Curvature-induced drift and deformation of magnetic skyrmions: Comparison of the ferromagnetic and antiferromagnetic cases

The influence of the geometrical curvature chiral magnetic films on static and dynamic properties hosted skyrmions is studied theoretically. We predict effects curvature-induced drift under action gradients without any external stimuli. strength driving force essentially depends skyrmion type, N\'eel or Bloch, while trajectory motion determined by type ordering: ferromagnetic antiferromagnetic. When moving surface, undergo deformations that depend skyrmion. In small-curvature limit, using collective-variable approach we show acting a linear in gradient mean curvature. Bloch much smaller: it proportional to product its gradient. contrast fast skyrmions, dynamics slow affected profile deformation. For sake simplicity, restrict ourselves case zero Gaussian consider cylindrical surfaces general type. Equations for antiferromagnetic curved are obtained terms collective variables. All analytical predictions confirmed numerical simulations.