Unified approach to the tunnel magnetoresistance and the non-equilibrium exchange interaction

The tunnel magnetoresistance and its connection to the interlayer exchange interaction is studied in ferromagnet-insulator-ferromagnet junctions. Buil ding on the nonequilibrium Keldysh formalism, we include a contact interact ion between localized spins and conduction electrons and derive an expressi on for the tunnel current that depends on the magnetization of the layers a s (SL SR) in correspondence with the exchange coupling. From this expressio n we also obtain a formula for the tunnel magnetoresistance. At low bias an d for systems where one can neglect size-quantization effects Julliere's fo rmula is rederived. The temperature dependence of the dynamical parameters arises from the system of localized spins, its interaction with the conduct ion electrons, and the thermal reservoirs.