From the flow to the polarization field: A cognitive way for ferroelectric vortex structures

The generation of topological domain structures can significantly influence the behaviors of ferroelectric materials, and, however, strategies and perspectives for treating and analyzing them are still lacking. Inspired by the fluid lines and vorticity in hydromechanics, a characterization method of polarization lines and polarization vorticity is proposed herein for characterizing the vortex structure evolution. The polarization vorticity has the same unit as charge density, and the polarization vortex size is identified as a structure for vorticity concentration. Observing the radius and vorticity of vortices, we find that the domain evolution can be divided into three stages and the vortices react to mechanical loading in two ways: increasing the vorticity and enlarging the radius. Moreover, vortices exhibit three-dimensional shape, just like the vortex tube, and their conservation is proved. This paper provides a basis for further research on topological domain structures and the mechanism of vortex evolution, which might help improve high energy density devices.