Quantum Brownian motion of a magnetic skyrmion

Within a microscopic theory, we study the quantum Brownian motion of a skyrmion in a magnetic insulator coupled to a bath of magnonlike quantum excitations. The intrinsic skyrmion-bath coupling gives rise to an effective mass for the skyrmion, which remains finite down to zero temperature due to the quantum nature of the magnon bath. We show that the quantum version of the fluctuation-dissipation theorem acquires a nontrivial temperature dependence. As a consequence, the skyrmion mean-square displacement is finite at zero temperature and has a fast thermal activation that scales quadratically with temperature, contrary to the linear increase predicted by the classical phenomenological theory. The effects of an external oscillating drive which couples directly to the magnon bath are investigated. We generalize the standard quantum theory of dissipation and we show that the external drive generates a time-periodic term linear in the skyrmion velocity, and a time-periodic magnus force correction, which are both absent in the static limit. The skyrmion response function inherits the time periodicity of the driving field and is thus enhanced and lowered over a driving cycle. Finally, we provide a generalized version of the nonequilibrium fluctuation-dissipation theorem valid for weakly driven baths.