Microscopic Keldysh Theory of Vortex Transport in the XY Magnet

Motivated by recent attention given to vortex-mediated spin transport, we examine vortex dynamics in a 2D easy-plane magnetic insulator coupled to an external metallic bath with an applied current. We construct a Keldysh path integral for the dual electrodynamic theory in which vortices and their currents act as charge and current sources. With the metallic current functioning as an effective temperature, we discuss the Berezinskii–Kosterlitz-Thouless transition for this driven-dissipative system. A coarse-grained Keldysh theory of vortices is then used to microscopically derive the drift-diffusion dynamics governing the motion of these topological excitations in the magnetic bulk. The metallic current gives rise to a viscous drag term in the vortex drift-diffusion equation whose magnitude and direction can be controlled by the current. A spintronics experiment to test our predictions is also discussed.