Tunneling through a spin-polarizing barrier: Boltzmann-equation study

We investigate the nonequilibrium distribution functions for electrons in the electrodes of a metal-insulator-metal junction where the insulator is a ferromagnet with its domains aligned parallel to the interfaces. In this geometry, the tunneling barrier for spin-up electrons differs from that for spin-down electrons, so that the two spins tunnel at different rates. If the junction is biased so that the Fermi levels on the right and left are shifted to (μ+eV/2) and (μ-eV/2), respectively, we find that the electrons are spin polarized in the steady state. Electrons in the right electrode are polarized in the direction opposite those on the left. The spin polarization increases with voltage and tunneling conductance and decreases as the spin relaxation time falls.