Theoretical investigation of the relationship between spin torque and magnetoresistance in spin-valves and magnetic tunnel junctions

A theoretical study is presented concerning the relationship between spin transfer torque and absolute current-perpendicular-to-plane magnetoresistance in metallic spin-valves (SV) and magnetic tunnel junctions. In a first step, using Valet and Fert Boltzmann-like theory extended to any metallic magnetic multilayers with non-collinear magnetizations, linear relationships between spin torque and absolute current-perpendicular-to-plane giant magnetoresistance are derived numerically, when varying the parameters of the structure one by one. The obtained results are compared with an extension of J.C. Slonczewski's circuit theory. The latter model gives an analytical expression of this linear dependence. In a second step, using an out-of-equilibrium perturbation formalism (Keldysh technique), we study the tunnel magnetoresistance (TMR) dependence of the spin torque amplitude in magnetic tunnel junctions when varying the parameters one by one in the junction. Once again, linear dependences are obtained, with different characteristics when the TMR vanishes. It is shown that these two equivalent behaviours are associated with different origins of the spin torque.