Flexo-Elastic Control Factors of Domain Morphology in Core-Shell Ferroelectric Nanoparticles: Soft and Rigid Shells

Abstract Within the framework of the Landau-Ginzburg-Devonshire approach we explore the impact of elastic anisotropy, electrostriction, flexoelectric couplings, and mismatch strain on the domain structure morphology in ferroelectric core-shell nanoparticles of spherical shape. We perform finite element modelling (FEM) for multiaxial ferroelectric nanoparticle cores covered with an elastically-isotropic soft or elastically-anisotropic rigid paraelectric shell, with and without mismatch strains. In the case of a core covered with a soft shell, the FEM results show that at room temperature a single polarization vortex with a dipolar kernel can be stable if the electrostriction coupling is relatively weak. With increasing anisotropic electrostriction coupling, the vortex disappears and is replaced by complex flux-closure structures. In contrast to this, FEM performed for a core covered with a rigid shell shows that, at room temperature, the anisotropic elastic properties of the shell can stabilize vortex-like structures with three flux-closure domains. The flexoelectric coupling leads to a noticeable curling of the flux-closure domain walls. A mismatch strain compensates the curling of the flux-closure domains in the core confined by the elastically-anisotropic rigid shell. Our analysis of the configuration of the polarization reveals different types of topological defects, namely Bloch point structures and Ising lines. Furthermore, we study the influence of the core radius on the temperature behavior of domain structure morphology, polarization value, and phase transition temperatures, and derive approximate analytical expressions to analyze the influence of the elastic properties of the shell as well as mismatch strain on the phase diagrams.