Topological polar phases in confined ferroelectrics*

The inherent mechanism of polarization texturing in confined ferroelectrics arises from the interplay between the electrostatic and confinement effects. Specifically, the polarization field tends to avoid the bound charges in order to minimize the energy associated with the depolarization electric field. This brings about the topological constraint of the divergenceless of the polarization field.

The theory of fundamental topological structures emerging in a divergenceless vector field was developed by Arnold [1] for hydrodynamics. In application to nanostructured ferroelectrics, only two types of elementary topological excitations of polarization field can exist – either 2D vortex states or 3D knotted structures, Hopfions. Both textures have been observed in confined geometries of ferroelectric thin films, superlattices, nanodots and nanoparticles [2-4].

We performed the theoretical study of emerging topological polar states in ferroelectric nanoparticles of various geometries. In particular, we consider PbTO₃ nanocylinders comprising strain-coupled polarization vortices [3] and PbZr_0.6Ti_0.4O₃ spherical nanoparticles hosting Hopfions [4], and discuss the role of geometry and anisotropy in stabilizing either of these basic configurations.

1. V.I. Arnold, B.A. Khesin. Topological methods in hydrodynamics. Springer Nature, 2021.

2. S. Das, et al. APL Materials 8(12), 120902 (2020).

3. S. Kondovych et al. arXiv:2112.10129 (2022).

4. I. Luk'yanchuk et al. Nat. Comm. 11, 2433 (2020).