Rashba torque beyond the Boltzmann regime

Abstract

We study spin torques induced by Rashba spin-orbit coupling in two-dimensional ferromagnets under the good-metal condition ϵFτ/1 (ϵF the Fermi energy, τ the electron lifetime) by employing the Kubo formula. We find that in the presence of spin-dependent disorder the Rashba torque changes greatly as the system evolves out of the weak-disorder limit where /τ is much smaller than any intrinsic energy scale characterizing the multiband structure. The antidamping-like component of Rashba torque can be comparable to and larger than the field-like one out of the weak-disorder limit. The semiclassical Boltzmann theory produces the same results as microscopic linear response calculations only in the weak-disorder limit. Our analysis indicates that rich behaviors of various nonequilibrium phenomena beyond the Boltzmann theory may also be present even when ϵFτ/1 in multiband systems where ϵF is not the unique intrinsic energy scale.