Metastable vortex-like polarization textures in ferroelectric nanoparticles of different shapes and sizes

The dependence of the polarization texture topology in ferroelectric PbTiO3 nanoparticles, embedded in a dielectric matrix, on the particle shape and size was investigated with a time-dependent Landau-Ginzburg-Devonshire approach combined with coupled-physics finite-element-method based simulations. Particle shapes belonging to the superellipsoidal family were probed, including octahedral, cubic, and intermediate geometries. For each shape, a parametric sweep of particle sizes ranging from 2 to 40 nm was conducted, revealing a general trend for the texture transformations from a monodomain, through a vortex-like, to a multidomain state, as the size increases. Critical particle sizes for the texture instabilities were found to be strongly dependent on the particle shape, with octahedral particles undergoing transitions at much larger volumes, compared to the cubic particles. Furthermore, for each of the considered non-spherical shapes of appropriate size, it was possible to obtain multiple vortex-like text...