Understanding and predicting geometrical constraint ferroelectric charged domain walls in a BiFeO₃ island via phase-field simulations

It has been known that ferroelectric charged domain walls (CDWs), which break the polarization continuity, may be electrically active with an elevated conductivity. However, the bound charge at CDWs may render them energetically unstable, and thus, forming CDWs naturally and manipulating them electrically is still challenging. Here, we theoretically utilize phase-field simulations to design spontaneously generated CDWs with center-type quad-domains in a single square-shaped BiFeO₃ nanoisland. It is shown that the stability of the spontaneously emerging head-to-head domain walls with center-convergent quad-domains is mainly determined by three contributions, namely, the geometrical constraint from approximately 45°-tilted bottom edges, the electric boundary condition, and the necessary screening free charges to compensate head-to-head domain walls. It is demonstrated that the center-convergent quad-domains with head-to-head CDWs can be electrically switched to the center-divergent one with tail-to-tail CDWs, providing guidance for achieving ferroelectric domain-wall-based nanodevices with low-power dissipation.