Collective control of a vortex array in a ferroelectric ultrathin film

Recently, the observation of ferroelectric vortex arrays has triggered the investigation of topological domain structures and their characteristics. Vortices are typical topological domain structures with chirality in nanoscale ferroelectric materials. The chirality of a single vortex in a nanodot can be easily manipulated, but the collective control of a vortex array is exceptionally difficult and has not yet been realized. This Letter proposes an effective scheme for the collective control of a vortex array and investigates it via phase-field simulations. The results indicate that the collective control of a vortex array with bidirectional switching can be realized by introducing a bending film with periodic large curvatures under alternative electric fields. Furthermore, a general rule for determining the electrically controllable chirality of ferroelectric vortices is proposed. This Letter demonstrates the feasibility of the collective control of vortex arrays and provides insights for developing ferroelectric nanoelectronic devices based on vortex arrays.