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Spin imbalance of charge carriers induced by an electric current
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We analyze the contribution of the inhomogeneous magnetic field induced by an electrical current to the spin Hall effect in metals. The Zeeman coupling between the field and the electron spin leads to a spin dependent force, and to spin accumulation at the edges. We compare the effect of this relativistic correction to the electron dynamics to the features induced by the spin-orbit interaction. The effect of current induced magnetic fields on the spin Hall effect can be comparable to the extrinsic contribution from the spin-orbit interaction, although it does not require the presence of heavy elements with a strong spin-orbit interaction. The induced spins are oriented normal to the metal slab.
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Direct and inverse spin Hall effect: Lorentz force and Zeeman energy
This paper derives the direct and inverse spin Hall effects from the Lorentz force and the Zeeman force on electron spins, without invoking quantum spin-orbit scattering.
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