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Analytical theory of a noisy nonlinear auto-oscillator : Spin-torque magnetic nano-oscillator

Vasil Tiberkevich - Department of Physics, Oakland University, Rochester, MI 48309, USA


Recently, it was shown that direct current, passing through a nano-sized magnetic multilayered structure, can lead to a self-sustained microwave magnetization precession in one of the magnetic layers. This spin-torque effect opens a possibility of creating a novel type of microwave oscillators for future nano-electronics. Due to extremely small sizes of spin-torque nano-oscillators (STNO), the thermal fluctuations become very important (the characteristic thermal energy kBT is comparable with the energy of self-sustained auto-oscillations). The second distinctive feature of STNOs is the strong nonlinear dependence of the oscillation frequency on the oscillation power. Thus, the correct description of STNO requires development of a theory of noisy nonlinear auto-oscillators.

Based on the classical spin wave Hamiltonian formalism, we derived Fokker-Planck equation that describes statistical properties of STNO, as well as any other auto-oscillating system with one degree of freedom. We obtained an analytical expression for the power, generated by an oscillator, which is valid in the whole range of parameters – from the thermal equilibrium state to the strongly supercritical regime. We derived analytical expressions for the generation linewidth and showed that the dependence of the oscillator frequency on its power leads to a significant linewidth broadening. Our theory explains a number of distinctive qualitative features of STNOs and gives a good quantitative description of recent experimental data.