Line shape distortion in a nonlinear auto-oscillator near generation threshold: Application to spin-torque nano-oscillators

The power spectrum of an auto-oscillator with a large frequency nonlinearity in a noisy environment is calculated. The power spectrum becomes strongly non-Lorentzian, broadened, and asymmetric near the generation threshold. A Lorentzian spectrum is recovered far below and far above the threshold, which suggests that line shape distortions provide a signature of the threshold. We show that the developed theory adequately describes the observed behavior of a strongly nonlinear spin-torque nano-oscillator.