Nanoscale Toroidal Ferroelectricity in PbTiO 3

Abstract

We applied a first-principles-based atomistic approach to investigate the formation of dipole patterns in isolated stress-free PbTiO3 nanoparticles of rectangular shape. We found that a sequence of topological transformations takes place as the aspect ratio of the nanostructure changes from elongated nanorods to flat nanoplatelets. Of a particular interest is the formation of a four-vortex state with cores aligned along a closed path. In this way, the vortex structure forms a ring-shaped torus, and a ferroelectric bubble is developed at the center of the ring. The thermal properties of the bubbles indicate that this state is suitable for the development of nanometric ferroelectric devices. Our results cover, for the first time, the gap between the nanodots and wires and between the nanodots and thin films, that is between 0D and 1D as well as between 0D and 2D objects.