A selfconsistent theory of current-induced switching of magnetization

A selfconsistent theory of the current-induced switching of magnetization using nonequilibrium Keldysh formalism is developed for a junction of two ferromagnets separated by a nonmagnetic spacer. It is shown that the spin-transfer torques responsible for current-induced switching of magnetization can be calculated from first principles in a steady state when the magnetization of the switching magnet is stationary. The spin-transfer torque is expressed in terms of one-electron surface Green functions for the junction cut into two independent parts by a cleavage plane immediately to the left and right of the switching magnet. The surface Green functions are calculated using a tight-binding Hamiltonian with parameters determined from a fit to an {\it ab initio} band structure.This treatment yields the spin transfer torques taking into account rigorously contributions from all the parts of the junction. To calculate the hysteresis loops of resistance versus current, and hence to determine the critical current for switching, the microscopically calculated spin-transfer torques are used as an input into the phenomenological Landau-Lifshitz equation with Gilbert damping. The present calculations for Co/Cu/Co(111) show that the critical current for switching is $\approx 10^7A/cm^2$, which is in good agreement with experiment.