Unusual vortex structure in ultrathin Pb(Zr0.5Ti0.5)O3 films

Using a first-principles-based approach, we determine the ferroelectric pattern in PbZr0.5Ti0.5O3 ultrathin film. It is found that vortex stripes are formed in the system. The relation between the vortex stripes and the 180° domains is discussed. 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.