Current-driven quantum criticality in itinerant electron ferromagnets

We determine the effect of an in-plane current flow on the critical properties of a two-dimensional itinerant electron system near a ferromagnetic-paramagnetic quantum critical point. We study a model in which a nonequilibrium steady state is established as a result of exchange of particles and energy with an underlying substrate. The current j gives rise not only to an effective temperature equal to the voltage drop over a distance of order the mean free path, but also to symmetry-breaking terms of the form in the effective action. The effect of the symmetry breaking on the fluctuational and critical properties is found to be small, although (in agreement with previous results) if rotational degrees of freedom are important, the current can make the classically ordered state dynamically unstable.