Polar toron structure in ferroelectric core-shell nanoparticles

Toron structures are three-dimensional topological solitons characterized by a double-twist of continuous physical fields. Despite their recent discovery in colloids, liquid crystals, and magnetic materials, they remain elusive and under-explored in the important class formed by ferroelectric materials. Here, we demonstrate self-assembled toron structures in BiFeO3/BaTiO3 core-shell nanoparticles as a result of combined effects between geometrical confinement and dipole interactions of different ferroelectric phases. The geometrical confinement supports the formation of polarization vortex configuration, while the interaction between rhombohedral and tetragonal phases gives rise to a twist of the vortex core line. The polar toron texture can be stable in a wide range of particle sizes and temperatures. In addition, the toron state is quantitatively characterized by hyper-toroidal moment. Furthermore, the chirality of the toron texture can be controlled by a homogeneous electric field. Our findings may enable myriads of solitonic polar structures and their technological applications.