Engineering Theory of Spin-Torque Microwave Oscillators
Thu, Jul. 05th 2007, 11:00
Bât. 1005 P.434D, CEA-Grenoble
It has been shown recently that a spin-polarized current passing through a thin magnetic layer creates effective negative magnetic damping in this layer and could excite microwave oscillations or/and waves in this layer. This spin-torque effect opens a possibility of creating a novel type of microwave oscillators, which can be tuned by both the external magnetic field and bias current, have nano-scale dimensions, and can be fabricated using modern planar technologies. Using the classical spin wave Hamiltonian formalism, we developed a simple engineering theory of spin-torque nano-oscillators driven by spin-polarized current. In our approach the dynamics of the spin-torque oscillator is described by one complex variable, which represents both amplitude and phase of the excited spin wave mode. All the parameters of the reduced equation for the spin wave amplitude (e.g., spin wave frequency, natural positive damping, effective current-induced negative damping, and thermally-induced random noise) have clear physical meaning and can be easily derived from the Landau-Lifshits equation of magnetization dynamics. The theory gives simple and quantitatively correct explanation of the recent experimental data on the spin wave excitation by direct current, predicting dependencies of the threshold currents, generated frequencies, etc. on the system parameters (magnitude and direction of the bias magnetic field, etc.). Using the above described nonlinear oscillator formalism we took into account the influence of the thermal noise on the characteristics of a spin-torque oscillator. In particular, we obtained theoretical expression for the linewidth of the generated microwave signal at a finite temperature. This expression predicts a critical reduction of the linewidth for the magnetization angle at which the nonlinear frequency shift vanishes, and explains a well-known experimental fact that the generation linewidth in a nano-contact geometry is much smaller than in the geometry of a nano-pillar with a well-defined lateral size. Based on our spin-wave approach, we have also developed a theory of phase-locking of spin-torque oscillator to an external microwave signal and the theory of mutual phase-locking in a system of weakly interacting oscillators. The obtained analytical expression for the frequency band of the mutual phase-locking of two oscillators shows good agreement with recent experimental data and proves that the main interaction mechanism leading to the phase-locking of two generating nano-contacts is the coupling through propagating spin waves.


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