Topology of the polarization field in PbTiO3 nanoparticles of different shapes by atomic-level simulations

Abstract

An atomistic model approach parameterized from first-principles calculations is used to investigate size and shape effects on the polarization field in isolated stress-free PbTiO3 nanoparticles. The study was carried out by molecular dynamics simulations in free-standing nanodots of cylindrical, spherical, and ellipsoidal shapes. We show that in cylinders with diameter equal to height, the size-induced transformation from the vortex to the flux-closure domain configuration causes an anomaly in the behavior of the toroidal moment and the volume of the system. During this transformation, the vortex core evolves into domain walls while the resulting structure is stabilized due to the non-homogeneous distribution of polarization and strain inside the domains. A similar behavior is observed in elongated cylinders, spheres, and spheroids. The increment in the diameter/height relation of the nanoparticles gives rise to a succession of topological transformations that include multi-vortex configurations, ferroelectric bubble states, and multi-domain patterns. While the transformation path for flat cylinders is similar to the one previously obtained for cuboids, the thinner edge region of the spheroids prevents the stabilization of one- and two-bubble states. Despite this last difference, our results indicate that the polarization pattern of a nanoparticle depends more on its aspect ratio than on its shape.