Generalized magnetoelectronic circuit theory and spin memory loss

Spin transport at metallic interfaces is an essential ingredient of various spintronic device concepts, such as giant magnetoresistance, spin-transfer torque, spin-orbit torque, spin Hall magnetoresistance, and spin pumping. Spin-orbit coupling plays an important role in many such devices. In particular, spin current is partially absorbed at the interface due to spin-orbit coupling. Here, we develop a general magnetoelectronic circuit theory and generalize the concept of spin mixing conductance accounting for various mechanisms responsible for spin-flip scattering . For the case when exchange interactions dominate, we give a simple expressions for the spin mixing conductance in terms of contributions responsible for spin memory loss, spin torque, and spin precession, where all contributions are amenable to ab initio treatment. We observe that in general there is no straightforward relation between the spin torque part and the spin memory loss part, where the latter is often expressed in terms of the spin loss parameter, δ.