Spin Swapping Transport and Torques in Ultrathin Magnetic Bilayers

Abstract

Planar spin transport in disordered ultrathin magnetic bilayers comprising a ferromagnet and a normal metal (typically used for spin pumping, spin Seebeck and spin-orbit torque experiments) is investigated theoretically. Using a tight-binding model that treats extrinsic spin Hall effect, spin swapping and spin relaxation on equal footing, we show that the nature of spin-orbit coupled transport dramatically depends on ratio between the layers thickness $d$ and the mean free path $\lambda$. While spin Hall effect dominates in the diffusive limit ($d\gg\lambda$), spin swapping dominates in Knudsen regime ($d\lesssim\lambda$). A remarkable consequence is that the symmetry of the spin-orbit torque exerted on the ferromagnet is entirely different in these two regimes.