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 puts the extrinsic spin Hall effect and spin swapping on equal footing, we show that the nature of spin-orbit coupled transport dramatically depends on the ratio between the layer thickness d and the mean free path λ. While the spin Hall effect dominates in the diffusive limit (d≫λ), spin swapping dominates in the Knudsen regime (d≲λ). A remarkable consequence is that spin swapping induces a substantial fieldlike torque in the Knudsen regime.