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

Abstract

The tunnel magnetoresistance and its connection to the interlayer exchange interaction is studied in ferromagnet-insulator-ferromagnet junctions. Building on the non- equilibrium Keldysh formalism, we include a contact interaction between localized spins and conduction electrons and derive an expression for the tunnel current that depends on the magnetization of the layers asSL · SRin correspondence with the exchange coupling. From this expression we also obtain a formula for the tunnel magnetoresistance. At low bias and for systems where one can neglect size-quantization effects Julliere's formula is rederived. The temperature dependence of the dynamical parameters arises from the system of localized spins, its interaction with the conduction electrons, and the thermal reservoirs.