Temperature dependence of nonlinear auto-oscillator linewidths: Application to spin-torque nano-oscillators

The temperature dependence of the generation linewidth for an auto-oscillator with a nonlinear frequency shift is calculated. It is shown that the frequency nonlinearity creates a finite correlation time τ=1/Γₚ for the phase fluctuations. In the low-temperature limit in which the spectral linewidth is smaller than Γₚ, the line shape is approximately Lorentzian and the linewidth is linear in temperature. In the opposite high-temperature limit, in which the linewidth is larger than Γₚ, the nonlinearity leads to an apparent ``inhomogeneous broadening'' of the line, which becomes Gaussian in shape and has a square-root dependence on temperature. The results are illustrated for the spin-torque nano-oscillator.