Nonlinear dispersion relation in anharmonic periodic mass-spring and mass-in-mass systems

The study of wave propagation in chains of anharmonic periodic systems is of fundamental importance to understand the response of dynamical absorbers of vibrations and acoustic metamaterials working in nonlinear regime. Here, we derive an analytical nonlinear dispersion relation for periodic chains of anharmonic mass-spring and mass-in-mass systems resulting from considering the hypothesis of weak anharmonic energy and a periodic distribution function as ansatz of a general solution of the nonlinear equations of motion. Numerical simulations show that this expression is valid for anharmonic potential energy up to 50% of the harmonic one. This work provides a simple tool to design and study nonlinear dynamics for a class of seismic metamaterials.Comment: 18 pages, 5 figure

Spin-torque driven magnetic vortex self-oscillations in perpendicular magnetic fields

We have employed complete micromagnetic simulations to analyze dc current driven self-oscillations of a vortex core in a spin-valve nanopillar in a perpendicular field by including the coupled effect of the spin-torque and the magnetostatic field computed self-consistently for the entire spin-valve. The vortex in the thicker nanomagnet moves along a quasi-elliptical trajectory that expands with applied current, resulting in blue-shifting of the frequency, while the magnetization of the thinner nanomagnet is non-uniform due to the bias current. The simulations explain the experimental magnetoresistance-field hysteresis loop and yield good agreement with the measured frequency vs. current behavior of this spin-torque vortex oscillator.Comment: 10 pages, 3 figures, to be appear on AP

Micromagnetic simulations of persistent oscillatory modes excited by spin-polarized current in nanoscale exchange-biased spin valves

We perform 3D micromagnetic simulations of current-driven magnetization dynamics in nanoscale exchange biased spin-valves that take account of (i) back action of spin-transfer torque on the pinned layer, (ii) non-linear damping and (iii) random thermal torques. Our simulations demonstrate that all these factors significantly impact the current-driven dynamics and lead to a better agreement between theoretical predictions and experimental results. In particular, we observe that, at a non-zero temperature and a sub-critical current, the magnetization dynamics exhibits nonstationary behaviour in which two independent persistent oscillatory modes are excited which compete for the angular momentum supplied by spin-polarized current. Our results show that this multi-mode behaviour can be induced by combined action of thermal and spin transfer torques.Comment: 7pages, 2 figures, submitted JAP via MMM 200

Domain wall dynamics driven by a localized injection of a spin-polarized current

This paper introduces an oscillator scheme based on the oscillations of magnetic domain walls due to spin-polarized currents, where the current is injected perpendicular to the sample plane in a localized part of a nanowire. Depending on the geometrical and physical characteristic of the system, we identify two different dynamical regimes (auto-oscillations) when an out-of-plane external field is applied. The first regime is characterized by nucleation of domain walls (DWs) below the current injection site and the propagation of those up to the end of the nanowire, we also found an oscillation frequency larger than 5GHz with a linear dependence on the applied current density. This simple system can be used as a tuneable steady-state domain wall oscillator. In the second dynamical regime, we observe the nucleation of two DWs which propagate back and forth in the nanowire with a sub-GHz oscillation frequency. The micromagnetic spectral mapping technique shows the spatial distribution of the output power is localized symmetrically in the nanowire. We suggest that this configuration can be used as micromagnetic transformer to decouple electrically two different circuits.Comment: 4 pages 3 figure

Time domain study of frequency-power correlation in spin-torque oscillators

This paper describes a numerical experiment, based on full micromagnetic simulations of current-driven magnetization dynamics in nanoscale spin valves, to identify the origins of spectral linewidth broadening in spin torque oscillators. Our numerical results show two qualitatively different regimes of magnetization dynamics at zero temperature: regular (single-mode precessional dynamics) and chaotic. In the regular regime, the dependence of the oscillator integrated power on frequency is linear, and consequently the dynamics is well described by the analytical theory of current-driven magnetization dynamics for moderate amplitudes of oscillations. We observe that for higher oscillator amplitudes, the functional dependence of the oscillator integrated power as a function of frequency is not a single-valued function and can be described numerically via introduction of nonlinear oscillator power. For a range of currents in the regular regime, the oscillator spectral linewidth is a linear function of temperature. In the chaotic regime found at large current values, the linewidth is not described by the analytical theory. In this regime we observe the oscillator linewidth broadening, which originates from sudden jumps of frequency of the oscillator arising from random domain wall nucleation and propagation through the sample. This intermittent behavior is revealed through a wavelet analysis that gives superior description of the frequency jumps compared to several other techniques.Comment: 11 pages, 4 figures to appear in PR

Combined frequency-amplitude nonlinear modulation: theory and applications

In this work we formulate a generalized theoretical model to describe the nonlinear dynamics observed in combined frequency-amplitude modulators whose characteristic parameters exhibit a nonlinear dependence on the input modulating signal. The derived analytical solution may give a satisfactory explanation of recent laboratory observations on magnetic spin-transfer oscillators and fully agrees with results of micromagnetic calculations. Since the theory has been developed independently of the mechanism causing the nonlinearities, it may encompass the description of modulation processes of any physical nature, a promising feature for potential applications in the field of communication systems.Comment: 8 pages, 4 figures, to be published on IEEE Transactions on Magnetic

Micromagnetic understanding of stochastic resonance driven by spin-transfertorque

In this paper, we employ micromagnetic simulations to study non-adiabatic stochastic resonance (NASR) excited by spin-transfer torque in a super-paramagnetic free layer nanomagnet of a nanoscale spin valve. We find that NASR dynamics involves thermally activated transitions among two static states and a single dynamic state of the nanomagnet and can be well understood in the framework of Markov chain rate theory. Our simulations show that a direct voltage generated by the spin valve at the NASR frequency is at least one order of magnitude greater than the dc voltage generated off the NASR frequency. Our computations also reproduce the main experimentally observed features of NASR such as the resonance frequency, the temperature dependence and the current bias dependence of the resonance amplitude. We propose a simple design of a microwave signal detector based on NASR driven by spin transfer torque.Comment: 25 pages 8 figures, accepted for pubblication on Phys. Rev.

Spin-Torque-Induced Rotational Dynamics of a Magnetic Vortex Dipole

We study, both experimentally and by numerical modeling, the magnetic dynamics that can be excited in a magnetic thin-film nanopillar device using the spin torque from a spatially localized current injected via a 10s-of-nm-diameter aperture. The current-driven magnetic dynamics can produce large amplitude microwave emission at zero magnetic field, with a frequency well below that of the uniform ferromagnetic resonance mode. Micromagnetic simulations indicate that the physical origin of this efficient microwave nano-oscillator is the nucleation and subsequent steady-state rotational dynamics of a magnetic vortex dipole driven by the localized spin torque. These results show this novel implementation of a spintronic nano-oscillator is a promising candidate for microwave technology applications.Comment: 19 pages, 4 figures