Spin-polarized tunnel current in magnetic-layer systems and its relation to the interlayer exchange interaction

The spin-polarized tunnel current and its connection to the interlayer exchange interaction is studied in ferromagnet-insulator-ferromagnet thin-film planar junctions out of equilibrium. Building on the nonequilibrium Keldysh formalism, it is possible to systematically include a contact interaction between localized spins and conduction electrons and extend previous treatments on spin currents and exchange interaction. In particular, a Landauer-type formula is derived for the spin current that explains the result found earlier [Schwabe, Wingreen, and Elliott, Phys. Rev. B 54, 12 953 (1996)] that the exchange interaction between the ferromagnetic slabs increases in proportion to the slab width. Furthermore, switching is shown to occur between parallel and antiparallel coupling of the slabs for different applied biases under feasible experimental conditions.