  The spin-orbit interaction is frequently the mechanism by which spin and
charge are coupled for spintronic applications. The discovery of spin, a
century ago, relied on spin-charge coupling by a magnetic field gradient; this
mechanism has received scant attention as a means for generating spin and
charge currents in semiconductors. Through the derivation of a set of coupled
spin-charge drift-diffusion equations, our work shows that magnetic field
gradients can be used to generate charge currents from non-equilibrium spin
polarization, 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 magnetic
gradient. This is understood by invoking the idea of co-current and
counter-current exchange which is a concept frequently invoked in fields as
disparate as animal physiology and thermal engineering.
