Coulomb drag, magnetoresistance, and spin-current injection in magnetic multilayers

We study the effect of spin Coulomb drag on the magnetoresistance and the spin-current injection efficiency of a layered structure consisting of a nonmagnetic semiconductor sandwiched between two ferromagnetic electrodes of spin polarization p. The calculations are done within the framework of the drift-diffusion theory, which we generalize to include the spin trans-conductivity σ_↑↓. We find that for p close to 100% the spin drag enhances the magnetoresistance, while for smaller values of p it reduces it. A new approach to the measurement of σ_↑↓ is suggested.