Mechanical writing of in-plane ferroelectric vortices by tip-force and their coupled chirality

Recent experiments have demonstrated the existence of vortex or flux-closure domains in ferroelectric nanostructures, which are attractive to develop high-density data storage and novel configurable electronic devices. However, it remains challenging to stabilize in-plane vortex or flux-closure domains in ferroelectric film for the absence of a lateral geometry confinement. Based on a 3D phase field model, here we show that stabilization of isolated or interacting in-plane vortices in ferroelectric film can be achieved via applying a mechanical tip-force. The formation of such dipole vortices is caused by a conjoint effect of the tip-force-induced depolarization effect and in-plane strain. The effects of factors like film thickness, misfit strain, tip force and temperature on the vortex formation are systematically revealed and summarized as phase diagrams. The interaction between tip-induced vortices is also investigated. It is found that as the two tips get closer than the critical distance, the two initially isolated vortices become coupled, with identical or opposite chirality, depending on the distance between the two tips. A maximum data storage density of isolated in-plane vortices in ferroelectric thin film is estimated to be ~1 Tb in^-2. Our work thus demonstrates a mechanical strategy to stabilize dipole vortices, and provides a comprehensive insight into the characteristics of ferroelectric film under a mechanical tip force.