Spin-wave Relaxation Research Articles

Giant anisotropic Gilbert damping and spin wave propagations in single-crystal magnetic insulator

Gilbert damping in magnetic systems describes the relaxation of magnetization. This term was phenomenologically introduced into the Landau–Lifschitz–Gilbert (LLG) equation to describe spin dynamics. In most studies, such as magnetic random access memory, spin-wave propagations, and microwave devices, it has been assumed that the Gilbert damping is an isotropic constant. In this study, we uncover a giant anisotropic Gilbert damping parameter of up to 431% in single-crystal thin films of epitaxial [100]-oriented yttrium iron garnet (YIG) using angle-dependent ferromagnetic resonance. In contrast, the Gilbert damping parameter of a [111]-oriented YIG film is almost isotropic. The observed anisotropic damping is shown to have a similar fourfold symmetry with magneto-crystalline anisotropy. The anisotropic spin-wave group velocity (vg), relaxation time (τ), and decay length (ld) were also experimentally evaluated through spin-wave spectra of [100]-oriented YIG thin film. We developed the LLG equation with the introduction of an anisotropic orbital Gilbert damping term. This anisotropic orbital damping originates from the crystal-field dominated anisotropic spin–orbit coupling and orbital-related magnon–phonon coupling. Our results extend the understanding of the mechanism of anisotropic Gilbert damping in single-crystal magnetic insulators with strong magneto-crystalline anisotropy.

Parametric generation of spin waves in nanoscaled magnonic conduits

The research feld of magnonics proposes a low-energy wave-logic computation technology based on spin waves to complement the established CMOS technology and provide a basis for emerging unconventional computation architectures. However, magnetic damping is a limiting factor for all-magnonic logic circuits and multi-device networks, ultimately rendering mechanisms to effciently manipulate and amplify spin waves a necessity. In this regard, parallel pumping is a versatile tool since it allows to selectively generate and amplify spin waves. While extensively studied in microscopic systems, nano-scaled systems are lacking investigation to assess the feasibility and potential future use of parallel pumping in magnonics. Here, we investigate a longitudinally magnetized 100 nm-wide magnonic nano-conduit using space and time-resolved micro-focused Brillouin-light-scattering spectroscopy. Employing parallel pumping to generate spin waves, we observe that the non-resonant excitation of dipolar spin waves is favored over the resonant excitation of short wavelength exchange spin waves. In addition, we utilize this technique to access the effective spin-wave relaxation time of an individual nano-conduit, observing a large relaxation time up to (115.0 +- 7.6) ns. Despite the significant decrease of the pumping effciency in the investigated nano-conduit, a reasonably small threshold is found rendering parallel pumping feasible on the nano-scale.

Strong high-frequency spin waves released periodically from a confined region

Efficient excitation of spin waves is a key issue in magnonics. Here, by using micromagnetic simulation and analytical analysis, we study the excitation of spin waves confined in a limited region by a microwave field with assistance of spin-transfer torque. The results show that the spin-transfer torque can decrease the effective damping constant and increase the spin wave relaxation time substantially. As a result, the amplitude of the excited spin waves is increased greatly. By periodically lifting and establishing the blocking areas, strong spin-wave pulses are released from the confined region. Such generated spin-wave pulses are much stronger than traditionally excited spin waves, especially for high-frequency spin waves. Our study provides a new method to generate strong high-frequency spin waves.

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.

Spin excitations in laser-molecular-beam epitaxy-grown nanosized YIG films: towards low relaxation and desirable magnetization profile

We describe the synthesis of nanosized Y3Fe5O12 (YIG) films grown by laser-molecular-beam epitaxy on Gd3Ga5O12 (GGG) and Nd3Ga5O12 (NdGG) substrates with (111) orientation and present the results of ferromagnetic resonance (FMR) and spin-wave propagation studies in these heterostructures. It is found that the magnetic parameters of YIG films grown on NdGG and GGG substrates are considerably different. FMR spectra of YIG/NdGG structures are characterized by a large number of narrow peaks, while FMR spectra of YIG/GGG structures consist of a small number of peaks or one peak. The effective magnetization of YIG films grown on NdGG substrates is less than that of YIG films grown on GGG and is more sensitive to the growth conditions. A lateral inhomogeneity of YIG/NdGG structures is observed in spin-wave propagation experiments. For YIG/NdGG and YIG/GGG structures, the FMR linewidth ΔH of a single peak sharply increases with temperature decrease from 298 to 67 K. The observed increase of ΔH is explained by typical relaxation processes caused by the presence of Fe2 + ions. From the spin-wave propagation study, it is also found that the relaxation of spin-waves explains only a minor part of the FMR single-peak linewidth in YIG/NdGG structures. On the basis of the obtained results, YIG/GGG/semiconductor- and YIG/NdGG/semiconductor-heterostructures with expected low spin-wave relaxation and desirable effective magnetization profile are proposed.

Determining Key Spin-Orbitronic Parameters via Propagating Spin Waves

We characterize spin wave propagation and its modification by an electrical current in Permalloy(Py)/Pt bilayers with Py thickness between 4 and 20 nm. First, we analyze the frequency non-reciprocity of surface spin waves and extract from it the interfacial Dzyaloshinskii-Moriya interaction constant $D_s$ accounting for an additional contribution due to asymmetric surface anisotropies. Second, we measure the spin-wave relaxation rate and deduce from it the Py/Pt spin mixing conductance $g^{\uparrow\downarrow}_{eff}$. Last, applying a \textit{dc} electrical current, we extract the spin Hall conductivity $\sigma_{SH}$ from the change of spin wave relaxation rate due to the spin-Hall spin transfer torque. We obtain a consistent picture of the spin wave propagation data for different film thicknesses using a single set of parameters $D_s=0.25$ pJ/m, $g^{\uparrow\downarrow}_{eff} = 3.2\times 10^{19}$ m$^{-2}$ and $\sigma_{SH}=4\times10^{5}$ S/m.

Magnetochiral nonreciprocity of spin wave damping in long-period structures

The spin wave in long-periodic spiral magnetic structures demonstrates the so-called magnetochiral nonreciprocity, i.e., a noninvariance of its dispersion when it propagates parallel and antiparallel to the chiral wave vector. Motivated by recent experiments on systems with magnetochiral long-periodic orders, we studied the effect of static spatially varying magnetization structure on spin wave relaxation. A description of an intrinsic nonlocal magnetization relaxation is given within the scope of a phenomenological equation called the Landau-Lifshitz-Baryakhtar equation (V. G. Bar'yakhtar, Zh. Eksp. Teor. Fiz. 87, 1501 (1984) [Sov. Phys. JETP 60, 863 (1984)]) for crystals of different symmetry. Spiral magnetic structures with a helicity step due to competitive exchange interactions or due to the Dzyaloshinskii-Moriya interaction are considered, and related dissipative functions are obtained. Within the general phenomenological approach, it is demonstrated that magnetochiral nonreciprocity manifests itself in different nonlocal dampings of spin waves with opposite wave vectors, as well. More fundamentally, we show that static but spatially varying magnetization causes a finite damping of the Goldstone mode. Understanding the peculiar nonlocal relaxation of the magnetization precession in materials with spatially varying magnetic order is important for applications of such magnets in magnonics and spintronics.

Propagating spin waves in nanometer-thick yttrium iron garnet films: Dependence on wave vector, magnetic field strength, and angle

We present a comprehensive investigation of propagating spin waves in nanometer-thick yttrium iron garnet (YIG) films. We use broadband spin-wave spectroscopy with integrated coplanar waveguides (CPWs) and microstrip antennas on top of continuous and patterned YIG films to characterize spin waves with wave vectors up to 10 rad/$\mu$m. All films are grown by pulsed laser deposition. From spin-wave transmission spectra, parameters such as the Gilbert damping constant, spin-wave dispersion relation, group velocity, relaxation time, and decay length are derived and their dependence on magnetic bias field strength and angle is systematically gauged. For a 40-nm-thick YIG film, we obtain a damping constant of $3.5 \times 10^{-4}$ and a maximum decay length of 1.2 mm. Our experiments reveal a strong variation of spin-wave parameters with magnetic bias field and wave vector. Spin-wave properties change considerably up to a magnetic bias field of about 30 mT and above a field angle of $\theta_{H} = 20^{\circ}$, where $\theta_{H} = 0^{\circ}$ corresponds to the Damon-Eshbach configuration.

Irreversible Markov chains in spin models: Topological excitations

We analyze the convergence of the irreversible event-chain Monte Carlo algorithm for continuous spin models in the presence of topological excitations. In the two-dimensional XY model, we show that the local nature of the Markov-chain dynamics leads to slow decay of vortex-antivortex correlations while spin waves decorrelate very quickly. Using a Fréchet description of the maximum vortex-antivortex distance, we quantify the contributions of topological excitations to the equilibrium correlations, and show that they vary from a dynamical critical exponent at the critical temperature to in the limit of zero temperature. We confirm the event-chain algorithm's fast relaxation (corresponding to z = 0) of spin waves in the harmonic approximation to the XY model. Mixing times (describing the approach towards equilibrium from the least favorable initial state) however remain much larger than equilibrium correlation times at low temperatures. We also describe the respective influence of topological monopole-antimonopole excitations and of spin waves on the event-chain dynamics in the three-dimensional Heisenberg model.

Spin wave amplification using the spin Hall effect in permalloy/platinum bilayers

We investigate the effect of an electrical current on the attenuation length of a 900 nm wavelength spin-wave in a permalloy/Pt bilayer using propagating spin-wave spectroscopy. The modification of the spin-wave relaxation rate is linear in current density, reaching up to 14% for a current density of 2.3 × 1011 A/m2 in Pt. This change is attributed to the spin transfer torque induced by the spin Hall effect and corresponds to an effective spin Hall angle of 0.13, which is among the highest values reported so far. The spin Hall effect thus appears as an efficient way of amplifying/attenuating propagating spin waves.

Spin-transfer torque based damping control of parametrically excited spin waves in a magnetic insulator

The damping of spin waves parametrically excited in the magnetic insulator Yttrium Iron Garnet (YIG) is controlled by a dc current passed through an adjacent normal-metal film. The experiment is performed on a macroscopically sized YIG(100 nm)/Pt(10 nm) bilayer of 4 × 2 mm2 lateral dimensions. The spin-wave relaxation frequency is determined via the threshold of the parametric instability measured by Brillouin light scattering spectroscopy. The application of a dc current to the Pt film leads to the formation of a spin-polarized electron current normal to the film plane due to the spin Hall effect. This spin current exerts a spin transfer torque in the YIG film and, thus, changes the spin-wave damping. Depending on the polarity of the applied dc current with respect to the magnetization direction, the damping can be increased or decreased. The magnitude of its variation is proportional to the applied current. A variation in the relaxation frequency of ±7.5% is achieved for an applied dc current density of 5 × 1010 A/m2.

Synthesis, magnetic properties and spin-wave propagation in thin Y3Fe5O12 films sputtered on GaN-based substrates

We describe the synthesis of submicron Y3Fe5O12 (YIG) films sputtered on GaN-based substrates and present the results of the investigation of ferromagnetic resonance (FMR) and spin wave propagation in YIG / GaN structures. It is found that spin waves propagated in deposited YIG films have low damping. At the frequency of 3.2 GHz the spin-wave damping parameter is less than . Sputtered YIG films have magnetic inhomogeneity, which gives the main contribution to the FMR linewidth. The FMR linewidth increase caused by the relaxation process is insignificant and is equal to low values (2.2–3.7% of the linewidth). The low relaxation of spin waves in deposited YIG films gives the opportunity to construct tuneable spin-wave band-pass filters with a high-quality factor on GaN substrates and to design radiation-tolerant monolithic microwave integrated circuits.

Controlling the relaxation of propagating spin waves in yttrium iron garnet/Pt bilayers with thermal gradients

The spin currents generated by thermal gradients through the spin Seebeck effect (SSE) are usually detected by the voltage generated in a normal metal by means of the inverse spin Hall effect. Here, we present a detailed account of an experimental investigation of the action of spin currents due to SSE on the relaxation rate of spin waves. Propagating spin-wave packets with a frequency in the range of 1--2 GHz are launched in film strips of single-crystal yttrium iron garnet, Y${}_{3}$Fe${}_{5}$O${}_{12}$ (YIG) while a thermal gradient is applied across the thickness in the so-called longitudinal SSE configuration. No change in damping is observed in bare YIG films. However, if the YIG film is covered with an ultrathin platinum layer, we observe a striking change in the amplitude of the detected spin-wave pulses. Depending on the sign of the gradient, the spin-wave relaxation rate can be increased or decreased, leading in the latter case to an apparent amplification. The change in the relaxation rate is attributed to the action of a spin current generated in the YIG film by the SSE while the role of the Pt layer is to supply or absorb the flow of spins.

Investigation of spin wave damping in three-dimensional magnonic crystals using the plane wave method

The Landau-Lifshitz equation with a scalar damping constant predicts that the damping of spin waves propagating in an infinite homogeneous magnetic medium does not depend on the direction of propagation. This is not the case in materials with a periodic arrangement of magnetic constituents (known as magnonic crystals). In this paper, the plane wave method is extended to include damping in the calculation of the dispersion and relaxation of spin waves in three-dimensional magnonic crystals. A model material system is introduced and calculations are then presented for magnonic crystals realized in the direct and inverted structure and for two different filling fractions. The ability of magnonic crystals to support the propagation of spin waves is characterized in terms of a figure of merit, defined as the ratio of the spin wave frequency to the decay constant. The calculations reveal that in magnonic crystals with a modulated value of the relaxation constant, the figure of merit depends strongly on the frequency and wave vector of the spin waves, with the dependence determined by the spatial distribution of the spin wave amplitude within the unit cell of the magnonic crystal. Bands and directions of exceptionally long spin wave propagation have been identified. The results are also discussed in terms of the use of magnonic crystals as metamaterials with designed magnetic permeability.

Spin Pumping Driven by Bistable Exchange Spin Waves

Spin pumping driven by bistable exchange spin waves is demonstrated in a Pt/Y3Fe5O12 film under parametric excitation. In the Pt/Y3Fe5O12 film, the spin pumping driven by parametric excitation selectively enhances the relaxation of short-wavelength exchange spin waves, indicating strong coupling between the exchange spin waves and spin currents at the interface through efficient spin transfer. The parametric spin pumping, furthermore, allows direct access to nonlinear spin wave dynamics in combination with the inverse spin Hall effect, revealing unconventional bistability of the exchange spin waves.

Dispersion relations and low relaxation of spin waves in thin magnetic films

We study spin excitations in thin magnetic films in the Heisenberg model with magnetic dipole and exchange interactions by the spin operator diagram technique and make comparison of their parameters with characteristics of spin waves in thick films. Dispersion relations of spin waves in thin magnetic films (in two-dimensional magnetic monolayer and bilayer lattices) and the spin-wave resonance spectrum in $N$-layer structures are found. For thick magnetic films, spin excitations are determined by simultaneous solution of the generalized Landau-Lifshitz equations and the equation for the magnetostatic potential. Generalized Landau-Lifshitz equations are derived from first principles and have the integral (pseudodifferential) form. It is found that dispersion relations of spin waves in monolayers and in bilayers differ from dispersion relations of spin waves in continuous thick magnetic films. For normal magnetized ferromagnetic films, the spin-wave damping is calculated in the one-loop approximation for a diagram expansion of the Green functions at low temperature. In thick magnetic films, the magnetic dipole interaction makes a major contribution to the relaxation of long-wavelength spin waves. Thin films have a region of the low relaxation of long-wavelength spin waves. In thin magnetic films, four-spin-wave processes take place and the exchange interaction makes a major contribution to the damping. It is found that the damping of spin waves propagating in a magnetic monolayer is proportional to the quadratic dependence on the temperature and is very low for spin waves with small wave vectors.

Competing hyperfine and spin-orbit couplings: Spin relaxation in a quantum Hall ferromagnet

Spin relaxation in a quantum Hall ferromagnet, where filling is $\nu=1, 1/3, 1/5,...$, can be considered in terms of spin wave annihilation/creation processes. Hyperfine coupling with the nuclei of the GaAs matrix provides spin non-conservation in the two-dimensional electron gas and determines spin relaxation in the quantum Hall system. This mechanism competes with spin-orbit coupling channels of spin-wave decay and can even dominate in a low-temperature regime where $T$ is much smaller than the Zeeman gap. In this case the spin-wave relaxation process occurs non-exponentially with time and does not depend on the temperature. The competition of different relaxation channels results in crossovers in the dominant mechanism, leading to non-monotonic behavior of the characteristic relaxation time with the magnetic field. We predict that the relaxation times should reach maxima at $B\simeq 18\,$T in the $\nu=1$ Quantum Hall system and at $B\simeq 12\,$T for that of $\nu=1/3\,$. We estimate these times as $\sim10\,-\,30\,\mu$s and $\sim2\,-\,5\,\mu$s, respectively.

Spin-wave population in nickel after femtosecond laser pulse excitation

The spin-wave relaxation mechanisms after intense laser excitation in ferromagnetic nickel films are investigated with all-optical pump-probe experiments. Uniform precession (Kittel mode), Damon-Eshbach surface modes and perpendicular standing spin waves can be identified by their dispersion f(H). However, different to other ferromagnets f(H) deviates from the expected behavior. Namely, a mode discontinuity is observed, that can be attributed to a non-linear process. Above a critical field the power spectrum reveals a redistribution of the energy within the spin-wave spectrum populated.

Skyrmion Effect on the Relaxation of Spin Waves in a Quantum Hall Ferromagnet

Spin relaxation of two-dimensional electrons in a GaAs/AlGaAs quantum well was studied by time-resolved Kerr rotation measurements using a two-color pump and probe technique. In quantum Hall ferromagnets, the spin-wave relaxation is strongly influenced by the photogenerated Skyrmion and anti-Skyrmion pairs. By tuning the pump and probe lights to the lowest optical transition, an intrinsic filling factor dependence of spin relaxation is obtained without photogeneration of Skyrmions. The relaxation time of the spin wave presents a sharp peak at odd filling factors, accompanied by dips on both sides of it. The peculiar filling factor dependence of the spin-wave relaxation around quantum Hall ferromagnets can be explained by the interaction between the spin wave and Skyrmion. Observation of a similar feature around ν=1, 3, and 5 may suggest the existence of Skyrmions around higher odd filling factors.

Optical Control of Ultrafast Spin-wave Relaxation by Magnetic Anisotropy in a Ferromagnet

Optical Control of Ultrafast Spin-wave Relaxation by Magnetic Anisotropy in a Ferromagnet