Unified approach to the tunnel magnetoresistance and the non-equilibrium exchange interaction
University of Oxford, Department of Physics,
Theoretical Physics 1 Keble Road, Oxford OX1 3NP, UK
Accepted: 10 February 2000
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 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.
PACS: 75.70.Pa – Giant magnetoresistance / 73.40.Rw – Metal-insulator-metal structures / 75.10.-b – General theory and models of magnetic ordering
© EDP Sciences, 2000