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The spin-orbit interaction is frequently the mechanism by which spin andcharge are coupled for spintronic applications. The discovery of spin, acentury ago, relied on spin-charge coupling by a magnetic field gradient; thismechanism has received scant attention as a means for generating spin andcharge currents in semiconductors. Through the derivation of a set of coupledspin-charge drift-diffusion equations, our work shows that magnetic fieldgradients can be used to generate charge currents from non-equilibrium spinpolarization, in solid state systems. We predict, in GaAs, an ``Stern-Gerlach"voltage comparable to what is measured by the inverse spin Hall effect.Non-intuitively, we find the spin diffusion length is reduced by the magneticgradient. This is understood by invoking the idea of co-current andcounter-current exchange which is a concept frequently invoked in fields asdisparate as animal physiology and thermal engineering.

Generation of charge current by the Inverse Stern-Gerlach Effect and the  suppression of spin transport due to spin counter-current exchange in  semiconductors