Tip-induced flexoelectricity, polar vortices, and magnetic moments in ferroelastic materials

Flexoelectricity in twinned ferroelastic thin films generates polarity inside twin walls. The electrical dipoles are typically aligned parallel to twin walls while out-of-plane dipoles are induced elastically by an atomic force microscopy (AFM) tip or by atomic steps in the substrate. Molecular dynamics modeling shows that the out-of-plane dipoles form polar vortex structures next to the domain walls. Flexoelectricity, e.g., by moving AFM tips, produces displacement currents inside these vortices. We estimate that these displacement currents generate magnetic fields with moments in the order of 10-9 μB per atomic layer.