A Keldysh-contour effective field theory is derived for magnetic vortices in the presence of current flow. The effect of adiabatic and non-adiabatic spin transfer torques on vortex motion is highlighted. Similarities to and differences from the superconducting case are presented and 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.
@article{arxiv.1104.1345,
title = {Current driven defect unbinding transition in an XY ferromagnet},
author = {Aditi Mitra and Andrew J. Millis},
journal= {arXiv preprint arXiv:1104.1345},
year = {2015}
}