Topological Defects and Domain Patterns in 2D and 3D Ferroics

Ferroic materials with topological defects exhibit unconventional and complex domain patterns, which can take fundamentally different forms depending on the morphology of the material and the type of defect. Some topological defects, such as vortex-antivortex pairs, may appear in both, 2D and 3D materials. The related domain patterns, domain sizes, as well as shapes and evolution of topological defects may differ significantly depending on the dimensionality of the studied compound, despite originating from the same underlying principles. Here, we present two cases of such contrasting behaviors that have been studied using phase-field simulations and analytical tools. In a first example, we show how the domain patterns and evolution of topological defects in an incommensurate stripe phase differs between 2D and 3D systems. We show how the extension to 3D allows for a flat energy landscape and topological defects with exceptionally long lifetimes. As a second example, we study hexagonal manganite thin films, which are lattice-distortively driven improper ferroelectrics, in going from 2D to 3D. We show how the domain pattern in thin films differs from an ideal 2D system because of the depolarizing field. Despite the stabilizing function of the topological defects, the depolarizing field appearing in thin films affects the domain size distribution in an inconspicuous yet significant way. We end by discussing 3D multiferroic materials and show how topological defects in ferroic materials can give insights on the difference between 2D and 3D ordered systems that exhibit topological defects at large.