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

Zhongqing Wu, Ningdong Huang, Zhirong Liu +3

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 sys…