Dynamics of skyrmions in chiral magnetic insulators

We study the quantum propagation of a skyrmion in chiral magnetic insulators by generalizing the micromagnetic equations of motion to a finite-temperature path integral formalism. The fluctuations around the skyrmionic configuration give rise to a time-dependent damping of the skyrmion motion, which in some limit reduces to a skyrmion mass. We demonstrate that a skyrmion in a confined geometry provided by a magnetic trap behaves as a massive particle owing to its quasi-one-dimensional confinement. An additional quantum mass term is predicted, independent of the effective spin, with an explicit temperature dependence which remains finite even at zero temperature. Moreover, we study the dynamics of a skyrmion in a magnetic insulating nanowire in the presence of time-dependent oscillating magnetic field gradients. These ac fields act as a net driving force on the skyrmion via its own intrinsic magnetic excitations. We include the unavoidable coupling of the external field to the magnons, which gives rise to time-dependent dissipation for the skyrmion. The ac driving of the magnon bath at resonance results in a unidirectional helical propagation of the skyrmion in addition to the otherwise periodic bounded motion.