Unusual vortex structure in ultrathin Pb(Zr_{0.5}Ti_{0.5})O₃ films

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