Spin Swapping Transport and Torques in Ultrathin Magnetic Bilayers

TL;DR

This paper theoretically investigates spin transport in ultrathin magnetic bilayers, revealing how the dominant spin-orbit effects and resulting torques depend on the ratio of layer thickness to mean free path, with implications for spintronic applications.

Contribution

It introduces a comprehensive tight-binding model that treats spin Hall effect, spin swapping, and relaxation equally, showing their dependence on layer thickness and mean free path.

Findings

Spin Hall effect dominates in the diffusive regime ($d\gg\lambda$).

Spin swapping dominates in the Knudsen regime ($d\lesssim\lambda$).

The symmetry of spin-orbit torque varies dramatically between regimes.

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.