Measurement of nonlinear frequency shift coefficient in spin-torque oscillators based on MgO tunnel junctions

The nonlinear frequency shift coefficient, which represents the strength of the transformation of amplitude fluctuations into phase fluctuations of an oscillator, is measured for MgO-based spin-torque oscillators by analyzing the current dependence of the power spectrum. We have observed that linewidth against inverse normalized power plots show linear behavior below and above the oscillation threshold as predicted by the analytical theories for spin-torque oscillators. The magnitude of the coefficient is determined from the ratio of the linear slopes. Small magnitude of the coefficient has been obtained for the device exhibiting narrow linewidth at high bias current.Comment: 4 pages, 5 figures; accepted for publication in Applied Physics Letter

Amplitude-Phase Coupling in a Spin-Torque Nano-Oscillator

The spin-torque nano-oscillator in the presence of thermal fluctuation is described by the normal form of the Hopf bifurcation with an additive white noise. By the application of the reduction method, the amplitude-phase coupling factor, which has a significant effect on the power spectrum of the spin-torque nano-oscillator, is calculated from the Landau-Lifshitz-Gilbert-Slonczewski equation with the nonlinear Gilbert damping. The amplitude-phase coupling factor exhibits a large variation depending on in-plane anisotropy under the practical external fields.Comment: 4 pages, 4 figures, submitted to Journal of Applied Physics via MMM 200