Modelling spin transfer torque and magnetoresistance in magnetic multilayers

Abstract

Theoretical models of spin-dependent transport in magnetic spin-valves and tunnel junctions are presented. A general definition of current-induced spin transfer torque (STT) and interlayer exchange coupling (IEC) based on the spin density continuity principle is given. We then present an extension of the Valet and Fert model, based on the Boltzmann description of spin-dependent transport in metallic structures. This model describes STT and IEC in any kind of magnetic metallic multilayer, for any orientation of the magnetization of the ferromagnetic layers. Simulation results show that spin torque and magnetoresistance originate from the same physical effect. In a second step, we model STT and IEC in magnetic tunnel junctions with an amorphous insulator, using the non-equilibrium Keldysh technique. The general features of STT and IEC are described, showing an important asymmetry in STT bias dependence. Moreover, the influence of a layer of impurities in the barrier is investigated and shows an important enhancement of STT and IEC at resonance. Finally, we apply this model to double magnetic tunnel junctions and show that a dramatic enhancement of spin torque can be obtained when the conditions of resonance in the free layer are fulfilled.