Current-induced motion in a skyrmion lattice

Abstract

For a skyrmion lattice phase of chiral magnets, we compare predictions of the Landau-Lifshitz-Gilbert (LLG) and Thiele equations for the current-induced drift velocity for a given constant spin velocity. Instead of integrating the equations over a unit cell, we only perform an angle average, while retaining information on the radial dependence of velocity within the skyrmion. Since the skyrmion-lattice dynamics draws from magnetostatic, chiral, and exchange forces, we find that different scales are involved for the m =-1 and m =-2 skyrmions, a fact that might be useful in "tuning" scales of the drift velocity. We note that the Thiele equation yields less information than the LLG equation and explain why the translation mode has not yet been observed.