Macroscopic description of current induced switching due to spin-transfer

摘要

We develop a macroscopic description of the current-induced torque due tospin transfer in a layered system consisting of two ferromagnetic layersseparated by a nonmagnetic layer. The description is based on i) the classicalspin diffusion equations for the distribution functions used in the theory ofCPP-GMR, ii) the relevant boundary conditions for the longitudinal andtransverse components of the spin current in the situation of quasi-interfacialabsorption of the transverse components in a magnetic layer. The torque isexpressed as a function of the usual parameters derived from CPP-GMRexperiments and two additional parameters involved in the transverse boundaryconditions. Our model is used to describe qualitatively normal and inverseswitching phenomena studied in recent experiments. We also present a structurefor which we predict only states of steady precession above a certain criticalcurrent. We finally discuss the limits of a small angle between magneticmoments of the ferromagnetic layers and of vanishing imaginary part of themixing conductance.