Quantitative MRFM characterization of the autonomous and forced dynamics in a spin transfer nano-oscillator

Using a magnetic resonance force microscope (MRFM), the power emitted by a spin transfer nano-oscillator consisting of a normally magnetized Py$|$Cu$|$Py circular nanopillar is measured both in the autonomous and forced regimes. From the power behavior in the subcritical region of the autonomous dynamics, one obtains a quantitative measurement of the threshold current and of the noise level. Their field dependence directly yields both the spin torque efficiency acting on the thin layer and the nature of the mode which first auto-oscillates: the lowest energy, spatially most uniform spin-wave mode. From the MRFM behavior in the forced dynamics, it is then demonstrated that in order to phase-lock this auto-oscillating mode, the external source must have the same spatial symmetry as the mode profile, i.e., a uniform microwave field must be used rather than a microwave current flowing through the nanopillar

Robust synchronization in networks of cyclic feedback systems

This paper presents a result on the robust synchronization of outputs of statically interconnected non-identical cyclic feedback systems that are used to model, among other processes, gene expression. The result uses incremental versions of the small gain theorem and dissipativity theory to arrive at an upper bound on the norm of the synchronization error between corresponding states, giving a measure of the degree of convergence of the solutions. This error bound is shown to be a function of the difference between the parameters of the interconnected systems, and disappears in the case where the systems are identical, thus retrieving an earlier synchronization result

Electronic control of the spin-wave damping in a magnetic insulator

It is demonstrated that the decay time of spin-wave modes existing in a magnetic insulator can be reduced or enhanced by injecting an in-plane dc current, $I_\text{dc}$, in an adjacent normal metal with strong spin-orbit interaction. The demonstration rests upon the measurement of the ferromagnetic resonance linewidth as a function of $I_\text{dc}$ in a 5~$\mu$m diameter YIG(20nm){\textbar}Pt(7nm) disk using a magnetic resonance force microscope (MRFM). Complete compensation of the damping of the fundamental mode is obtained for a current density of $\sim 3 \cdot 10^{11}\text{A.m}^{-2}$, in agreement with theoretical predictions. At this critical threshold the MRFM detects a small change of static magnetization, a behavior consistent with the onset of an auto-oscillation regime.Comment: 6 pages 4 figure

Perfect and robust phase-locking of a spin transfer vortex nano-oscillator to an external microwave source

We study the synchronization of the auto-oscillation signal generated by the spin transfer driven dynamics of two coupled vortices in a spin-valve nanopillar to an external source. Phase-locking to the microwave field hrf occurs in a range larger than 10% of the oscillator frequency for drive amplitudes of only a few Oersteds. Using synchronization at the double frequency, the generation linewidth is found to decrease by more than five orders of magnitude in the phase-locked regime (down to 1 Hz, limited by the resolution bandwidth of the spectrum analyzer) in comparison to the free running regime (140 kHz). This perfect phase-locking holds for frequency detuning as large as 2 MHz, which proves its robustness. We also analyze how the free running spectral linewidth impacts the main characteristics of the synchronization regime

Autonomous and forced dynamics in a spin-transfer nano-oscillator: Quantitative magnetic-resonance force microscopy

Using a magnetic-resonance force microscope (MRFM), the power emitted by a spin-transfer nano-oscillator consisting of a normally magnetized Py|Cu|Py circular nanopillar is measured both in the autonomous and forced regimes. From the power behavior in the subcritical region of the autonomous dynamics, one obtains a quantitative measurement of the threshold current and of the noise level. Their field dependence directly yields both the spin torque efficiency acting on the thin layer and the nature of the mode which first auto-oscillates: the lowest energy, spatially most uniform spin-wave mode. From the MRFM behavior in the forced dynamics, it is then demonstrated that in order to phase lock this auto-oscillating mode, the external source must have the same spatial symmetry as the mode profile, i.e., a uniform microwave field must be used rather than a microwave current flowing through the nanopillar. © 2012 American Physical Society

Perfect and robust phase-locking of a spin transfer vortex nano-oscillator to an external microwave source

We study the synchronization of the auto-oscillation signal generated by the spin transfer driven dynamics of two coupled vortices in a spin-valve nanopillar to an external source. Phase-locking to the microwave field h rf occurs in a range larger than 10% of the oscillator frequency for drive amplitudes of only a few Oersteds. Using synchronization at the double frequency, the generation linewidth is found to decrease by more than five orders of magnitude in the phase-locked regime (down to 1 Hz, limited by the resolution bandwidth of the spectrum analyzer) in comparison to the free running regime (140 kHz). This perfect phase-locking holds for frequency detuning as large as 2 MHz, which proves its robustness. We also analyze how the free running spectral linewidth impacts the main characteristics of the synchronization regime. © 2014 AIP Publishing LLC

Improved Spectral Stability in Spin-Transfer Nano-Oscillators: Single Vortex Versus Coupled Vortices Dynamics

© 2015 IEEE. We perform a comparative study of spin-transfer-induced excitation of the gyrotropic motion of a vortex core with either uniform or vortex spin polarizers. The microwave output voltage associated with the vortex dynamics, detected in both cases, displays a strong reduction of phase fluctuations in the case of the vortex polarizer, with a decrease of the peak linewidth by one order of magnitude down to 200 kHz at zero field. A thorough study of radio frequency emission features for the different accessible vortex configurations shows that this improvement is related to the excitation of coupled vortex dynamics by spin-transfer torques

Origin of spectral purity and tuning sensitivity in a spin transfer vortex nano-oscillator

We investigate the microwave characteristics of a spin transfer nano-oscillator (STNO) based on coupled vortices as a function of the perpendicular magnetic field H. Interestingly, we find that our vortex-based oscillator is quasi-isochronous independently of H and for a dc current ranging between 18 and 25 mA. It means that the severe nonlinear broadening usually observed in STNOs can be suppressed on a broad range of bias. Still, the generation linewidth displays strong variations on H (from 40 kHz to 1 MHz), while the frequency tunability in current remains almost constant (7MHz/mA). This demonstrates that isochronicity does not necessarily imply a loss of frequency tunability, which is here governed by the current induced Oersted field. It is not sufficient either to achieve the highest spectral purity in the full range of H. We show that the observed linewidth broadenings are due to the excited mode interacting with a lower energy overdamped mode, which occurs at the successive crossings between harmonics of these two modes. These findings open new possibilities for the design of STNOs and the optimization of their performance. © 2014 American Physical Society

Full control of the spin-wave damping in a magnetic insulator using spin-orbit torque

© 2014 American Physical Society. It is demonstrated that the threshold current for damping compensation can be reached in a 5μm diameter YIG(20nm)|Pt(7nm) disk. The demonstration rests upon the measurement of the ferromagnetic resonance linewidth as a function of Idc using a magnetic resonance force microscope (MRFM). It is shown that the magnetic losses of spin-wave modes existing in the magnetic insulator can be reduced or enhanced by at least a factor of 5 depending on the polarity and intensity of an in-plane dc current Idc flowing through the adjacent normal metal with strong spin-orbit interaction. Complete compensation of the damping of the fundamental mode by spin-orbit torque is reached for a current density of ∼3×1011A·m-2, in agreement with theoretical predictions. At this critical threshold the MRFM detects a small change of static magnetization, a behavior consistent with the onset of an auto-oscillation regime

Efficient Synchronization of Dipolarly Coupled Vortex-Based Spin Transfer Nano-Oscillators

© 2015, Nature Publishing Group. All rights reserved. Due to their nonlinear properties, spin transfer nano-oscillators can easily adapt their frequency to external stimuli. This makes them interesting model systems to study the effects of synchronization and brings some opportunities to improve their microwave characteristics in view of their applications in information and communication technologies and/or to design innovative computing architectures. So far, mutual synchronization of spin transfer nano-oscillators through propagating spinwaves and exchange coupling in a common magnetic layer has been demonstrated. Here we show that the dipolar interaction is also an efficient mechanism to synchronize neighbouring oscillators. We experimentally study a pair of vortex-based spin transfer nano-oscillators, in which mutual synchronization can be achieved despite a significant frequency mismatch between oscillators. Importantly, the coupling efficiency is controlled by the magnetic configuration of the vortices, as confirmed by an analytical model and micromagnetic simulations highlighting the physics at play in the synchronization process