Geometry-induced motion of magnetic skyrmions in curved ferro- and antiferromagnetic films

Here, we present the effect of the spontaneous drift of a magnetic skyrmion in curved films under the action of the curvature gradients without any external stimuli. The strength of the curvature-induced driving is determined by the type of Dzyaloshinskii-Moriya interaction, while the trajectory is determined by the type of magnetic ordering. Using rigid particle-like assumption, we show that for the case of Neel skyrmions the driving force is linear with respect to the gradient of the curvature, while for Bloch skyrmions the driving is proportional to the product of the mean curvature and its gradient. During the motion along the surface, the skyrmion experiences deformation which depends on the skyrmion type. The equations of motion for Neel and Bloch magnetic skyrmions in curved ferromagnetic and antiferromagnetic materials are obtained in terms of collective variables. All analytical predictions are confirmed by numerical simulations.