Macrospin models of spin transfer dynamics

The current-induced magnetization dynamics of a spin valve are studied using a macrospin (single-domain) approximation and numerical solutions of a generalized Landau-Lifshitz-Gilbert equation. For the purpose of quantitative comparison to experiment [S. I. Kiselev, J. C. Sankey, I. N. Krivortov, N. C. Emley, R. J. Schoelkopf, R. A. Buhrman, and D. C. Ralph, Nature 425, 380 (2003)], we calculate the resistance and microwave power as a function of current and external field, including the effects of anisotropies, damping, spin-transfer torque, thermal fluctuations, spin-pumping, and incomplete absorption of transverse spin current. Although many features of experiment appear in the simulations, there are two significant discrepancies: the current dependence of the precession frequency and the presence and/or absence of a microwave quiet magnetic phase with a distinct magnetoresistance signature. Comparison is made to micromagnetic simulations designed to model the same experiment.