64 research outputs found
Topologically non-trivial magnon bands in artificial square spin ices subject to Dzyaloshinskii-Moriya interaction
Systems that exhibit topologically protected edge states are interesting both
from a fundamental point of view as well as for potential applications, the
latter because of the absence of back-scattering and robustness to
perturbations. It is desirable to be able to control and manipulate such edge
states. Here, we show that artificial square ices can incorporate both
features: an interfacial Dzyaloshinksii-Moriya gives rise to topologically
non-trivial magnon bands, and the equilibrium state of the spin ice is
reconfigurable with different configurations having different magnon
dispersions and topology. The topology is found to develop as odd-symmetry bulk
and edge magnon bands approach each other, so that constructive band inversion
occurs in reciprocal space. Our results show that topologically protected bands
are supported in square spin ices.Comment: 27 pages, 6 figure
Vortex-antivortex proliferation from an obstacle in thin film ferromagnets
Magnetization dynamics in thin film ferromagnets can be studied using a
dispersive hydrodynamic formulation. The equations describing the
magnetodynamics map to a compressible fluid with broken Galilean invariance
parametrized by the longitudinal spin density and a magnetic analog of the
fluid velocity that define spin-density waves. A direct consequence of these
equations is the determination of a magnetic Mach number. Micromagnetic
simulations reveal nucleation of nonlinear structures from an impenetrable
object realized by an applied magnetic field spot or a defect. In this work,
micromagnetic simulations demonstrate vortex-antivortex pair nucleation from an
obstacle. Their interaction establishes either ordered or irregular
vortex-antivortex complexes. Furthermore, when the magnetic Mach number exceeds
unity (supersonic flow), a Mach cone and periodic wavefronts are observed,
which can be well-described by solutions of the steady, linearized equations.
These results are reminiscent of theoretical and experimental observations in
Bose-Einstein condensates, and further supports the analogy between the
magnetodynamics of a thin film ferromagnet and compressible fluids. The
nucleation of nonlinear structures and vortex-antivortex complexes using this
approach enables the study of their interactions and effects on the stability
of spin-density waves.Comment: 23 pages, 7 figure
Symmetry-broken dissipative exchange flows in thin-film ferromagnets with in-plane anisotropy
Planar ferromagnetic channels have been shown to theoretically support a
long-range ordered and coherently precessing state where the balance between
local spin injection at one edge and damping along the channel establishes a
dissipative exchange flow, sometimes referred to as a spin superfluid. However,
realistic materials exhibit in-plane anisotropy, which breaks the axial
symmetry assumed in current theoretical models. Here, we study dissipative
exchange flows in a ferromagnet with in-plane anisotropy from a dispersive
hydrodynamic perspective. Through the analysis of a boundary value problem for
a damped sine-Gordon equation, dissipative exchange flows in a ferromagnetic
channel can be excited above a spin current threshold that depends on material
parameters and the length of the channel. Symmetry-broken dissipative exchange
flows display harmonic overtones that redshift the fundamental precessional
frequency and lead to a reduced spin pumping efficiency when compared to their
symmetric counterpart. Micromagnetic simulations are used to verify that the
analytical results are qualitatively accurate, even in the presence of nonlocal
dipole fields. Simulations also confirm that dissipative exchange flows can be
driven by spin transfer torque in a finite-sized region. These results
delineate the important material parameters that must be optimized for the
excitation of dissipative exchange flows in realistic systems.Comment: 20 pages, 5 figure
Tunable mode coupling in nano-contact spin torque oscillators
Recent experiments on spin torque oscillators have revealed interactions
between multiple magnetodynamic modes, including mode-coexistence,
mode-hopping, and temperature-driven cross-over between modes. Initial
multimode theory has indicated that a linear coupling between several dominant
modes, arising from the interaction of the subdynamic system with a magnon
bath, plays an essential role in the generation of various multimode behaviors,
such as mode hopping and mode coexistence. In this work, we derive a set of
rate equations to describe the dynamics of coupled magnetodynamic modes in a
nano-contact spin torque oscillator. Expressions for both linear and nonlinear
coupling terms are obtained, which allow us to analyze the dependence of the
coupled dynamic behaviors of modes on external experimental conditions as well
as intrinsic magnetic properties. For a minimal two-mode system, we further map
the energy and phase difference of the two modes onto a two-dimensional phase
space, and demonstrate in the phase portraits, how the manifolds of periodic
orbits and fixed points vary with external magnetic field as well as with
temperature.Comment: 13 pages, 8 figures; 2 figures (Figs.5 & 6) corrected and redrawn; 2
new figures (Figs.7 & 8) added; Accepted by Physical Review Applie
Hydrodynamic description of long-distance spin transport through noncollinear magnetization states: the role of dispersion, nonlinearity, and damping
Nonlocal compensation of magnetic damping by spin injection has been
theoretically shown to establish dynamic, noncollinear magnetization states
that carry spin currents over micrometer distances. Such states can be
generically referred to as dissipative exchange flows (DEFs) because spatially
diffusing spin currents are established by the mutual exchange torque exerted
by neighboring spins. Analytical studies to date have been limited to the weak
spin injection assumption whereby the equation of motion for the magnetization
is mapped to hydrodynamic equations describing spin flow and then linearized.
Here, we analytically and numerically study easy-plane ferromagnetic channels
subject to spin injection of arbitrary strength at one extremum under a unified
hydrodynamic framework. We find that DEFs generally exhibit a nonlinear profile
along the channel accompanied by a nonlinear frequency tuneability. At large
injection strengths, we fully characterize a novel magnetization state we call
a contact-soliton DEF (CS-DEF) composed of a stationary soliton at the
injection site, which smoothly transitions into a DEF and exhibits a negative
frequency tuneability. The transition between a DEF and a CS-DEF occurs at the
maximum precessional frequency and coincides with the Landau criterion: a
subsonic to supersonic flow transition. Leveraging the hydraulic-electrical
analogy, the current-voltage characteristics of a nonlinear DEF circuit are
presented. Micromagnetic simulations of nanowires that include
magnetocrystalline anisotropy and non-local dipole fields are in qualitative
agreement with the analytical results. The magnetization states found here
along with their characteristic profile and spectral features provide
quantitative guidelines to pursue an experimental demonstration of DEFs in
ferromagnetic materials and establishes a unified description for long-distance
spin transport
Controllable vortex shedding from dissipative exchange flows in ferromagnetic channels
Ferromagnetic channels subject to spin injection at one extremum sustain long-range coherent textures that carry spin currents known as dissipative exchange flows (DEFs). In the weak injection regime, spin currents carried by DEFs decay algebraically and extend through the length of the channel, a regime known as spin superfluidity. Similar to fluids, these structures are prone to phase slips that manifest as vortex-antivortex pairs. Here, we numerically study vortex shedding from DEFs excited in a magnetic nanowire with a physical obstacle. Using micromagnetic simulations, we find regimes of laminar flow and vortex shedding as a function of obstacle position tunable by the spin injection sign and magnitude. Vortex-antivortex pairs translate forward (VF regime) or backward (VB regime) with respect to the detector's extremum, resulting in well-defined spectral features. Qualitatively similar results are obtained when temperature, anisotropy, and weak nonlocal dipole fields are included in the simulations. These results provide clear features associated with DEFs that may be detected experimentally in devices with nominally identical boundary conditions. Furthermore, our results suggest that obstacles can be considered as DEF control gates, opening an avenue to manipulate DEFs via physical defects
Transverse instabilities of stripe domains in magnetic thin films with perpendicular magnetic anisotropy
Stripe domains are narrow, elongated, reversed regions that exist in magnetic
materials with perpendicular magnetic anisotropy. Stripe domains appear as a
pair of domain walls that can exhibit topology with a nonzero chirality. Recent
experimental and numerical investigations identify an instability of stripe
domains in the long direction as a means of nucleating isolated magnetic
skyrmions. Here, the onset and nonlinear evolution of transverse instabilities
for a dynamic stripe domain known as the bion stripe are investigated. Both
non-topological and topological variants of the bion stripe are shown to
exhibit a long-wavelength transverse instability with different characteristic
features. In the former, small transverse variations in the stripe's width lead
to a neck instability that eventually pinches the non-topological stripe into a
chain of two-dimensional breathers composed of droplet soliton pairs. In the
latter case, small variations in the stripe's center results in a snake
instability whose topological structure leads to the nucleation of dynamic
magnetic skyrmions and antiskyrmions as well as perimeter-modulated droplets.
Quantitative, analytical predictions for both the early, linear evolution and
the long-time, nonlinear evolution are achieved using an averaged Lagrangian
approach that incorporates both exchange (dispersion) and anisotropy
(nonlinearity). The method of analysis is general and can be applied to other
filamentary structures.Comment: 8 figures, 13 page
Magnonic Band Structure Established by Chiral Spin-Density Waves in Thin Film Ferromagnets
Recent theoretical studies have demonstrated the possibility to excite and
sustain noncollinear magnetization states in ferromagnetic nanowires. The
resulting state is referred to as a spin-density wave (SDW). SDWs can be
interpreted as hydrodynamic states with a constant fluid density and fluid
velocity in systems with easy-plane anisotropy. Here, we consider the effect of
the nonlocal dipole field arising from the finite thickness of magnetic thin
films on the spatial profile of the SDW and on the associated magnon
dispersion. Utilizing a hydrodynamic formulation of the Larmor torque equation,
it is found that the nonlocal dipole field modulates the fluid velocity. Such a
modulation induces a magnonic band structure unlike the typical dispersion
relation for magnons on uniform magnetization. The analytical results are
validated by micromagnetic simulations. Band gaps on the order of GHz are
numerically observed to depend on the SDW fluid velocity and film thickness for
realistic material parameters. The presented results suggest that SDWs can find
applications as reconfigurable magnonic crystals.Comment: 5 pages, 5 figure
Dynamics of reconfigurable artificial spin ice: toward magnonic functional materials
Over the past few years, the study of magnetization dynamics in artificial spin ices has become a vibrant field of study. Artificial spin ices are ensembles of geometrically arranged, interacting magnetic nanoislands, which display frustration by design. These were initially created to mimic the behavior in rare earth pyrochlore materials and to study emergent behavior and frustration using two-dimensional magnetic measurement techniques. Recently, it has become clear that it is possible to create artificial spin ices, which can potentially be used as functional materials. In this perspective, we review the resonant behavior of spin ices in the GHz frequency range, focusing on their potential application as magnonic crystals. In magnonic crystals, spin waves are functionalized for logic applications by means of band structure engineering. While it has been established that artificial spin ices can possess rich mode spectra, the applicability of spin ices to create magnonic crystals hinges upon their reconfigurability. Consequently, we describe recent work aiming to develop techniques and create geometries allowing full reconfigurability of the spin ice magnetic state. We also discuss experimental, theoretical, and numerical methods for determining the spectral response of artificial spin ices and give an outlook on new directions for reconfigurable spin ices
Deterministic drift instability and stochastic thermal perturbations of magnetic dissipative droplet solitons
The magnetic dissipative droplet is a strongly nonlinear wave structure that can be stabilized in a thin film ferromagnet exhibiting perpendicular magnetic anisotropy by use of spin transfer torque. These structures have been observed experimentally at room temperature, showcasing their robustness against noise. Here, we quantify the effects of thermal noise by deriving stochastic equations of motion for a droplet based on soliton perturbation theory. First, it is found that deterministic droplets are linearly unstable at large bias currents, subject to a drift instability. When the droplet is linearly stable, our framework allows us to analytically compute the droplet's generation linewidth and center variance. Additionally, we study the influence of nonlocal and Oersted fields with micromagnetic simulations, providing insight into their effect on the generation linewidth. These results motivate detailed experiments on the current and temperature-dependent linewidth as well as drift instability statistics of droplets, which are important figures-of-merit in the prospect of droplet-based applications
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