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

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

A strategy for the design of skyrmion racetrack memories

Magnetic storage based on racetrack memory is very promising for the design of ultra-dense, low-cost and low-power storage technology. Information can be coded in a magnetic region between two domain walls or, as predicted recently, in topological magnetic objects known as skyrmions. Here, we show the technological advantages and limitations of using Bloch and Neel skyrmions manipulated by spin current generated within the ferromagnet or via the spin-Hall effect arising from a non-magnetic heavy metal underlayer. We found that the Neel skyrmion moved by the spin-Hall effect is a very promising strategy for technological implementation of the next generation of skyrmion racetrack memories (zero field, high thermal stability, and ultra-dense storage). We employed micromagnetics reinforced with an analytical formulation of skyrmion dynamics that we developed from the Thiele equation. We identified that the excitation, at high currents, of a breathing mode of the skyrmion limits the maximal velocity of the memory

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

Magnetization switching driven by spin-transfer-torque in high-TMR magnetic tunnel junctions

This paper describes a numerical experiment of magnetization switching driven by spin-polarized current in high-TMR magnetic tunnel junctions (TMR>100%). Differently from other works, the current density distribution throughout the cross-sectional area of the free-layer is here computed dinamically, by modeling the ferromagnet/insulator/ferromagnet trilayer as a series of parallel resistances. The validity of the main postulated hypothesis, which states that the current density vector is perpendicular to the sample plane, has been verified by numerically solving the Poisson equation. Our results show that the nonuniform current density distribution is a source of asymmetry for the switching. Furthermore, we found out that the switching processes are characterized by well defined localized pre-switching oscillation modes.Comment: 19 pages and 8 figures, submmitted to JMM

Robust-to-outliers square-root LASSO, simultaneous inference with a MOM approach

We consider the least-squares regression problem with unknown noise variance, where the observed data points are allowed to be corrupted by outliers. Building on the median-of-means (MOM) method introduced by Lecue and Lerasle Ann.Statist.48(2):906-931(April 2020) in the case of known noise variance, we propose a general MOM approach for simultaneous inference of both the regression function and the noise variance, requiring only an upper bound on the noise level. Interestingly, this generalization requires care due to regularity issues that are intrinsic to the underlying convex-concave optimization problem. In the general case where the regression function belongs to a convex class, we show that our simultaneous estimator achieves with high probability the same convergence rates and a similar risk bound as if the noise level was unknown, as well as convergence rates for the estimated noise standard deviation. In the high-dimensional sparse linear setting, our estimator yields a robust analog of the square-root LASSO. Under weak moment conditions, it jointly achieves with high probability the minimax rates of estimation $s^{1/p} \sqrt{(1/n) \log(p/s)}$ for the $\ell_p$-norm of the coefficient vector, and the rate $\sqrt{(s/n) \log(p/s)}$ for the estimation of the noise standard deviation. Here $n$ denotes the sample size, $p$ the dimension and $s$ the sparsity level. We finally propose an extension to the case of unknown sparsity level $s$, providing a jointly adaptive estimator $(\widetilde \beta, \widetilde \sigma, \widetilde s)$. It simultaneously estimates the coefficient vector, the noise level and the sparsity level, with proven bounds on each of these three components that hold with high probability.Comment: 70 page

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