Bias dependence in spin-polarized tunneling

We discuss the transport of electrons through ferromagnetic tunnel junctions. The spin-up and spin-down chemical potentials are different at the insulator-ferromagnet interfaces by different amounts between the parallel and the antiparallel configuration. As a result, the tunneling probabilities fdr the spin-up and spin-down channels change differently as the external voltages are increased. There is a strong bias dependence of the magnetoresistance ratio, consistent with experimental results.