Phase-field simulations of topological conservation in multi-vortex induced by surface charge in BiFeO_(3)thin films

The creations and manipulations of vortexes in ferroelectric materials with external stimuli are expected to be used in the design and fabrication of sensing materials and multifunctional electronic devices.In this work,we investigated the surface charge-induced multi-vortex evolution using the phase-field simulations in BiFeO_(3).A combination of domain morphology,polarization distribution and winding number calculation was considered.The results show that vortex and anti-vortex exist simultaneously in pairs,and the total value of winding numbers is always 0.In addition,the minimum distanceΔl between the surface charge regions is 9 nm when the vortex domains are independent of each other.This work provides a reference for the manipulation of ferroelectric vortex induced by surface charges,which lays a theoretical foundation for the design and fabrication of high-density vortex memories.