Spin Orbit Torques in Disordered Multiband Electron Systems: Boltzmann Regime and Beyond

We study spin-orbit torques (SOT) in nondegenerate multiband electron systems. In the weak-disorder limit, a semiclassical Boltzmann approach equivalent to the microscopic Kohn-Luttinger linear-response approach is formulated. This semiclassical framework accounts for the interband-coherence effects induced by both the electric field and static impurity scattering, as well as the recently highlighted coherent skew scatterig. Using the two-dimensional Rashba ferromagnet as a model system, we show that the antidamping-like SOT arising from disorder-induced interband-coherence effects is very sensitive to the structure of disorder potential in the internal space. On the other hand, we show that the Boltzmann theory produces the same results as Kubo diagrammatic 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 within the good metal limit in multiband systems where the Fermi energy is not the unique intrinsic energy scale.