Phase-field simulations of surface charge-induced ferroelectric vortex

Ferroelectric vortices are characterized by their small size and exotic physical properties, which have great potential for application in high-density information storage. However, the influence of the shape of the external field on such topological vortex domain morphology and domain percentage is still lacking research. Here, the ferroelectric domain evolution induced by a circular-, square-, and triangular-shaped surface charge are investigated in BiFeO3 thin films by phase-field simulations. The shape symmetry of the surface charge distribution determines the 4R domain percentage in one single vortex. Triangle-shaped surface charge distribution with odd number symmetry axes has the greatest influence on the percentage of 4R domain, while that of circular- and square-shaped with even number symmetry axes have almost no influence on the 4R domain ratio. Compared to the triangle, an antivortex can be observed around the vortex domain in the circular- and square-shaped surface charge. The rotating triangle affects the domain percentage of the vortex and the emergence of an antivortex. Here, the difference of domain percentage is determined by the choice of nucleation position and the domain switching mechanism. It was found that the percentage of domain along the edge is greater than the corner of the triangle. Among them, 71 domain switching is more likely to happen than 109 and 180 domain switching. These findings provide a fundamental understanding for ferroelectric domain manipulation in a single vortex from an external field with different shapes.