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 ${\epsilon }_F\tau /\hslash \gg 1$ (${\epsilon }_F$ the Fermi energy, $\tau$ 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 $\hslash /\tau$ 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 ${\epsilon }_F\tau /\hslash \gg 1$ in multiband systems where ${\epsilon }_F$ is not the unique intrinsic energy scale.

6 pages, 2 figures

References in corpus (11)

• Intrinsic vs. extrinsic anomalous Hall effect in ferromagnets
• Quantum transport theory of anomalous electric, thermoelectric, and thermal Hall effects in ferromagnets
• Semiclassical theories of the anomalous Hall effect
• Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach
• Spin-Hall effect in a disordered 2D electron-system
• Charge and spin Hall conductivity in metallic graphene
• Intraband and interband spin-orbit torques in non-centrosymmetric ferromagnets
• Anomalous Hall effect in a two-dimensional electron gas
• Angular dependence of spin-orbit spin transfer torques
• Anomalous Hall Effect in Disordered Multiband Metals
• Spin-Orbit Torques in Two-Dimensional Rashba Ferromagnets