Analysis of thermally induced magnetization dynamics in spin-transfer nano-oscillators

The thermally induced magnetization dynamics in the presence of spin-polarized currents injected into a spin-valve-like structure used as microwave spin-transfer nano-oscillator (STNO) is considered. Magnetization dynamics is described by the stochastic Landau-Lifshitz-Slonczewski (LLS) equation. First, it is shown that, in the presence of thermal fluctuations, the spectrum of the output signal of the STNO exhibits multiple peaks at low and high frequencies. This circumstance is associated with the occurrence of thermally induced transitions between stationary states and magnetization self-oscillations. Then, a theoretical approach based on the separation of time-scales is developed to obtain a stochastic dynamics only in the slow state variable, namely the energy. The stationary distribution of the energy and the aforementioned transition rates are analytically computed and compared with the results of direct integration of the LLS dynamics, showing very good agreement.