  Recently spin textures called skyrmions have been discovered in certain
chiral magnetic materials without spatial inversion symmetry, and 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. While Skyrmions behave as particles, no particle level
description of their dynamics exists to date. Such a model would have
tremendous impact on understanding skyrmion dynamics by theoretical analysis
and computational modeling. Here we derive the equation of motion 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.
