A Keldysh-contour effective field theory is derived for magnetic vortices in the presence of current flow. The effect of adiabatic and nonadiabatic spin-transfer torques on vortex motion is highlighted. Similarities to and differences from the superconducting case are presented and are explained. Current flow across a magnetically ordered state is shown to lead to a defect-unbinding phase transition, which is intrinsically nonequilibrium in the sense of not being driven by a variation in effective temperature. The dependence of the density of vortices on the current density is determined.

• Received 7 April 2011

DOI:https://doi.org/10.1103/PhysRevB.84.054458