Current-Induced Dynamics in a Skyrmion Lattice

We study the Thiele equation for the motion of skyrmions in a lattice under a spin current of electrons. We show that a threshold current for conduction electrons exists below which skyrmions are blocked. By mimicking a pinning center with a localized attractive potential, we study the effects of the Magnus force and the damping force and find that skyrmions cannot be pinned by a single pinning center. Pinning can be achieved with two attractive potentials. We study the effects of a mass term which can lead to cyclotron motion and estimate the cyclotron frequency.