Polar vortex generation and control in a ferroelectric nanodisk

Chirality exists universally in nature and is closely related to various exotic physical phenomena. In nanoscale functional materials, various chiral topological structures exist fruitfully together, forming an exotic chiral topological zoo. Chirality has always been challenging to control. Ferroelectric vortices, as well-known in-plane chiral topological domain structures, have been extensively studied experimentally and theoretically in recent years. Compared with ferromagnetic vortices, ferroelectric vortices are two-dimensional, and their chirality only includes circulation but no polarity, which has led to the longstanding misconception that polar vortices, like Bloch-type merons, do not exist in ferroelectric materials. In this paper, we conduct a series of phase-field simulations using ferroelectric epitaxial nanodisks to propose an effective scheme for constructing a three-dimensional polar vortex domain structure with central polarity and a series of strategies for manipulating the chirality of polar vortices (including circulation and polarity), providing inspiration for the design of multistate information memories. The results show that misfit strain, the aspect ratio of a nanodisk, and the mole fraction of Zr and Ti atoms in $\mathrm{PbZ}{\mathrm{r}}_{1\ensuremath{-}x}\mathrm{T}{\mathrm{i}}_{x}{\mathrm{O}}_{3}$ are decisive factors to polar vortex generation. Furthermore, applying either an axial electric field or in-plane torque, the polarity of a polar vortex can be changed while keeping its circulation unchanged; the combined application of the axial electric field and in-plane torque realizes alternating changes in the polarity and circulation of a polar vortex. In this paper, we enrich the understanding of ferroelectric topological physics, which is conducive to facilitating the development of ferroelectric nanoelectronic devices.