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We analyze the contribution of the inhomogeneous magnetic field induced by anelectrical current to the spin Hall effect in metals. The Zeeman couplingbetween the field and the electron spin leads to a spin dependent force, and tospin accumulation at the edges. We compare the effect of this relativisticcorrection to the electron dynamics to the features induced by the spin-orbitinteraction. The effect of current induced magnetic fields on the spin Halleffect can be comparable to the extrinsic contribution from the spin-orbitinteraction, although it does not require the presence of heavy elements with astrong spin-orbit interaction. The induced spins are oriented normal to themetal slab.

Spin imbalance of charge carriers induced by an electric current