Stochastic theory of spin-transfer oscillator linewidths

We present a stochastic theory of linewidths for magnetization oscillations in spin-valve structures driven by spin-polarized currents. Starting from a nonlinear oscillator model derived from spin-wave theory, we derive Langevin equations for amplitude and phase fluctuations due to the presence of thermal noise. We find that the spectral linewidths are inversely proportional to the spin-wave intensities with a lower bound that is determined purely by modulations in the oscillation frequencies. Reasonable quantitative agreement with recent experimental results from spin-valve nanopillars is demonstrated.