Recently spin textures called skyrmions have been discovered in certain chiral magnetic materials without spatial inversion symmetry, and they have attracted enormous attention due to their promising application in spintronics since only a low applied current is necessary to drive their motion. When a conduction electron moves around the skyrmion, its spin is fully polarized by the spin texture and acquires a quantized phase; thus, the skyrmion yields an emergent electrodynamics that in turn determines skyrmion motion and gives rise to a finite Hall angle. As topological excitations, skyrmions behave as particles. In this paper we derive the equation of motion for skyrmions as rigid point particles from a microscopic continuum model and obtain the short-range interaction between skyrmions and the interaction between skyrmions and defects. Skyrmions also experience a Magnus force perpendicular to their velocity due to the underlying emergent electromagnetic field. We validate the equation of motion by studying the depinning transition using both the particle and the continuum models. By using the particle description, we explain the recent experimental observations of the rotation of a skyrmion lattice in the presence of a temperature gradient. We also predict quantum and thermal creep motion of skyrmions in the pinning potential.

• Received 22 April 2013

DOI:https://doi.org/10.1103/PhysRevB.87.214419