Abstract
The correlation of phase fluctuations in any type of oscillator fundamentally defines its spectral shape. However, in nonlinear oscillators, such as spin torque nano-oscillators, the frequency spectrum can become particularly complex. This is specifically true when not only considering thermal but also colored 1/f flicker noise processes, which are crucial in the context of the oscillator’s long term stability. In this study, we address the frequency spectrum of spin torque oscillators in the regime of large-amplitude steady oscillations experimentally and as well theoretically. We particularly take both thermal and flicker noise into account. We perform a series of measurements of the phase noise and the spectrum on spin torque vortex oscillators, notably varying the measurement time duration. Furthermore, we develop the modelling of thermal and flicker noise in Thiele equation based simulations. We also derive the complete phase variance in the framework of the nonlinear auto-oscillator theory and deduce the actual frequency spectrum. We investigate its dependence on the measurement time duration and compare with the experimental results. Long term stability is important in several of the recent applicative developments of spin torque oscillators. This study brings some insights on how to better address this issue.
Highlights
The correlation of phase fluctuations in any type of oscillator fundamentally defines its spectral shape
This type of STNOs exploits the gyrotropic motion of a magnetic vortex in a circular shaped nanodisk and converts its dynamics, which is sustained by spin transfer torque, into an electric rf signal due to the magnetoresistive effect[42]
In order to analyze these results, we perform simulations of the oscillator’s noise properties by including the thermal contribution and as well, more originally, the flicker noise processes existing in the vortex dynamics in STVOs
Summary
The correlation of phase fluctuations in any type of oscillator fundamentally defines its spectral shape. We have shown in a phenomenological model how the existence of both thermal noise and flicker noise is affecting the noise properties (phase and amplitude power spectral densities, PSDs) in the low offset frequency regime, and notably how the oscillator’s nonlinearities play an important r ole[30]. We demonstrate how the spectral shape changes from a Lorentz shape at short measurement durations associated to white noise correlation, to a Voigt—or even Gaussian—shape at longer durations with colored 1/f correlation, as reported but not yet fully understood in Ref.[40] In complement to these experimental results, we develop a simulation scheme including both a basic flicker noise process and thermal fluctuations. We present a theoretical model (see “Theoretical model” section) in which the variance functions of the phase fluctuations are derived allowing to predict the shape of the frequency spectrum of STVOs in particular, but generalizable to all types of S TNOs1,32,41
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