Spin-wave Dynamics Research Articles

Investigation of spin wave dynamics in Au/CoFeB/Au multilayers with perpendicular magnetic anisotropy

We have carried out an experimental investigation of the spin-wave dynamics in the Au/CoFeB/Au multilayer consisting of a ferromagnetic film with thicknesses of 0.8, 0.9 and 1.0 nm. We employed the Brillouin light scattering spectroscopy to measure the frequency of the spin waves in dependence on the wave vector. Additionally, we characterized the samples by ferromagnetic resonance measurements. We found that the considered samples exhibit perpendicular magnetic anisotropy with low damping, indicating small pumping effects. Furthermore, we found a nonreciprocal dispersion relation pointing at a non-negligible Dzyaloshinskii–Moriya interaction. These results make the Au/CoFeB/Au multilayer a compelling subject for further analysis and as a potential material for future applications within magnonics.

Spin wave dynamics in CoFeB bilayers with wedged Au spacer

This paper presents the experimental studies of ferromagnetic layers separated by a heavy metal wedge. The studied system consists of two thin layers of CoFeB separated by a wedged Au spacer. By performing Brillouin light scattering measurements of the spin-wave dispersion relations, and dependences on the magnetic field, we extract magnetic parameters in the studied ferromagnetic layers as a function of heavy metal thickness. We concluded that for thin ferromagnetic double layers, the magnetic properties strongly depend on the thickness of the wedge gold layer spacer. In particular, the presence of perpendicular magnetic anisotropy diminishes as the thickness of the magnetic material is increased, and at the spacers thicker than 2.5 nm the dynamic coupling between propagating spin waves in both layers is negligible. These findings have potential advantages for the development of future spintronic devices.

Direct Observation of Propagating Spin Waves in the 2D van der Waals Ferromagnet Fe5GeTe2.

Magnetism in reduced dimensionalities is of great fundamental interest while also providing perspectives for applications of materials with novel functionalities. In particular, spin dynamics in two dimensions (2D) have become a focus of recent research. Here, we report the observation of coherent propagating spin-wave dynamics in a ∼30 nm thick flake of 2D van der Waals ferromagnet Fe5GeTe2 using X-ray microscopy. Both phase and amplitude information were obtained by direct imaging below TC for frequencies from 2.77 to 3.84 GHz, and the corresponding spin-wave wavelengths were measured to be between 1.5 and 0.5 μm. Thus, parts of the magnonic dispersion relation were determined despite a relatively high magnetic damping of the material. Numerically solving an analytic multilayer model allowed us to corroborate the experimental dispersion relation and predict the influence of changes in the saturation magnetization or interlayer coupling, which could be exploited in future applications by temperature control or stacking of 2D-heterostructures.

Real-time observation of magnetization and magnon dynamics in a two-dimensional topological antiferromagnet MnBi2Te4

Atomically thin van der Waals magnetic materials have not only provided a fertile playground to explore basic physics in the two-dimensional (2D) limit but also created vast opportunities for novel ultrafast functional devices. Here we systematically investigate ultrafast magnetization dynamics and spin wave dynamics in few-layer topological antiferromagnetic MnBi2Te4 crystals as a function of layer number, temperature, and magnetic field. We find laser-induced (de)magnetization processes can be used to accurately track the distinct magnetic states in different magnetic field regimes, including showing clear odd–even layer number effects. In addition, strongly field-dependent AFM magnon modes with tens of gigahertz frequencies are optically generated and directly observed in the time domain. Remarkably, we find that magnetization and magnon dynamics can be observed in not only the time-resolved magneto-optical Kerr effect but also the time resolved reflectivity, indicating strong correlation between the magnetic state and electronic structure. These measurements present the first comprehensive overview of ultrafast spin dynamics in this novel 2D antiferromagnet, paving the way for potential applications in 2D antiferromagnetic spintronics and magnonics as well as further studies of ultrafast control of both magnetization and topological quantum states.

High-resolution Brillouin light scattering study on Ti/Au/Co/Ni multilayer

The topic of this paper addresses the Brillouin light scattering (BLS) study of the spin-wave and surface acoustic wave dynamics in the multilayer consisting of Ti/Au/Co/Ni deposited on Si substrate. We make the quantitative analysis of spin-wave frequency under a range of wave vectors to determine the dispersion relation and to study the effect of the magnetic field. These findings were correlated with theoretical models to determine the magnetic system parameters, such as magnetization, Lande g factor, exchange stiffness constant etc. In addition to this, we have conducted finite element method based simulations to understand the nature of surface phonons and to determine the elastic tensor parameters for the Ti/Au/Co/Ni layer from the fitting of simulation results with the experiment data points.

Observation of c -axis magnetization at low temperatures in the weak ferromagnet FeBO3 reveals a spin-reorientation transition

The weak ferromagnet $\mathrm{Fe}{\mathrm{BO}}_{3}$ is well known for being a unique system for modeling and testing magnetic dynamics primarily due to relatively simple and localized magnetic structure and its interesting spin wave dynamics. At room temperature, it has slightly canted iron moments lying in the $a\text{\ensuremath{-}}b$ plane that result in a strong antiferromagnetic moment and a weak ferromagnetic moment, which results in pronounced ferromagnetic and antiferromagnetic spin modes. However, some previous studies have shown unusual low-temperature behavior that suggests a phase transition. By performing low-temperature magnetization measurements, both in bulk and on the mesoscale, we have observed a low-temperature magnetic texture in this material in which a large $c$-axis magnetization occurs. Magnetic fields along the $c$ axis as high as 1300 Oe were observed close to the sample's surface. This presents evidence for the onset of a Morin transition or another type of spin-reorientation phase transition wherein the ${\mathrm{Fe}}^{3+}$ moments would acquire a $c$-axis component to their canting below a critical temperature. The observation of this $c$-axis magnetization suggests that there is a different ground state in this material than has been previously expected and could be due to as yet unexplored intricacies of the Dzyaloshinskii-Moriya interaction.

Spin-Wave Spectral Analysis in Crescent-Shaped Ferromagnetic Nanorods

The research on the properties of spin waves (SWs) in three-dimensional nanosystems is an innovative idea in the field of magnonics. Mastering and understanding the nature of magnetization dynamics and binding of SWs at surfaces, edges, and in-volume parts of three-dimensional magnetic systems enables the discovery of alternative phenomena and suggests other possibilities for their use in magnonic and spintronic devices. In this work, we use numerical methods to study the effect of geometry and external magnetic field manipulations on the localization and dynamics of SWs in crescent-shaped (CS) waveguides. It is shown that changing the magnetic field direction in these waveguides breaks the symmetry and affects the localization of eigenmodes with respect to the static demagnetizing field. This, in turn, has a direct effect on their frequency. Furthermore, CS structures are found to be characterized by significant saturation at certain field orientations, resulting in a cylindrical magnetization distribution. Thus, we present chirality-based nonreciprocal dispersion relations for high-frequency SWs, which can be controlled by the field direction (shape symmetry) and its amplitude (saturation).

Learning Trajectories from Spin-Wave Dynamics

The efficacy of a physical reservoir computer model based on traveling spin waves in a spin-wave delay-line active-ring resonator was demonstrated recently. In the present work, we investigate how this neuromorphic device can be adapted for sensing applications. In this ``reservoir computing for sensing'' framework, we exploit strong coupling of the physical reservoir to its environment to utilize the reservoir as a sensing element. The dynamics of traveling spin waves in delay-line active rings are strongly dependent on the magnetic field and carrier frequency of those spin waves. Treating the spin-wave frequency as an environmental variable, we excite the active ring into different dynamical states by modulating the carrier frequency of a drive signal of microwave pulses injected into the ring. Training a linear regression on the time-multiplexed output from the ring allows the periodic amplitude patterns of the spin waves to be mapped reproducibly onto two-dimensional trajectories, representing periodic ``behavioral'' targets. Our work demonstrates the versatility of a magnonic resonator as a multipurpose computing and sensing device.

A two-color dual-comb system for time-resolved measurements of ultrafast magnetization dynamics using triggerless asynchronous optical sampling.

We report on an Er-doped fiber (EDF)-laser-based dual-comb system that allows us to perform triggerless asynchronous optical sampling pump-probe measurements of ultrafast demagnetization and spin precession in magnetic materials. Because the oscillation frequencies of the two frequency-comb light sources are highly stabilized, the pulse-to-pulse timing jitter is sufficiently suppressed, and data accumulation without any trigger signals is possible. To effectively induce spin precession in ferromagnetic thin films, the spectral bandwidth of the output of one of the EDF frequency comb sources is broadened by a highly nonlinear fiber and then amplified at a wavelength of about 1030nm by a Yb-doped fiber amplifier. The output of the other frequency comb source is converted to about 775nm by second harmonic generation. We used this system to observe ultrafast demagnetization and spin precession dynamics on the picosecond and nanosecond time scales in a permalloy thin film. This time-domain spectroscopy system is promising for the rapid characterization of spin-wave generation and propagation dynamics in magnetic materials.

Spin-wave dynamics controlled by tunable ac magnonic crystal

The magnonic crystal, which has a spatial modulation wave vector $q$, couples the spin wave with wave vector $k$ to the one with wave vector $k\ensuremath{-}q$. For a conventional magnonic crystal with direct current (dc) supply, the spin waves around $q/2$ are resonantly coupled to the waves near $\ensuremath{-}q/2$, and a band gap is opened at $k=\ifmmode\pm\else\textpm\fi{}q/2$. If instead of the dc current the magnonic crystal is supplied with an alternating current (ac), then the band gap is shifted to $k$ satisfying $|{\ensuremath{\omega}}_{s}(k)\ensuremath{-}{\ensuremath{\omega}}_{s}(k\ensuremath{-}q)|={\ensuremath{\omega}}_{\mathrm{ac}}$; here ${\ensuremath{\omega}}_{s}(k)$ is the dispersion of the spin wave, while ${\ensuremath{\omega}}_{\mathrm{ac}}$ is the frequency of the ac modulation. The resulting gap in the case of the ac magnonic crystal is the half of the one caused by the dc with the same amplitude of modulation. The time evolution of the resonantly coupled spin waves controlled by properly suited ac pulses can be well interpreted as the motion on a Bloch sphere. The tunability of the ac magnonic crystal broadens the perspective of spin-wave computing.

Tunability of spin-wave spectra in a 2D triangular shaped magnonic fractals

Reprogramming the structure of the magnonic bands during their operation is important for controlling spin waves in magnonic devices. Here, we report the tunability of the spin-wave spectra for a triangular shaped deterministic magnonic fractal, which is known as Sierpinski triangle by solving the Landau–Lifshitz–Gilbert equation using a micromagnetic simulations. The spin-wave dynamics change significantly with the variation of iteration number. A wide frequency gap is observed for a structure with an iteration number exceeding some value and a plenty of mini-frequency bandgaps at structures with high iteration number. The frequency gap could be controlled by varying the strength of the magnetic field. A sixfold symmetry in the frequency gap is observed with the variation of the azimuthal angle of the external magnetic field. The spatial distributions of the spin-wave modes allow to identify the bands surrounding the gap. The observations are important for the application of magnetic fractals as a reconfigurable aperiodic magnonic crystals.

The effect of anisotropic field on magnon dispersion of antiferromagnetic metal fluoride materials

This article investigates the dynamics of spin waves in two sublattice antiferromagnetic (AFM) system spins’ interaction and magnon dispersion relation. The analysis is done starting with a standard model that includes a uniaxial magnetic anisotropy field. Quantum field theory is employed in formulating the problem, and double-time temperature-dependent Green function technique is used to obtain magnon dispersion, whereby random phase approximation is considered to decouple and diagonalize the higher order terms. At low temperatures and long wavelength approximation, dispersion of uniaxial symmetric AFM crystal lattice of metallic fluoride materials, such as MnF2, FeF2, and RbMnF3, is analyzed for illustration. Our findings indicate that as the anisotropic field increases, the magnon dispersion vs wave vector k gradually varies, attempts linearity from being curved, and attains a sinusoidal structure when extended further in the first Brillouin zone. Perhaps, these results are useful to understand the feature of magnon dispersion of stable similar AFM materials for practical application.

Magnon-Fluxon Interaction in Coupled Superconductor/Ferromagnet Hybrid Periodic Structures

We study the magnon propagation in a micrometer-size ferromagnetic waveguide affected by the proximity to a superconductor that hosts a vortex formation. By solving the time-dependent Ginzburg-Landau equations of superconductivity, we obtain the equilibrium state of the vortex configuration and the associated stray fields that act on the magnetic dynamics. Spin wave dynamics in the presence of the superconductors are inferred from the Landau-Lifschitz equation. For a quantitative comparison, the simulations are performed under the experimental conditions as reported by Dobrovolskiy et al. (Nature Physics, 15, 477 (2019)). We found that the presence of the vortex lattice leads to the formation of a Bloch-like band structure in the magnon spectrum. The width and the number of allowed bands are found to depend mainly on the in-plane component of the vortex field along the waveguide. A shift to lower energies of the lowest-order-allowed bands occurs due to the confinement of the magnonic modes above the locations of the superconductor vortices. We also studied the role of the films thickness. At least two GHz-frequency backward-volume magnetostatic spin waves modes are observed at the top and bottom surfaces (in addition to these magnetostatic surface modes, the vertical confinement can also give rise to longer-wavelength and low-frequency perpendicular standing spin waves). Effects of the vortex fields are found to depend strongly on the type of the magnon modes. It is found that the effect of the superconducting vortices of the spin waves can be emulated well by the stray fields of air-separated magnetic nanocubes of appropriate dimensions.

Broadband microwave detection using electron spins in a hybrid diamond-magnet sensor chip

Quantum sensing has developed into a main branch of quantum science and technology. It aims at measuring physical quantities with high resolution, sensitivity, and dynamic range. Electron spins in diamond are powerful magnetic field sensors, but their sensitivity in the microwave regime is limited to a narrow band around their resonance frequency. Here, we realize broadband microwave detection using spins in diamond interfaced with a thin-film magnet. A pump field locally converts target microwave signals to the sensor-spin frequency via the non-linear spin-wave dynamics of the magnet. Two complementary conversion protocols enable sensing and high-fidelity spin control over a gigahertz bandwidth, allowing characterization of the spin-wave band at multiple gigahertz above the sensor-spin frequency. The pump-tunable, hybrid diamond-magnet sensor chip opens the way for spin-based gigahertz material characterizations at small magnetic bias fields.

The BKT transition and its dynamics in a spin fluid.

We study the effect of particle mobility on phase transitions in a spin fluid in two dimensions. The presence of a phase transition of the BKT universality class is shown in an off-lattice model of particles with purely repulsive interaction employing computer simulations. A critical spin wave region 0 < T < TBKT is found with a nonuniversal exponent η(T) that follows the shape suggested by BKT theory, including a critical value consistent with ηBKT = 1/4. One can observe a transition from power-law decay to exponential decay in the static correlation functions at the transition temperature TBKT, which is supported by finite-size scaling analysis. A critical temperature TBKT = 0.17(1) is suggested. Investigations into the dynamic aspects of the phase transition are carried out. The short-time behavior of the incoherent spin autocorrelation function agrees with the Nelson-Fisher prediction, whereas the long-time behavior differs from the finite-size scaling known for the static XY model. Analysis of coherent spin wave dynamics shows that the spin wave peak is a propagating mode that can be reasonably well fitted by hydrodynamic theory. The mobility of the particles strongly enhances damping of the spin waves, but the model still lies within the dynamic universality class of the standard XY model.

Bias field orientation driven reconfigurable magnonics and magnon−magnon coupling in triangular shaped Ni80Fe20 nanodot arrays

Reconfigurable magnonics have attracted intense interest due to their myriad advantages including energy efficiency, easy tunability and miniaturization of on-chip data communication and processing devices. Here, we demonstrate efficient reconfigurability of spin-wave (SW) dynamics as well as SW avoided crossing by varying bias magnetic field orientation in triangular shaped Ni80Fe20 nanodot arrays. In particular, for a range of in-plane angles of bias field, we achieve mutual coherence between two lower frequency modes leading to a drastic modification in the ferromagnetic resonance frequency. Significant modification in magnetic stray field distribution is observed at the avoided crossing regime due to anisotropic dipolar interaction between two neighbouring dots. Furthermore, using micromagnetic simulations we demonstrate that the hybrid SW modes propagate longer through an array as opposed to the non-interacting modes present in this system, indicating the possibility of coherent energy transfer of hybrid magnon modes. This result paves the way for the development of integrated on-chip magnonic devices operating in the gigahertz frequency regime.

Lock-in thermographic study of spin-wave propagation in magnonic crystals

We have investigated the spin-wave dynamics in a one-dimensional magnonic crystal (MC) with respect to the heat radiation due to the damping of the spin waves. The spin waves were excited by applying microwaves via a wire antenna. The heat induced by the excitation and propagation of spin waves was measured using the lock-in thermography (LIT) technique by periodically modulating the microwave power. The LIT measurements resolved the heat source distributions inside the MC, which is made of an yttrium iron garnet film and periodic grooves with a sub-mm interval, in the backward volume wave geometry. The temperature distribution induced by the spin-wave excitation notably depends on the frequency or wave number of the spin waves, as a result of the formation of rejection bands in the MC. The observed temperature modulation profiles are complicated, but their behavior is consistent with a calculation based on the microwave transmission line approximation of the MCs, demonstrating the applicability of the LIT measurements to the investigation of the spin-wave dynamics in sub-mm scale MCs.

Controlling High-Frequency Spin-Wave Dynamics Using Double-Pulse Laser Excitation

Manipulating spin waves is highly required for the development of innovative data transport and processing technologies. Recently, the possibility of triggering high-frequency standing spin waves in magnetic insulators using femtosecond laser pulses was discovered, raising the question about how one can manipulate their dynamics. Here we explore this question by investigating the ultrafast magnetization and spin-wave dynamics induced by double-pulse laser excitation. We demonstrate a suppression or enhancement of the amplitudes of the standing spin waves by precisely tuning the time delay between the two pulses. The results can be understood as the constructive or destructive interference of the spin waves induced by the first and second laser pulses. Our findings open exciting perspectives towards generating single-mode standing spin waves that combine high frequency with large amplitude and low magnetic damping.

Origin and dynamics of umbrella states in rare-earth iron garnets

Rare-earth iron garnets R3Fe5O12 are fascinating insulators with very diverse magnetic phases. Their strong potential in spintronic devices has encouraged a renewal of interest in the study of their low temperature spin structures and spin wave dynamics. A striking feature of rare-earth garnets with R-ions exhibiting strong crystal-field effects like Tb-, Dy-, Ho-, Er-, Tm- and Yb-ions is the observation of low-temperature non-collinear magnetic structures featuring “umbrella-like” arrangements of the rare-earth magnetic moments. In this study, we demonstrate that such umbrella magnetic states are naturally emerging from the crystal-field anisotropies of the rare-earth ions. By means of a general model endowed with only the necessary elements from the crystal structure, we show how umbrella-like spin structures can take place and calculate the canting-angle as a result of the competition between the exchange-interaction of the rare-earth and the iron ions as well as the crystal-field anisotropy. Our results are compared to experimental data, and a study of the polarised spin wave dynamics is presented. Our study improves the understanding of umbrella-like spin structures and paves the way for more complex spin wave calculations in rare-earth iron garnets with non-collinear magnetic phases.

Reconfigurable Magnonic Crystals Based on Imprinted Magnetization Textures in Hard and Soft Dipolar-Coupled Bilayers.

Reconfigurable magnetization textures offer control of spin waves with promising properties for future low-power beyond-CMOS systems. However, materials with perpendicular magnetic anisotropy (PMA) suitable for stable magnetization-texture formation are characterized by high damping, which limits their applicability in magnonic devices. Here, we propose to overcome this limitation by using hybrid structures, i.e., a PMA layer magnetostatically coupled to a low-damping soft ferromagnetic film. We experimentally show that a periodic stripe-domain texture from a PMA layer is imprinted upon the soft layer and induces a nonreciprocal dispersion relation of the spin waves confined to the low-damping film. Moreover, an asymmetric bandgap features the spin-wave band diagram, which is a clear demonstration of collective spin-wave dynamics, a property characteristic for magnonic crystals with broken time-reversal symmetry. The composite character of the hybrid structure allows for stabilization of two magnetic states at remanence, with parallel and antiparallel orientation of net magnetization in hard and soft layers. The states can be switched using a low external magnetic field; therefore, the proposed system obtains an additional functionality of state reconfigurability. This study offers a link between reconfigurable magnetization textures and low-damping spin-wave dynamics, providing an opportunity to create miniaturized, programmable, and energy-efficient signal processing devices operating at high frequencies.