Phenomenological theory of current driven exchange switching in   ferromagnetic nanojunctions
  Phenomenological approach is developed in the theory of spin-valve type ferromagnetic junctions to describe exchange switching by current flowing perpendicular to interfaces. Forward and backward current switching effects are described and they may be principally different in nature. Mobile electron spins are considered as being free in all the contacting ferromagnetic layers. Joint action of the following two current effects is investigated: the nonequilibrium longitudinal spin-injection effective field and the transverse spin-transfer surface torque. Dispersion relation for fluctuations is derived and solved for a junction model having spatially localized spin transfer torque: depth of the torque penetration into the free layer is assumed much smaller than the total free layer thickness. Some critical value of the well known Gilbert damping constant is established for the first time. Spin transfer torque dominates in the instability threshold determination for small enough damping constants, while the spin-injection effective field dominates for high damping. Fine interplay between spin transfer torque and spin injection is necessary to provide a hysteretic behavior of the resistance versus current dependence. The state diagram building up shows the possibility of non-stationary (time dependent) nonlinear states arising due to instability development. Calculations lead to the instability rise time values of the order of 0.1 ns. Spin wave resonance frequency spectrum softening occurs under the current growing to the instability threshold. Magnetization fluctuations above the threshold rise oscillating with time for low damping, but rise aperiodically and much more rapid for high damping. 
E. M. Epshtein, Yu. V. Gulyaev, P. E. Zilberman