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

Abstract

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 textures whose paraelectric cores are aligned with every rotational axis of the particle point symmetry group. The shape-dependent metastability of the vortex-like textures opens up new avenues for controlling polarization at the nanoscale in a variety of technological applications.

Controlling the domain structure of ferroelectric nanoparticles using tunable shells

“…Wang et al [46] calculated the electrocaloric effect of PbTiO 3 nanoparticles with complicated vortex-like domain structure. Pitike et al [47] used LGD phenomenology to model ferroelectric nanoparticles and have found that the critical particle sizes of the texture instabilities are strongly dependent on the particle shape. Zhu et al [48] modeled polar properties of ferroelectric nanoparticles with different shapes and sizes.…”

Hopfions emerge in ferroelectrics

“…In turn, the selfconsistent interactions result in a nonuniform texture that minimizes electrostatic energy costs associated with these depolarization effects. The corresponding topologically nontrivial textures include regular patterns of Kittel domains [1][2][3][4][5] , which can be also viewed as the periodic array of vortex-antivortex pairs 6 and lattice of skyrmions 7 in the films and superlattices, vortices and skyrmions in the nanords, nanodots [8][9][10][11][12][13][14][15] , and nanoparticles 16,17 . As we show below, a geometrical restriction of a ferroelectric brings about a fundamental class of the topological formations, Hopfions, that appear inherent to a broad variety of nature phenomena [18][19][20][21][22][23][24][25][26][27][28][29] .…”

Electromechanical control of polarization vortex ordering in an interacting ferroelectric-dielectric composite dimer

“…Formation of topological polarization patterns in isolated FE particles has also been studied with different coarse-grained theoretical approaches, such as phase-field 12,28,31,32 , semianalytic [33][34][35][36] , and effective hamiltonian 37,38 methods. For example, in previous work 32,39 , we evaluated size and shape dependent phase transitions in individual FE nanoparticles embedded in a dielectric matrix, observing a monodomain to vortex-like to polydomain sequence of transformations for the increasing particle size. However, in a composite system, this situation corresponds to a highly dispersed arrangement of particles within the matrix, with negligible electrostatic and elastic interactions between them.…”