Torsion-induced vortex switching and skyrmion-like state in ferroelectric nanodisks.

The controllability of vortex state in ferroelectric nanodisks under the effect of external torsion is investigated in this work based on phase-field simulation. We discover a novel Bloch skyrmion-like state in ferroelectric nanodisks due to the combining effect of the torsion and the depolarization field. Moreover, a new strategy is proposed to achieve deterministic switching of the vortex chirality in the ferroelectric nanodisks. On the one hand, if a fixed external electric field is applied to the nanodisk, the vortex chirality can be switched by the torsion force. On the other hand, if we apply a fixed torsion force to the nanodisk, the vortex chirality can be readily switched by an external electric field. The feasibility of both mechanical and electrical switching of the vortex in the ferroelectric nanodisks is based on the trilinear coupling between the toroidization, polarization and shear strain of the system. The influences of temperature, electric field, torsion, and size of the nanodisk on the control of the vortex state are further revealed. Our findings shed light on the practical control and application of ferroelectric dipole vortices.