Dynamics of Skyrmion Crystals in Metallic Thin Films

We study the collective dynamics of the Skyrmion crystal (SkX) in thin films of ferromagnetic metals resulting from the nontrivial Skyrmion topology. We show that the current-driven motion of the crystal reduces the topological Hall effect and the Skyrmion trajectories bend away from the direction of the electric current (the Skyrmion Hall effect). We find a new dissipation mechanism in non-collinear spin textures that can lead to a much faster spin relaxation than Gilbert damping, calculate the dispersion of phonons in the SkX, and discuss effects of impurity pinning of Skyrmions.