Influence of flicker noise and nonlinearity on the frequency spectrum of spin torque nano-oscillators

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.

Beyond the gyrotropic motion: dynamic C-state in vortex spin torque oscillators

“…Importantly, the emission power is much higher than for the G-state oscillation (factor 3-4 in the presented measurement) and does furthermore not systematically change with the applied dc current. Note that however, the power is subject to rather large fluctuations at constant linewidth, potentially caused by an enhanced flicker noise in this regime 27,28 . For very high current values above 17 mA, the linewidth increases again.…”

Stabilization of phase noise in spin torque nano oscillators by a phase locked loop

“…The corresponding phase noise (fig. 4b) of the free running state has the typical 1/f 2 noise dependence 22,23,42 in the full offset-frequency range, while the phase noise upon PLL operation is constant within a given bandwidth ∆ω BW and hence is efficiently reduced by more than 50 dB at a 10 kHz offset from the carrier frequency.…”

“…( 7)) it is: ψ = v e and the diffusion describes a Gaussian noise process with variance ∆ψ 2 = ψ 2 − ψ 2 = 2D e t, i.e. a 1/f 2 phase noise PSD characteristics 23 . If phase slips occur, the STNO is never perfectly locked in terms of a noise plateau at low offset frequencies.…”

“…This specifically allows tuning of the STNO frequency via the dc current. However, the STNO's nanoscale size and nonlinearity come at the cost of a relatively poor phase noise performance, identified as the major drawback in order to exploit STNOs in real practical applications 22,23 , especially in the field of rf communications. In order to substantially improve the phase and frequency stability, a standard means is the integration of the oscillator into a phase locked loop (PLL) system, which on a circuit level continuously corrects the oscillator's phase fluctuations through comparison with an external reference.…”

Flicker and random telegraph noise between gyrotropic and dynamic C-state of a vortex based spin torque nano oscillator

“…of Maryland, College Park, 20899-6202, MD, USA c) Present address: GFMC, Departamento de Física de Materiales, Universidad Complutense de Madrid, 28040 Madrid, Spain d) vincent.cros@cnrs-thales.fr is necessary to be reduced and better understood. Flicker noise, that is dominant at longer timescales of sought stability, has been studied and classified mainly in the gyrotropic regime 17,18 of a STVO. We recently found in particular a dependence of the noise level on the active magnetic volume V of the oscillation, along with the nonlinear dynamical parameters 17 , and predict a Hooge-like increase 19 with I 2 dc when the volume V is constant.…”