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

Abstract

PACS. 75.10.-b – General theory and models of magnetic ordering. 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 as 〈SL · SR 〉 in 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. There is much evidence to believe that the interaction between the ferromagnetic layers and the effect of giant magnetoresistance (GMR) are directly related. The simplest model which provides a reasonable approximation for transition metals is to assume that the exchange inter-action between the magnetic d-electrons arises through coupling to the conduction s-electrons which then transmit an effective spin-interaction across the spacer through the Ruderman-