain structure Sky1 transforms into the first flux-closed domain Flux1. When the applied electric field is further adjusted negatively to approximately -0.45 MV / cm, the first flux-closed domain Flux1 transforms into the flipped skyrmion Sky2. When the applied electric field direction changes from negative to positive and is adjusted to approximately +0.33 MV / cm, the flipped skyrmion Sky2 transforms into the second flux-closed domain Flux2. When the applied electric field continues to be adjusted positively to approximately +0.46 MV / cm, the second flux-closed domain Flux2 reverts to the initial skyrmion domain structure Sky1.

[0189] Example 9:

[0190] The oxygen vacancy concentration was set at 7.5 × 10⁻⁶. 20 cm -3 Other parameters are the same as in Example 1.

[0191] Example 10:

[0192] The oxygen vacancy concentration was set to 8 × 10⁻⁶. 20 cm -3 Other parameters are the same as in Example 1.

[0193] Comparative example:

[0194] Set the oxygen vacancy concentration to 0 cm⁻¹-3 That is, there are no anaerobic vacancies, and other parameters are the same as in Example 1.

[0195] like Figure 5 As shown, under oxygen-vacancy-free conditions, the domain structure in PTO ferroelectric thin films undergoes a reversible switching between the initial skyrmion Sky1 and the flipped skyrmion Sky2. Compared to the multi-topological domain cycling path under oxygen-vacancy conditions, fewer intermediate domain states are accessible under oxygen-vacancy-free conditions, and intermediate topological domain states such as the first flux-closed domain Flux1, the stripe domain L, and the second flux-closed domain Flux2 are not clearly experienced.

[0196] Therefore, oxygen vacancies do not merely participate in the calculation as additional defects, but rather further influence the path after polarization reversal, the domain wall movement process, and the formation of intermediate topological domain states by altering the space charge distribution, local potential distribution, and built-in electric field distribution within the thin film. Introducing oxygen vacancies allows PTO ferroelectric thin films to... The pathway involves multi-topological domain cyclic transformation; while under anaerobic vacancy conditions, the system mainly exhibits the following characteristics: Different skyrmions can be reversibly switched. This comparative result indicates that oxygen vacancies can enrich the topological domain transition pathways of PTO ferroelectric thin films and provide a regulatory basis for the expansion of multi-state storage.

[0197] The specific embodiments described above are for illustrative purposes only and are not intended to limit the scope of the invention. Therefore, any modifications, equivalent substitutions, or improvements made to the model dimensions, boundary conditions, material parameters, applied electric field sequence, oxygen vacancy concentration, numerical solution method, and visualization processing method without departing from the inventive concept of the invention should be included within the scope of protection of the invention.

Claims

1. A phase-field method for multi-topological domain cyclic conversion of lead titanate (PTO) ferroelectric thin films, comprising the following steps: Step (1): Establish a three-dimensional model of the PTO ferroelectric thin film and determine the polarization P and potential. Displacement u and oxygen vacancy concentration As a field variable; Step (2), establish the expression for the total free energy of PTO ferroelectric thin films based on Ginzburg-Landau theory: ； Among them, f lan For the Landau energy density, f elas f is the elastic energy density. grad f is the gradient energy density. ele Let σ be the electrostatic energy density. 0 E represents the applied stress, ε represents the strain, and E represents the strain. 0 For an external electric field; Step (3) introduces the oxygen vacancy transport process and couples the oxygen vacancy with the electrostatic field to establish the coupling relationship between the oxygen vacancy, the electric field and the polarization field, so as to achieve coordinated control of the electric field and the oxygen vacancy. Step (4): Combine the time-dependent Ginzburg-Landau kinetic equation, mechanical equilibrium equation, electrostatic equilibrium equation and Nernst-Planck equation to establish a phase-field model of PTO ferroelectric thin film coupled with oxygen vacancies and multiple physical fields. Step (5): Construct a stable initial skymin domain structure Sky1 in the PTO ferroelectric thin film phase field model; Step (6) involves applying a preset uniform electric field sequence to achieve fine control of the electric field, driving the domain structure in the PTO ferroelectric thin film to cyclically switch between skyrmions and flux-closed domains and / or stripe domains.

2. The method according to claim 1, characterized in that, The oxygen vacancy transport process in step (3) includes oxygen vacancy flux, oxygen vacancy diffusion coefficient and mobility, and oxygen vacancy concentration distribution: The oxygen vacancy flux is calculated using the Nernst-Planck equation. , Where is the oxygen vacancy concentration, and E is the electric field strength. and These are the oxygen vacancy diffusion coefficient and mobility, respectively; Among them, the oxygen vacancy diffusion coefficient and mobility satisfy the Einstein relation. k B Where is Boltzmann constant, T is temperature, δ is the number of effective vacancy charges, and q0 is unit charge; Among them, the oxygen vacancy concentration distribution satisfies the mass conservation relationship. .

3. The method according to claim 1 or 2, characterized in that, The coupling of oxygen vacancies with the electrostatic field in step (3) includes the oxygen vacancy space charge density and the electrostatic field distribution: The oxygen vacancy space charge density is expressed as: ; The electrostatic field distribution satisfies the electrostatic equilibrium equation: D is the electric displacement vector.

4. The method according to any one of claims 1-3, characterized in that, The phase-field model of PTO ferroelectric thin film coupled with oxygen vacancies and multiphysics fields established in step (4) is as follows: r(x1,x2,x3) are spatial coordinates, t is time, L is the kinetic coefficient, and F is the total free energy of the system; the elastic field satisfies the mechanical equilibrium equations: , σ ij Let be the stress tensor.

5. The method according to claims 1-4, characterized in that, The time step for the oxygen vacancy concentration distribution is 0.001≤Δt1≤0.005, and the time step for the polarization distribution is 0.005≤Δt2≤0.02, where Δt1 is the time step for the oxygen vacancy concentration distribution and Δt2 is the time step for the polarization distribution.

6. The method according to any one of claims 1-5, characterized in that, In step (5), the initial Skymin domain structure Sky1 is obtained by setting the initial polarization configuration, in-plane periodic boundary conditions, thickness direction open-circuit electrical boundary conditions, free boundary on the upper surface of the thin film, fixed boundary on the lower surface of the thin film, and in-plane mismatch strain. Preferably, it is obtained by establishing a three-dimensional calculation model of PTO ferroelectric thin film and discretizing the PTO three-dimensional calculation model. The mechanical boundary conditions are set as follows: the upper surface of the thin film is free and the lower surface is fixed. The electrical boundary conditions are set as ideal open circuit conditions in the thickness direction. Biaxial compressive mismatch strains e1= e2=-1% are introduced in the in-plane direction of the thin film. Under the combined action of the mechanical boundary conditions, electrical boundary conditions and in-plane biaxial compressive mismatch strains, the PTO ferroelectric thin film system first forms regular 90° domains. On the basis of the regular 90° domains, temperature field and electric field are further applied to control the evolution, and finally it evolves into a periodically distributed skyrmion array.

7. The method according to any one of claims 1-6, characterized in that, An oxygen vacancy concentration of 4 × 10⁻⁶ was introduced into the initial Skyming subdomain structure Sky1. 20 -8×10 20 cm -3 .

8. The method according to any one of claims 1-7, characterized in that, When the oxygen vacancy concentration introduced into the initial Skyming subdomain structure Sky1 is 4 × 10 20 -7×10 20 cm -3 In step (6), the preset uniform electric field sequence drives the topological domain structure in the PTO ferroelectric thin film to complete one cycle ① according to the following path: ; When the oxygen vacancy concentration introduced into the initial Skyming subdomain structure Sky1 is 7 × 10⁻⁶ 20 -8×10 20 cm -3 In step (6), the preset uniform electric field sequence drives the topological domain structure in the PTO ferroelectric thin film to complete one cycle ② according to the following path: Sky1 is the initial skymin subdomain structure, Flux1 is the first type of flux-closed domain, L is the stripe domain, Sky2 is the flipped skymin subdomain structure, and Flux2 is the second type of flux-closed domain. When the preset uniform electric field sequence is repeatedly applied, the recovered initial skymin subdomain structure Sky1 serves as the starting state of the next cycle, causing the topological domain structure in the PTO ferroelectric thin film to undergo repeated cyclic transformations along the above-mentioned cycle ① or ②.

9. The method according to any one of claims 1-8, characterized in that, The preset uniform electric field sequence applied in step (6) is a segmented cyclic electric field sequence applied along the thickness direction of the PTO ferroelectric thin film. The segmented cyclic electric field sequence includes a negative electric field loading segment, a positive electric field loading segment, and a repeated cyclic loading segment. The repeated cyclic loading segment refers to repeatedly applying the external electric field in the order of the negative electric field loading segment and the positive electric field loading segment, thereby realizing the continuous cyclic conversion of the multi-topological domain structure in the PTO ferroelectric thin film; wherein the oxygen vacancy concentration introduced is 7×10 20 -8×10 20 cm -3 At that time, the absolute value of the adjustment step size of the applied electric field is 0.01 MV / cm, which specifically includes the following process: In the first stage, the negative electric field loading section is gradually adjusted from 0 MV / cm to -0.35 MV / cm, with an electric field step size of -0.01 MV / cm. During this stage, the domain structure in the PTO ferroelectric thin film evolves from the initial skyminton domain structure Sky1 to the first flux-closed domain Flux1, and the first flux-closed domain Flux1 is formed in the range of -0.25 MV / cm to -0.35 MV / cm. In the second stage, the applied electric field is adjusted negatively from -0.35MV / cm to -0.40MV / cm, with a step size of -0.01MV / cm. In this stage, the first flux closed domain Flux1 is transformed into a striped domain L, and striped domain L is formed in the range of -0.35MV / cm to -0.40MV / cm. In the third stage, the applied electric field is adjusted negatively from -0.40MV / cm to -0.50MV / cm, with a step size of -0.01MV / cm. In this stage, the stripe domain L evolves into the skymin subdomain structure Sky2, and the skymin subdomain structure Sky2 is formed in the range of -0.45MV / cm to -0.50MV / cm. In the fourth stage, the direction of the applied electric field changes from negative to positive and is gradually adjusted from -0.50MV / cm to +0.35MV / cm, with a field step size of +0.01MV / cm. In this stage, the Skymin domain structure Sky2 evolves into the second flux-closed domain Flux2 and forms the second flux-closed domain Flux2 in the range of +0.25MV / cm to +0.35MV / cm. In the fifth stage, the applied electric field is further adjusted in the positive direction from +0.35 MV / cm to +0.50 MV / cm, with a field step size of +0.01 MV / cm. In this stage, the second type of flux-closed domain... The original skymin subdomain structure Sky1 was restored, and the restored original skymin subdomain structure Sky1 was formed in the range of +0.45MV / cm to +0.50MV / cm; The first to fifth stages constitute a complete cycle. The segmented cyclic electric field sequence is repeatedly applied to complete a complete cycle, causing the topological domain structure in the PTO ferroelectric thin film to undergo repeated cyclic transformations in the order of Sky1, Flux1, L, Sky2, Flux2 and Sky1. When the introduced oxygen vacancy concentration is 4 × 10 20 -7×10 20 cm -3 At that time, the absolute value of the adjustment step size of the applied electric field is 0.01 MV / cm, which specifically includes the following process: In the first stage, the negative electric field loading section is gradually adjusted from 0 MV / cm to -0.35 MV / cm, with an electric field step size of -0.01 MV / cm. During this stage, the domain structure in the PTO ferroelectric thin film evolves from the initial skyminton domain structure Sky1 to the first flux-closed domain Flux1, and the first flux-closed domain Flux1 is formed in the range of -0.25 MV / cm to -0.35 MV / cm. In the second stage, the applied electric field is adjusted negatively from -0.35MV / cm to -0.50MV / cm, with a field step size of -0.01MV / cm. In this stage, the first flux closed domain Flux1 evolves into the skymin subdomain structure Sky2, and the skymin subdomain structure Sky2 is formed in the range of -0.45MV / cm to -0.50MV / cm. In the third stage, the direction of the applied electric field changes from negative to positive and is gradually adjusted from -0.50MV / cm to +0.35MV / cm, with a field step size of +0.01MV / cm. During this stage, the Skymin domain structure Sky2 evolves into the second flux-closed domain Flux2 and forms the second flux-closed domain Flux2 in the range of +0.25MV / cm to +0.35MV / cm. In the fourth stage, the applied electric field is further adjusted in the positive direction from +0.35 MV / cm to +0.50 MV / cm, with a field step size of +0.01 MV / cm. In this stage, the second type of flux-closed domain... The original skymin subdomain structure Sky1 was restored, and the restored original skymin subdomain structure Sky1 was formed in the range of +0.45MV / cm to +0.50MV / cm; The first to fourth stages constitute a complete cycle. The segmented cyclic electric field sequence is repeatedly applied to complete a complete cycle, causing the topological domain structure in the PTO ferroelectric thin film to undergo repeated cyclic transformations in the order of Sky1, Flux1, Sky2, Flux2 and Sky1.

10. The method described in any one of claims 1-9 is used to realize information polymorphic storage and the design of ferroelectric topological domain polymorphic storage devices.

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