88 research outputs found
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
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