Labyrinthine domains in ferroelectric nanoparticles: a manifestation of gradient-driven morphological transition

TL;DR

This study uses the Landau-Ginzburg-Devonshire model to explore how size and surface effects induce complex labyrinthine domain structures in ferroelectric nanoparticles, revealing a new gradient-driven morphological transition.

Contribution

It uncovers the formation of stable labyrinthine domains in uniaxial ferroelectric nanoparticles due to a balance of energies, highlighting a novel gradient-driven transition mechanism.

Findings

Labyrinthine domains are stable in certain ferroelectric nanoparticles.

Domain branching increases rapidly below a critical polarization gradient.

The mechanism may apply to various confined ferroic materials.

Abstract

In the framework of the Landau-Ginzburg-Devonshire (LGD) approach we studied finite size effects of the phase diagram and domain structure evolution in spherical nanoparticles of uniaxial ferroelectric. The particle surface is covered by a layer of screening charge characterized by finite screening length. The phase diagram, calculated in coordinates "particle radius vs. screening length" has a wide region of versatile poly-domain structures separating single-domain ferroelectric and nonpolar paraelectric phases. Unexpectedly, we revealed a region of stable irregular labyrinthine domains in the nanoparticles of uniaxial ferroelectric CuInP2S6 with the first order paraelectric-ferroelectric phase transition. We established that the origin of labyrinthine domains is the mutual balance of LGD, polarization gradient and electrostatic energies. The branching of the domain walls appears and increases rapidly when the polarization gradient energy decreases below the critical value. Allowing for the generality of LGD approach, we expect that the gradient-induced morphological transition can be the source of labyrinthine domains appearance in many spatially-confined ferroics with long-range order parameter, including relaxors, ferromagnetics, antiferrodistortive materials and materials with incommensurate ferroic phases.