Size-dependent polarization distribution in ferroelectric nanostructures: Phase field simulations

From phase field simulations, we investigate the size-dependent polarization distribution in ferroelectric nanostructures embedded in a nonferroelectric medium. The simulation results exhibit that vortex structures of polarizations and single-domain structures are formed in ferroelectric nanodots and nanowires, respectively. Furthermore, a single-vortex structure is formed in the ferroelectric nanodots if the aspect ratio of thickness to lateral size is less than a critical value, whereas the ferroelectric nanodots are in a multivortex state if the aspect ratio exceeds the critical value. When the aspect ratio approaches infinity, nanodots will become nanowires, in which polarizations are homogeneous.