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

Oscillatory transient regime in the forced dynamics of a spin torque nano-oscillator

We demonstrate that the transient non-autonomous dynamics of a spin torque nano-oscillator (STNO) under a radio-frequency (rf) driving signal is qualitatively different from the dynamics described by the Adler model. If the external rf current $I_{rf}$ is larger than a certain critical value $I_{cr}$ (determined by the STNO bias current and damping) strong oscillations of the STNO power and phase develop in the transient regime. The frequency of these oscillations increases with $I_{rf}$ as $\propto\sqrt{I_{rf} - I_{cr}}$ and can reach several GHz, whereas the damping rate of the oscillations is almost independent of $I_{rf}$. This oscillatory transient dynamics is caused by the strong STNO nonlinearity and should be taken into account in most STNO rf applications.Comment: 4 page, 3 figure