  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.
