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Register a new userLow offset frequency $1/f$ flicker noise in spin torque vortex oscillators
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Low frequency noise close to the carrier remains little explored in spin torque nano oscillators. However, it is crucial to investigate as it limits the oscillators frequency stability. This work addresses the low offset frequency flicker noise of a TMR-based spin-torque vortex oscillator in the regime of large amplitude steady oscillations. We first phenomenologically expand the nonlinear auto-oscillator theory aiming to reveal the properties of this noise. We then present a thorough experimental study of the oscillators $1/f$ flicker noise and discuss the results based on the theoretical predictions. Hereby, we connect the oscillators nonlinear dynamics with the concept of flicker noise and furthermore refer to the influence of a standard $1/f$ noise description based on the Hooge formula, taking into account the non-constant magnetic oscillation volume, which contributes to the magnetoresistance.
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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 oscillators 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.
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