Spin Swapping Transport and Torques in Ultrathin Magnetic Bilayers

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 $λ$. While spin Hall effect dominates in the diffusive limit ($d\ggλ$), spin swapping dominates in Knudsen regime ($d\lesssimλ$). A remarkable consequence is that the symmetry of the spin-orbit torque exerted on the ferromagnet is entirely different in these two regimes.

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