Spin-wave instabilities in spin-transfer-driven magnetization dynamics

We study the stability of magnetization precessions induced in spin-transfer devices by the injection of spin-polarized electric currents. Instability conditions are derived by introducing a generalized, far-from-equilibrium interpretation of spin-waves. It is shown that instabilities are generated by distinct groups of magnetostatically coupled spin-waves. Stability diagrams are constructed as a function of external magnetic field and injected spin-polarized current. These diagrams show that applying larger fields and currents has a stabilizing effect on magnetization precessions. Analytical results are compared with numerical simulations of spin-transfer-driven magnetization dynamics.Comment: 4 pages, 2 figure

Magnetization dynamics in a three-dimensional interconnected nanowire array

Three-dimensional magnetic nanostructures have recently emerged as artificial magnetic material types with unique properties bearing potential for applications, including magnonic devices. Interconnected magnetic nanowires are a sub-category within this class of materials that is attracting particular interest. We investigate the high-frequency magnetization dynamics in a cubic array of cylindrical magnetic nanowires through micromagnetic simulations based on a frequency-domain formulation of the linearized Landau-Lifshitz-Gilbert equation. The small-angle high-frequency magnetization dynamics excited by an external oscillatory field displays clear resonances at distinct frequencies. These resonances are identified as oscillations connected to specific geometric features and micromagnetic configurations. The geometry- and configuration-dependence of the nanowire array's absorption spectrum demonstrates the potential of such magnetic systems for tuneable and reprogrammable magnonic applications.Comment: 7 pages, 5 figure

Midpoint geometric integrators for inertial magnetization dynamics

We consider the numerical solution of the inertial version of Landau-Lifshitz-Gilbert equation (iLLG), which describes high-frequency nutation on top of magnetization precession due to angular momentum relaxation. The iLLG equation defines a higher-order nonlinear dynamical system with very different nature compared to the classical LLG equation, requiring twice as many degrees of freedom for space-time discretization. It exhibits essential conservation properties, namely magnetization amplitude preservation, magnetization projection conservation, and a balance equation for generalized free energy, leading to a Lyapunov structure (i.e. the free energy is a decreasing function of time) when the external magnetic field is constant in time. We propose two second-order numerical schemes for integrating the iLLG dynamics over time, both based on implicit midpoint rule. The first scheme unconditionally preserves all the conservation properties, making it the preferred choice for simulating inertial magnetization dynamics. However, it implies doubling the number of unknowns, necessitating significant changes in numerical micromagnetic codes and increasing computational costs especially for spatially inhomogeneous dynamics simulations. To address this issue, we present a second time-stepping method that retains the same computational cost as the implicit midpoint rule for classical LLG dynamics while unconditionally preserving magnetization amplitude and projection. Special quasi-Newton techniques are developed for solving the nonlinear system of equations required at each time step due to the implicit nature of both time-steppings. The numerical schemes are validated on analytical solution for macrospin terahertz frequency response and the effectiveness of the second scheme is demonstrated with full micromagnetic simulation of inertial spin waves propagation in a magnetic thin-film.Comment: 19 pages, 4 figure

Efficient adaptive pseudo-symplectic numerical integration techniques for Landau-Lifshitz dynamics

Numerical time integration schemes for Landau-Lifshitz magnetization dynamics are considered. Such dynamics preserves the magnetization amplitude and, in the absence of dissipation, also implies the conservation of the free energy. This property is generally lost when time discretization is performed for the numerical solution. In this work, explicit numerical schemes based on Runge-Kutta methods are introduced. The schemes are termed pseudo-symplectic in that they are accurate to order p, but preserve magnetization amplitude and free energy to order q > p. An effective strategy for adaptive time-stepping control is discussed for schemes of this class. Numerical tests against analytical solutions for the simulation of fast precessional dynamics are performed in order to point out the effectiveness of the proposed methods

Micromagnetic study of inertial spin waves in ferromagnetic nanodots

Here we report the possibility to excite ultra-short spin waves in ferromagnetic thin-films by using time-harmonic electromagnetic fields with terahertz frequency. Such ultra-fast excitation requires to include inertial effects in the description of magnetization dynamics. In this respect, we consider the inertial Landau-Lifshitz-Gilbert (iLLG) equation and develop analytical theory for exchange-dominated inertial spin waves. The theory predicts a finite limit for inertial spin wave propagation velocity, as well as spin wave spatial decay and lifetime as function of material parameters. Then, guided by the theory, we perform numerical micromagnetic simulations that demonstrate the excitation of ultra-short inertial spin waves (20 nm long) propagating at finite speed in a confined magnetic nanodot. The results are in agreement with the theory and provide the order of magnitude of quantities observable in realistic ultra-fast dynamics experiments.Comment: The following article has been accepted by Physical Review B. After it is published, it will be found at https://journals.aps.org/prb/. Revised version, 9 pages, 6 figures. Changes made in v2: added some references, minor edits and correction

Large Scale Finite-Element Simulation of Micromagnetic Thermal Noise

An efficient method for the calculation of ferromagnetic resonant modes of magnetic structures is presented. Finite-element discretization allows flexible geometries and location dependent material parameters. The resonant modes can be used for a semi-analytical calculation of the power spectral density of the thermal white-noise, which is relevant for many sensor applications. The proposed method is validated by comparing the noise spectrum of a nano-disk with time-domain simulations

Analysis in k-space of Magnetization Dynamics Driven by Strong Terahertz Fields

Demagnetization in a thin film due to a terahertz pulse of magnetic field is investigated. Linearized LLG equation in the Fourier space to describe the magnetization dynamics is derived, and spin waves time evolution is studied. Finally, the demagnetization due to spin waves dynamics and recent experimental observations on similar magnetic system are compared. As a result of it, the marginal role of spin waves dynamics in loss of magnetization is established.Comment: 5 pages, 6 figure

Magnetization reversal driven by low dimensional chaos in a nanoscale ferromagnet

Energy-efficient switching of magnetization is a central problem in nonvolatile magnetic storage and magnetic neuromorphic computing. In the past two decades, several efficient methods of magnetic switching were demonstrated including spin torque, magneto-electric, and microwave-assisted switching mechanisms. Here we report the discovery of a new mechanism giving rise to magnetic switching. We experimentally show that low-dimensional magnetic chaos induced by alternating spin torque can strongly increase the rate of thermally-activated magnetic switching in a nanoscale ferromagnet. This mechanism exhibits a well-pronounced threshold character in spin torque amplitude and its efficiency increases with decreasing spin torque frequency. We present analytical and numerical calculations that quantitatively explain these experimental findings and reveal the key role played by low-dimensional magnetic chaos near saddle equilibria in enhancement of the switching rate. Our work unveils an important interplay between chaos and stochasticity in the energy assisted switching of magnetic nanosystems and paves the way towards improved energy efficiency of spin torque memory and logic

Interpretation of spin wave modes in Co/Ag nanodot arrays probed by broadband ferromagnetic resonance

Ferromagnetic resonance (FMR) and the measurement of magnetization dynamics in general have become sophisticated tools for the study of magnetic systems at the nanoscale. Nanosystems, such as the nanodots of this study, are technologically important structures, which find applications in a number of devices, such as magnetic storage and spintronic systems. In this work, we describe the detailed investigation of cobalt nanodots with a 200 nm diameter arranged in a square pitch array with a periodicity of 400 nm. Due to their size, such structures can support standing spin-wave modes, which can have complex spectral responses. To interpret the experimentally measured broadband FMR, we are comparing the spectra of the nanoarray structure with the unpatterned film of identical thickness. This allows us to obtain the general magnetic properties of the system, such as the magnetization, g-factor and magnetic anisotropy. We then use state-of-the-art simulations of the dynamic response to identify the nature of the excitation modes. This allows us to assess the boundary conditions for the system. We then proceed to calculate the spectral response of our system, for which we obtained good agreement. Indeed, our procedure provides a high degree of confidence, since we have interpreted all the experimental data to a good degree of accuracy. In presenting this work, we provide a full description of the theoretical framework and its application to our system, and we also describe in detail the novel simulation method used.Comment: 20 pages, 14 figure

Degenerate and non-degenerate parametric excitation in YIG nanostructures

We study experimentally the processes of parametric excitation in microscopic magnetically saturated disks of nanometer-thick Yttrium Iron Garnet. We show that, depending on the relative orientation between the parametric pumping field and the static magnetization, excitation of either degenerate or non-degenerate magnon pairs is possible. In the latter case, which is particularly important for applications associated with the realization of computation in the reciprocal space, a single-frequency pumping can generate pairs of magnons whose frequencies correspond to different eigenmodes of the disk. We show that, depending on the size of the disk and the modes involved, the frequency difference in a pair can vary in the range 0.1-0.8 GHz. We demonstrate that in this system, one can easily realize a practically important situation where several magnon pairs share the same mode. We also observe the simultaneous generation of up to six different modes using a fixed-frequency monochromatic pumping. Our experimental findings are supported by numerical calculations that allow us to unambiguously identify the excited modes. Our results open new possibilities for the implementation of reciprocal-space computing making use of low damping magnetic insulators.Comment: 18 pages, 4 figure