Unusual vortex structure in ultrathin Pb(Zr$_{0.5}$Ti$_{0.5}$)O$_3$ films

摘要

Using a first-principles-based approach, we determine the ferroelectricpattern in PbZr$_{0.5}$Ti$_{0.5}$O$_3$ ultrathin film. It is found that vortexstripes are formed in the system and they are responsible for the 180$^\circ$domains observed. When a local external field is exerted, the vortex stripetransforms into the vortex loop structure, which leads to the formation of asmaller domain with the polarization antiparallel to the field in the center ofthe field region. This may provide a convenient way to manipulate nanodomainsin thin films.