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

TL;DR

This paper investigates how temperature affects the linewidth of nonlinear auto-oscillators, especially spin-torque nano-oscillators, revealing different behaviors in low and high-temperature regimes due to frequency nonlinearity.

Contribution

It provides a theoretical framework for understanding temperature-dependent linewidth broadening in nonlinear auto-oscillators, with specific application to spin-torque nano-oscillators.

Findings

Linewidth is linear in temperature at low temperatures.

Linewidth exhibits a square-root dependence on temperature at high temperatures.

Line shape transitions from Lorentzian to Gaussian with increasing temperature.

Abstract

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, tau, for the phase fluctuations. In the low-temperature limit in which the spectral linewidth is smaller than 1/tau, 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 1/tau, 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.