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We theoretically study the crossover between spin Hall effect and spinswapping, a recently predicted phenomenon that consists in the interchangebetween the current flow and its spin polarization directions [Lifshits andDyakonov, Phys. Rev. Lett. 103, 186601 (2009)]. Using a tight-binding modelwith spin-orbit coupled disorder, spin Hall effect, spin relaxation and spinswapping are treated on equal footing. We demonstrate that spin Hall effect andspin swapping present very different dependences as a function of thespin-orbit coupling and disorder strengths. As a consequence, we show that spinswapping may even exceed spin Hall effect. Three set-ups are proposed for theexperimental observation of the spin swapping effect in metals.

Crossover between spin swapping and Hall effect in metallic systems