Spin diffusion in CPP spin valves

We present in this paper an analytic model to describe the effect of spin diffusion in CPP (current perpendicular to the plan) spin valves. Two ferromagnetic electrodes are separated by a nonmagnetic metal, organic or inorganic semiconducting spacer. We base our calculations on the evolution of the spin polarized density of states of the saturated ferromagnetic electrodes under an applied rotating magnetic field and the spin diffusion in the spacer. Without treating the mechanism of spin relaxation and dephasing in the spacer, we establish a general model with the cosine evolution of the magnetoresistance modulated by the effect of spin diffusion. Throughout our treatment we consider a tunnel junction at the interface between each ferromagnetic electrode and the spacer.