Toroidal ferroelectricity in PbTiO3 nanoparticles.

We report from first-principles-based atomistic simulations that ferroelectricity can be sustained in PbTiO(3) nanoparticles of only a few lattice constants in size as a result of a toroidal ordering. We find that size-induced topological transformations lead to the stabilization of a ferroelectric bubble by the alignment of vortex cores along a closed path. These transformations, which are driven by the aspect ratio of the nanostructure, change the topology of the polarization field, producing a rich variety of polar configurations. For sufficiently flat nanostructures, a multibubble state bridges the gap between 0D nanodots and 2D ultrathin films. The thermal properties of the ferroelectric bubbles indicate that this state is suitable for the development of nanometric devices.