In spin transfer devices a dc electric current is capable of exciting stable precession states of the magnetic moment. These auto-oscillations are powered by the current source and were found to have many remarkable properties, e.g., very narrow line widths, tunability by both bias magnetic field and bias direct current. Precession regimes are thought to be useful for engineering on-chip nano-generators of microwave power. At finite temperatures the auto-oscillations of spin-transfer devices are influenced by the thermal fluctuations. As a result of thermal noise, the line shape with finite width is formed. In many cases devices are additionally subjected to external periodic RF perturbation. Sufficiently strong external signal can lead to the locking of the auto-oscillations to the frequency of the perturbation, tune the oscillations frequency and force the device to amplify the RF signals. A theory of a strongly nonlinear spin-torque auto-oscillator in the presence of external periodic signal and/or thermal noise is developed [1,2,3]. Thermal noise leads to the probabilistic description of the dynamics in terms of a Fokker-Plank equation. It is shown how the nonlinearity of the spin-torque oscillator produces the asymmetry, broadening, and non-Lorentzian shape of the generation line near the auto-oscillation threshold . In addition, the developed analytic model of a nonlinear spin-torque nano-oscillator makes possible the calculation of the generation power in both sub-critical and super-critical regime, and provides a simple method for the experimental determination of the auto-oscillation threshold [5,6].
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 A.N. Slavin and V.S. Tiberkevich, IEEE Trans. Mag. , 45, 1875 (2009).