Phase-field simulations of vortex chirality manipulation in ferroelectric thin films

Chirality, the left-handed or right-handed nature of objects, is a significant property in materials science, with applications in diverse fields, including polarization optics and sensors. Recently, nanoscale textures in ferroelectric materials, such as polar vortices and skyrmions, have shown chiral properties, sparking interest in their potential for high-density, low-energy data storage devices. Controllable manipulation of this vortex chirality remains a challenge. BiFeO₃ (BFO) is a prototypical ferroelectric material with eight polarization orientations determined by its rhombohedral structure, leading to diverse domain wall (DW) types (180°, 109°, 71°). Previous research has speculated on DW chirality due to depolarization fields and stress/strain inhomogeneities, with experimental confirmation in triclinic ferroelectrics and BFO films. Theoretical studies have shown that electric fields, strain, and flexoelectricity influence vortex formation and chirality. This work employs phase-field simulation to explore the formation and manipulation of chiral vortices in BFO thin films under local surface charge or electric fields, focusing on the mechanisms governing chirality and its reversible control.

Existing literature extensively explores the impact of various factors on the formation and properties of ferroelectric vortices. Studies have shown the influence of curled electric fields on vortex chirality by switching the toroidal moment. Local radial electric stimulation has been demonstrated to create or annihilate vortex pairs by carefully selecting polarization locations. The role of graded composition and mechanical fields in controlling vortex morphology has also been investigated, with the interface strain shown to promote polarization rotation and the formation of vortex pairs. The influence of flexoelectricity on polarization switching and DW formation has received significant attention, highlighting its sensitivity to vortex evolution, which can be quantified using phase-field methods. However, a comprehensive understanding of controllable chirality manipulation, especially its reversible nature, remains underdeveloped. This study addresses this gap.

The researchers used phase-field simulations to model the ferroelectric polarization evolution in BiFeO₃ thin films. The time-dependent Ginzburg-Landau equation was employed, with the total free energy density comprising Landau free energy, gradient energy, electrostatic energy, elastic energy, and flexoelectric energy. The Landau free energy was expressed as a sixth-order polynomial of polarization components, incorporating dielectric stiffness and higher-order stiffness coefficients. Gradient energy was represented using polarization gradients and a gradient energy coefficient tensor. Flexoelectric energy was included, considering flexoelectric coupling coefficients and elastic strain. The elastic energy density incorporated the elastic stiffness tensor and elastic strain, with eigenstrain considered to account for electrostrictive coupling. The electrostatic energy density included contributions from spontaneous polarization and energy storage in the vacuum space. The electrostatic potential was solved using Poisson’s equation with short-circuit boundary conditions, considering surface charge density on the top surface. Three-dimensional simulations were performed for single and bi-domain configurations with varying dimensions and material coefficients for BiFeO₃ (listed in Table 1). The simulations explored the effect of different surface charge densities, electric fields, and bi-domain arrangements on vortex formation and chirality. The simulations also considered the flexoelectric effect on the vortex morphology and stability.

The simulations revealed several key findings: 1. In single-domain BFO films, applying positive/negative surface charge generated vortices with random chirality due to degenerate energy states. The downward polarization switching was observed in the charged region, with upward polarization domains surrounding the vortex. The percentage of different R domains (formed through 71°, 109°, and 180° polarization switching) depended on the initial domain and surface charge density. Increasing surface charge density led to a more evenly distributed 4 R-domain vortex and shifted the vortex core towards the film center. 2. In bi-domain films, the initial bi-domain arrangement determined the vortex chirality. A 180° DW yielded opposite chiralities for reversed bi-domain arrangements (R3+R3- vs. R3-R3+), while 109° DWs (R3+R2- vs. R2-R3+) also influenced chirality, demonstrating controllable chirality manipulation. 3. Elastic strain analysis showed significant changes in axial strains near the vortex core, with tensile and compressive strains present. Shear strains exhibited distinct behaviors, strongly correlating with vortex vorticity. The flexoelectric effect influenced vortex morphology but not chirality. 4. Reversible chirality switching was demonstrated by alternating surface charge or electric fields, with the external field changing vortex polarity while leaving vorticity unchanged. Vortex stability post-field removal was linked to the size of the initially charged region. Large charged regions ensured stability; smaller regions resulted in vortex merging with surrounding domains.

This study successfully demonstrates the controllable manipulation of vortex chirality in ferroelectric thin films using phase-field simulations. The findings highlight the crucial role of initial bi-domain arrangements and the applied electric fields in determining the final vortex state. The reversible chirality switching achieved is particularly significant for potential applications in data storage, offering possibilities for high-density, low-energy devices with improved fatigue tolerance. The correlation between shear strains and vortex vorticity provides valuable insights into the underlying physics. The influence of flexoelectricity on vortex morphology without chirality change adds further understanding to the complex interplay of factors governing vortex behavior. The stability analysis provides practical guidelines for designing devices that can maintain the chiral state after removing external stimuli. This research significantly advances our theoretical understanding of vortex domain evolution in ferroelectric materials and paves the way for future experimental investigations aiming at realizing practical applications of this phenomenon.

This research successfully demonstrates the controllable and reversible manipulation of vortex chirality in BFO thin films through phase-field simulations. The findings show that initial bi-domain arrangements and applied electric fields are key factors controlling chirality. Reversible switching and stability after field removal highlight the potential for practical applications in non-volatile memory devices. Future work could focus on experimental verification of these findings and exploration of further optimization strategies for enhanced stability and control.

The study relies on phase-field simulations, which are based on certain simplifying assumptions and models of the material behavior. Experimental validation is necessary to confirm the simulated results. The study focuses on BiFeO₃; the generalizability of the findings to other ferroelectric materials needs further investigation. The simulation parameters, such as the flexoelectric coupling coefficients, are based on existing literature estimates, which may have some uncertainties. Further research could refine these parameters using more accurate experimental data.