Damping Of Spin Waves Research Articles

Nonreciprocal damping of spin waves propagating in magnetic domain walls induced by Dzyaloshinskii-Moriya interaction

The nonreciprocity of spin waves refers to the phenomenon that spin waves propagating in opposite directions display different features. This phenomen becomes a fundamental requirement for implementing magnon logic architectures. The nonreciprocal transportion of spin waves induced by Dzyaloshinskii-Moriya interaction (DMI) has been studied extensively. It is characterized by a shift of spin-wave dispersion. Here we report another feature of the DMI-induced nonreciprocity, i.e., the nonreciprocal spin wave damping. We find that the spin waves propagating with opposite wave vectors in magnetic domain wall have different damping, which is frequency dependent and especially evident in low frequancy range. For spin waves with sufficient low frequencies (around 1 GHz), the damping nonreciprocity is so extreme that spin waves can transport only in one direction, thus realizing the spin-wave diode function. The theoretical predictions are validated by micromagnetic simulations. The findings in this work points out a new feature of DMI-induced spin wave nonreciprocity and may be exploited for designing novel magnonic devices.

Evolution of static and dynamic magnetic properties of Re/Co/Pt and Pt/Co/Re trilayers with enhanced Dzyaloshinskii-Moriya interaction

The influence of Re layer insertion either at the bottom or top interface of epitaxially grown Pt/Co/Pt heterostructures on their static and dynamic magnetic properties is discussed in terms of their crystalline structure. Magnetic properties were studied as a function of both Re and Co layer thicknesses (dRe and dCo, respectively) in the matrix-like samples with a double-wedge structure, in which the layer thickness gradients were oriented orthogonally. The comprehensive investigations of the changes in coercivity, perpendicular magnetic anisotropy, spin reorientation transition, interfacial Dzyaloshinskii-Moriya interaction (iDMI) and spin wave damping are reported. Two different magnetic phases depending on the Co layer thickness with volume anisotropies (determined without demagnetization term) of KV∼0.25 (low) and KV∼0.75 MJ/m3 (high) were observed. The relation between these phases depends on the stack sequence and thickness of Re inserted layer. For dRe = 0.2 ÷ 0.7 nm deposited as the bottom interface, dCo induced transition at dtr ∼ 2 nm from low to high volume anisotropy phases was observed. Low and high volume anisotropy phases are associated to Co fcc and hcp structural phases. The insertion of half atomic layer of Re had no influence on surface anisotropy but significantly enhanced iDMI above 1 pJ/m and reduced spin wave damping.

Orientation-dependent two-dimensional magnonic crystal modes in an ultralow-damping ferrimagnetic waveguide containing repositioned hexagonal lattices of Cu disks

Two-dimensional (2D) hexagonal lattices of Cu disks are shown to induce orientation-dependent magnonic crystal (MC) modes for propagating forward volume spin waves in a single-crystal yttrium iron garnet (YIG) film. The width and depth of the magnonic band gaps are 0.022 GHz and –15.2 dB at the frequency of 1.815 GHz. Integrating differently oriented lattices on the same YIG film and positioning them between the microwave antenna surrounded by magnon absorbers consisting of Au films, we clearly resolve a characteristic frequency shift of the magnonic band gap by altering the incident angle of the spin waves to the 2D MC. The shift amounts to approximately 10 MHz when the incident angle is changed between 10° and 30°. The obtained results show a good agreement with calculations using the finite integration technique and are a step toward complete band-gap investigations in YIG of ultralow spin-wave damping. Published by the American Physical Society 2024

Larmor precession in strongly correlated itinerant electron systems

Many-electron systems undergo a collective Larmor precession in the presence of a magnetic field. In a paramagnetic metal, the resulting spin wave provides insight into the correlation effects generated by the electron-electron interaction. Here, we use dynamical mean-field theory to investigate the collective Larmor precession in the strongly correlated regime, where dynamical correlation effects such as quasiparticle lifetimes and non-quasiparticle states are essential. We study the spin excitation spectrum, which includes a dispersive Larmor mode as well as electron-hole excitations that lead to Stoner damping. We also extract the momentum-resolved damping of slow spin waves. The accurate theoretical description of these phenomena relies on the Ward identity, which guarantees a precise cancellation of self-energy and vertex corrections at long wavelengths. Our findings pave the way towards a better understanding of spin wave damping in correlated materials.

Spin wave dispersion of ultra-low damping hematite ( α−Fe2O3 ) at GHz frequencies

Low magnetic damping and high group velocity of spin waves (SWs) or magnons are two crucial parameters for functional magnonic devices. Magnonics research on signal processing and wave-based computation at GHz frequencies focused on the artificial ferrimagnetic garnet ${\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$ (YIG) so far. We report on spin wave spectroscopy studies performed on the natural mineral hematite ($\ensuremath{\alpha}{\text{-Fe}}_{2}{\text{O}}_{3}$), which is a canted antiferromagnet. By means of broadband GHz spectroscopy and inelastic light scattering, we determine a damping coefficient of $1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ and magnon group velocities of a few 10 km/s, respectively, at room temperature. Covering a large regime of wave vectors up to $k\ensuremath{\approx}24\phantom{\rule{0.16em}{0ex}}\mathrm{rad}/\textmu{}\mathrm{m}$, we find the exchange stiffness length to be relatively short and only about 1 \AA{}. In a small magnetic field of 30 mT, the decay length of SWs is estimated to be 1.1 cm similar to the best YIG. Still, inelastic light scattering provides surprisingly broad and partly asymmetric resonance peaks. Their characteristic shape is induced by the large group velocities, low damping, and distribution of incident angles inside the laser beam. Our results promote hematite as an alternative and sustainable basis for magnonic devices with fast speeds and low losses based on a stable natural mineral.

Scaling analysis of anomalous Hall resistivity and magnetoresistance in the quasi-two-dimensional ferromagnet Fe3GeTe2

${\mathrm{Fe}}_{3}{\mathrm{GeTe}}_{2}$ is a two-dimensional van der Waals bonded layered compound that shows high-temperature itinerant ferromagnetism. We study aspects of the scattering mechanism in the single crystal of high-${T}_{\text{C}}\phantom{\rule{4pt}{0ex}}{\mathrm{Fe}}_{3}{\mathrm{GeTe}}_{2}$ via resistivity, magnetotransport, and Hall effect measurements. The quadratic temperature dependence of electrical resistivity below the ${T}_{\text{C}}$ (210 K) points towards the dominance of electron-magnon scattering. A nonsaturating positive magnetoresistance (MR) is observed at low temperatures when the magnetic field is applied parallel to the sample plane. The linear negative MR at high fields for $T<{T}_{\text{C}}$ corroborates to the suppression in the magnon population due to the damping of spin waves. In the high-temperature regime ($T>{T}_{\text{C}}$), MR can be described by the scattering from spin fluctuations using the Khosla and Fischer model. Isothermal Hall resistivity curves unveil the presence of anomalous Hall resistivity. The correlation between magnetoresistance and side jump mechanism further reveals that the electron-magnon scattering is responsible for the side jump contribution to the anomalous Hall effect. Our results provide a clear understanding of the role of electron-magnon scattering on the temperature-driven evolution of the anomalous Hall effect that rules out its origin to be the topological band structure.

Field evolution of magnetic phases and spin dynamics in the honeycomb lattice magnet Na2Co2TeO6 : Na23 NMR study

We report on the results of 23Na NMR in the honeycomb lattice magnet Na2Co2TeO6 which has been nominated as a Kitaev material. Measurements of magnetic shift and width of the NMR line as functions of temperature and magnetic field show that a spin-disordered phase does not appear up to a field of 9 T. In the antiferromagnetic phase just below the Neel temperature TN, we find a temperature region extending down to ~TN/2 where the nuclear spin-lattice relaxation rate 1/T1 remains enhanced and is further increased by a magnetic field. This region crosses over to a low temperature region characterized by the rapidly decreasing 1/T1 which is less field-sensitive. These observations suggest incoherent spin excitations with a large spectral weight at low energies in the intermediate temperature region transforming to more conventional spin-wave excitations at low temperatures. The drastic change of the low-energy spin dynamics is likely caused by strong damping of spin waves activated only in the intermediate temperature region, which may be realized for triple-q magnetic order possessing partially-disordered moments as scattering centers of spin waves. In the paramagnetic phase near TN, dramatic field suppression of 1/T1 is observed. From analysis of the temperature dependence of 1/T1 based on the renormalized-classical description of a two-dimensional quantum antiferromagnet, we find the field-dependent spin stiffness constant that scales with TN as a function of magnetic field. This implies field suppression of the energy scale characterizing both two-dimensional spin correlations and three-dimensional long-range order, which may be associated with an increasing effect of frustration in magnetic fields.

Microscopic nonlinear magnonic phase shifters based on ultrathin films of a magnetic insulator

Since magnonics takes advantage of not only the amplitude of spin waves but also their phase, tunable phase shifters are key elements for the implementation of magnonic circuits. Therefore, one of the major challenges in nano-magnonics is to find a physical mechanism to manipulate the spin-wave phase practically in simple and miniature devices. In this work, we experimentally demonstrate that intrinsic magnetic nonlinearities allow the implementation of efficient microscopic tunable phase shifters, where the phase is controlled by wave intensity. In the proposed devices, we achieve the tunability of the phase shift of more than 360° by a microwave power of few milliwatts over a propagation distance of about 10 μm. We show that the figure of merit of the demonstrated phase shifters is close to that of macroscopic devices based on alternative technologies. Our results also indicate that the ability to control the phase shift is primarily limited by nonlinear spin-wave damping and can be significantly improved by suppressing this effect. Our findings are important for the further development of integrated nano-magnonics for beyond-Moore computing.

Investigation of stiffness and damping constant of spin waves in a soft magnet Co100−xBx alloy

In ferromagnets, alloying provides tunability of magnetic, electrical, and mechanical properties; however, its effect on magnetization has mostly been studied in terms of static properties. In this study, we investigate the stiffness and damping of spin waves in a cobalt-boron (Co100−xBx) alloy using an optical pump-probe technique. Coherent spin waves in Co100−xBx were excited by an optical spin–orbit torque from Pt. The dynamics of the spin wave were monitored on a picosecond timescale using the magneto-optical Kerr effect. From the oscillation period and relaxation of the spin wave, the stiffness and damping of the spin waves were determined. As the boron concentration increases from 0% to 35%, the spin wave stiffness decreases from 4.3 to 1.0 meV nm2, and the damping constant of the spin wave increases from 0.02 to 0.11. Such a large change suggests that B alloying has a significant impact on the spin-wave properties.

Superlattice on the surface of a nanotube

The results of theoretical studies of the thermodynamic, kinetic, and high-frequency properties of the electron gas on the surface of a nanotube in a magnetic field in the presence of a longitudinal superlattice are presented. Nano-dimensions of the motion area lead to energy quantization. Its multiply connected structure in the presence of a magnetic field leads to effects that are derived from the Aharonov–Bohm effect. It is shown that the curvature of a nanotube, even in the absence of a magnetic field, causes new macroscopic oscillation effects such as de Haas–van Alphen oscillations, which are associated with the quantization of the transverse electron motion energy and with the root peculiarities of the density of electron states on the nanotube surface. Thermodynamic potentials and heat capacity of the electron gas on the tube are calculated in the gas approximation. The Kubo formula for the conductivity tensor of the electron gas on the nanotube surface is obtained. The Landau damping regions of electromagnetic waves on a tube are determined and the beats are theoretically predicted on the graph of the dependence of conductivity on tube parameters. In the hydrodynamic approximation, the plasma waves on the surface of a semiconductor nanotube with a superlattice are considered. It is shown that optical and acoustic plasmons can propagate along a tube with one kind of carrier. Electron spin waves on the surface of a semiconductor nanotube with a superlattice in a magnetic field are studied. The spectra and areas of collisionless damping of these waves are found. We have shown that the spin wave damping is absent in these areas if the tubes with a degenerate electron gas have small radius.

Damping of dipole-exchange spin waves in ferromagnetic thin films at elevated temperatures

A non-bosonic technique, based on the drone-fermion perturbation method and a high-density expansion, is employed to study the spin-wave (SW) scattering processes in a ferromagnetic thin film with exchange and dipole–dipole interactions. Specifically, the diagrammatic contributions to the spin–spin Green’s functions are evaluated within a 1/z perturbation expansion, where z is the number of spins interacting with any given spin. The results are used to calculate the SW damping at temperatures below the Curie temperature T C. It is found that, apart from the usual contributions due to three-magnon and four-magnon processes in the film, which are dominant at relatively low temperatures (consistent with boson expansion methods), there is an additional mechanism that becomes important for temperatures above about This is spin disorder damping, previously studied in bulk magnetic materials; it occurs when a spin wave is scattered by the instantaneous disorder produced when a longitudinal spin component undergoes a large thermal fluctuation. Numerical estimates are presented for thin films of Permalloy and EuO.

Spin-Wave Relaxation by Eddy Currents in Y3Fe5O12/Pt Bilayers and a Way to Suppress It

Because of their record-low intrinsic magnetic damping properties, single-crystal yttrium-iron-garnet (YIG) films serve as an excellent model medium for studying magnon-induced spintronic phenomena such as spin pumping and the spin-orbit torque effect. For this purpose, YIG films are covered with sub-skin-depth layers of nonmagnetic heavy metals with strong spin-orbit coupling. In the present work, we show experimentally and theoretically that ohmic losses of spin-wave-induced microwave eddy currents in the heavy-metal layer deliver a strong contribution to spin-wave damping in these hybrid structures. We demonstrate that this adverse effect can be controlled and largely eliminated by placing a highly conducting metal plate near to the surface of the YIG/$\mathrm{Pt}$ structures. These findings are of value for a proper interpretation of experiments on the magnon spintronic effects and for the design of future magnon spintronic devices.

Exchange stiffness and damping constants of spin waves in CoFeB films

Exchange stiffness and damping of spin waves in a soft ferromagnet of CoFeB are investigated using a time-resolved pump-probe technique. A pump pulse excites coherent spin waves in CoFeB via optical spin-orbit torque from Pt, and a probe pulse detects the phase of the spin waves via magneto-optic Kerr effect. From the frequency of spin waves, exchange stiffness is determined to be 13 pJ m−1, which is nearly independent of the CoFeB thickness from 6 to 16 nm and the annealing temperature of 400 °C. Damping constant of spin waves is determined from the relaxation of spin waves. Importantly, the spin wave damping increases with decreasing the CoFeB thickness, suggesting the spin pumping effect at the interface between CoFeB and Pt. The thickness dependence of damping becomes stronger after annealing at 400 °C, and the spin wave damping of >0.08 is obtained at a CoFeB thickness of 6.3 nm. Such large damping of spin waves would have an important effect on the operation of the CoFeB-based memory devices.

On the dissipative coherent states of magnons

Research in spintronics has attracted much attention in the last few years due to the technological progress in generating and manipulating spin currents in miniaturized devices. Notwithstanding dissipative effects are inherent to experiments, in many theoretical works the damping of spin waves is included later by phenomenological arguments or even disregarded. Among the many techniques that have been used to treat magnetic models, bosonic representations is one of them. In this work, we chose the Holstein–Primakoff bosonic formalism to treat a ferromagnetic model with a priori inclusion of the damping term. Damping is included through a non-Hermitian term in the Hamiltonian and we showed that the well-known coherent state formalism can be generalized to properly represent the dissipative magnon model. The obtained results are then used to describe the precession magnetization in spintronic experiments, as the spin pumping process.

Reservoir Computing Using a Spin-Wave Delay-Line Active-Ring Resonator Based on Yttrium-Iron-Garnet Film

The authors demonstrate the use of a propagating spin waves for implementing a reservoir computing architecture. The proposed concept utilises an active ring resonator comprising a magnetic thin film delay line integrated into a feedback loop. These systems exhibit strong nonlinearity and delayed response behaviour, two important properties required for an effective reservoir computing implementation. In a simple design, we exploit the nonlinear damping of spin waves at different feedback gains to inject input data into the active ring resonator and use a microwave diode to read out the amplitude of the spin waves circulating in the ring. We employ two baseline tasks, namely the short term memory and parity check tasks, to evaluate the suitability of this architecture for processing time series data.

Chiral Spin-Wave Velocities Induced by All-Garnet Interfacial Dzyaloshinskii-Moriya Interaction in Ultrathin Yttrium Iron Garnet Films.

Spin waves can probe the Dzyaloshinskii-Moriya interaction (DMI), which gives rise to topological spin textures, such as skyrmions. However, the DMI has not yet been reported in yttrium iron garnet (YIG) with arguably the lowest damping for spin waves. In this work, we experimentally evidence the interfacial DMI in a 7-nm-thick YIG film by measuring the nonreciprocal spin-wave propagation in terms of frequency, amplitude, and most importantly group velocities using all electrical spin-wave spectroscopy. The velocities of propagating spin waves show chirality among three vectors, i.e., the film normal direction, applied field, and spin-wave wave vector. By measuring the asymmetric group velocities, we extract a DMI constant of 16 μJ/m^{2}, which we independently confirm by Brillouin light scattering. Thickness-dependent measurements reveal that the DMI originates from the oxide interface between the YIG and garnet substrate. The interfacial DMI discovered in the ultrathin YIG films is of key importance for functional chiral magnonics as ultralow spin-wave damping can be achieved.

Damping of Standing Spin Waves in Bismuth-Substituted Yttrium Iron Garnet as Seen via the Time-Resolved Magneto-Optical Kerr Effect

We investigate spin-wave resonance modes and their damping in insulating thin films of bismuth-substituted yttrium iron garnet by performing femtosecond magneto-optical pump-probe experiments. For large magnetic fields in the range below the magnetization saturation, we find that the damping of high-order standing spin-wave (SSW) modes is about 40 times lower than that for the fundamental one. The observed phenomenon can be explained by considering different features of magnetic anisotropy and exchange fields that, respectively, define the precession frequency for fundamental and high-order SSWs. These results provide further insight into SSWs in iron garnets and may be exploited in many new photomagnonic devices.

Propagation of Spin Waves in Microstructures Based on Yttrium–Iron Garnet Films Decorated by a Ferromagnetic Metal

Propagation of spin waves in an yttrium–iron garnet film decorated by nickel-film microstructures have been studied experimentally and theoretically. A choice of the geometry of the nickel microstructures is shown to enable controlling the spin-wave damping and the formation of wave beams of spin waves.

Investigating optically excited terahertz standing spin waves using noncollinear magnetic bilayers

We investigate optically excited terahertz standing spin waves in noncollinear magnetic bilayers. Using femtosecond laser-pulse excitation, a spin current is generated in the first ferromagnetic (FM) layer, and flows through a conductive spacer layer to be injected into the second (transverse) FM layer, where it exerts a spin-transfer torque on the magnetization and excites higher-order standing spin waves. We show that the noncollinear magnetic bilayer is a convenient tool that allows easy excitation of terahertz spin waves, and can be used to investigate the dispersion and thereby the spin-wave stiffness parameter in the thin-film regime. This is experimentally demonstrated using wedge-shaped Co and CoB (absorption) layers. Furthermore, the damping of these terahertz spin waves is investigated, showing a strong increase of the damping with decreasing absorption layer thickness, much stronger than expected from interface spin pumping effects. Additionally, a previously unseen sudden decrease in the damping for the thinnest films is observed. A model for the additional damping contribution incorporating both these observations is proposed.

Control of Spin-Wave Damping in YIG Using Spin Currents from Topological Insulators

Yttrium iron garnet (YIG) is a material with unique properties that make it very attractive for use in microwave applications, such as frequency-selective limiters and logic processing. However, the decay of a spin wave's amplitude as it propagates in the material curbs the use of YIG in practical applications. To surmount this limitation, in this study the surface spin currents of a topological insulator are used to enhance the spin-wave amplitude in adjacent YIG. In addition, interesting properties of magnons are observed and investigated, to advance spintronics.