Dynamics of Skyrmion crystals in metallic thin films.

We study the collective dynamics of the Skyrmion crystal in thin films of ferromagnetic metals resulting from the nontrivial Skyrmion topology. It is shown 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 noncollinear spin textures that can lead to a much faster spin relaxation than Gilbert damping, calculate the dispersion of phonons in the Skyrmion crystal, and discuss the effects of impurity pinning of Skyrmions.