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Spin Hall effect

Spin Hall effects are a collection of relativistic spin-orbit coupling phenomena in which electrical currents can generate transverse spin currents and vice versa. Although first observed only a decade ago, these effects are already ubiquitous within spintronics as standard spin-current generators and detectors. Here we review the experimental and theoretical results that have established this sub-field of spintronics. We focus on the results that have converged to give us a clear understanding of the phenomena and how they have evolved from a qualitative to a more quantitative measurement of spin-currents and their associated spin-accumulation. Within the experimental framework, we review optical, transport, and magnetization-dynamics based measurements and link them to both phenomenological and microscopic theories of the effect. Within the theoretical framework, we review the basic mechanisms in both the extrinsic and intrinsic regime which are linked to the mechanisms present in their closely related phenomenon in ferromagnets, the anomalous Hall effect. We also review the connection to the phenomenological treatment based on spin-diffusion equations applicable to certain regim