Spin Hall effect (SHE) refers to the generation of transverse spin current in nonmagnetic solids by an applied electric field due to relativistic spin-orbit coupling. Spin current generation, detection and manipulation are three key elements of the emerging spintronics. Large room temperature SHE not only provides dissipationless spin current but also is used to probe spin current and to drive magneto-electronic devices with little power consumption. Recent intensive research on SHE has also led us to such topical fields as topological insulators and spin caloritronics. In this talk, I will first give an overview on SHE. This will be followed by a presentation of my own theoretical investigations on SHE, including Berry phase theory and ab initio relativistic band structure method [1,2], large intrinsic SHE in metals [2-3] and gigantic SHE due to multi-orbital Kondo effect in gold with iron impurities [4-5].
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