Spin-wave Modes Research Articles

Special features of low-temperature microwave ferromagnetic resonance in nanometer ferrite layer patterned by macroporous silicon substrate

Experimental magnetic resonance spectra for nanometer ferrite brand 1SCh4 layer deposited on macroporous silicon substrate, obtained at T = 300 and 4.2 K in the frequency ranges of 5–15 and 60–75 GHz, respectively, were analyzed. In addition to the ferromagnetic resonance mode, additional peaks were found in the magnetoresonance spectra. An analysis using the known theoretical concepts of the modern spin dynamic theory, together with the results of micromagnetic simulation, showed the formation of spin-wave oscillation modes that arise due to the structurization of the ferrite layer by a substrate of macroporous silicon.

Reconfigurable magnon interference by on-chip dynamic wavelength conversion

Spin waves (SWs), an ultra-low power magnetic excitation in ferro or antiferromagnetic media, have tremendous potential as transport less data carriers for post-CMOS technology using their wave interference properties. The concept of magnon interference originates from optical interference, resulting in a historical taboo of maintaining an identical wavevector for magnon interference-based devices. This makes the attainment of on-chip design reconfigurability challenging owing to the difficulty in phase tuning via external fields. Breaking the taboo, this study explores a novel technique to systematically control magnon interference using asymmetric wavevectors from two different SW modes (magnetostatic surface SWs and backward volume magnetostatic SWs) in a microstructured yttrium iron garnet crossbar. Using this system, we demonstrate phase reconfigurability in the interference pattern by modulating the thermal landscape, modifying the dispersion of the interfering SW modes. Thus, we manifest that such a tunable interference can be used to implement reconfigurable logic gates operating between the XNOR and XOR modes by using symmetric and asymmetric interference, respectively.

Large Anomalous Frequency Shift in Perpendicular Standing Spin Wave Modes in BiYIG Films Induced by Thin Metallic Overlayers.

Interface-driven effects on magnon dynamics are studied in magnetic insulator-metal bilayers using Brillouin light scattering. It is found that the Damon-Eshbach modes exhibit a significant frequency shift due to interfacial anisotropy generated by thin metallic overlayers. In addition, an unexpectedly large shift in the perpendicular standing spin wave mode frequencies is also observed, which cannot be explained by anisotropy-induced mode stiffening or surface pinning. Rather, it is suggested that additional confinement may result from spin pumping at the insulator-metal interface, which results in a locally overdamped interface region. These results uncover previously unidentified interface-driven changes in magnetization dynamics that may be exploited to locally control and modulate magnonic properties in thin-film heterostructures.

Injection Locking of Linearlike and Soliton Spin-Wave Modes in Nanoconstriction Spin Hall Nano-oscillators

We study injection locking of two different spin wave (SW) modes (a field-localized linearlike interior mode and a self-localized SW bullet soliton) in a single nanoconstriction-based spin Hall nano-oscillator. Mode selection is achieved by varying the oblique magnetic field angle and magnitude. The two modes show dramatically different responses to injection locking, in terms of locking bandwidth and linewidth and output power in the locked state. Extracting the locking range graphically from the experimental data yields apparent thresholds for the required injected power, with the bullet mode showing a larger threshold than the linearlike mode. By instead fitting the full detuning behavior using a model including thermal noise, the apparent threshold vanishes, while the very different locking behavior of the two modes can instead be ascribed to the order of magnitude difference in their mode volumes.

Hybrid spin Hall nano-oscillators based on ferromagnetic metal/ferrimagnetic insulator heterostructures

Spin-Hall nano-oscillators (SHNOs) are promising spintronic devices to realize current controlled GHz frequency signals in nanoscale devices for neuromorphic computing and creating Ising systems. However, traditional SHNOs devices based on transition metals have high auto-oscillation threshold currents as well as low quality factors and output powers. Here we demonstrate a new type of hybrid SHNO based on a permalloy (Py) ferromagnetic-metal nanowire and low-damping ferrimagnetic insulator, in the form of epitaxial lithium aluminum ferrite (LAFO) thin films. The superior characteristics of such SHNOs are associated with the excitation of larger spin-precession angles and volumes. We further find that the presence of the ferrimagnetic insulator enhances the auto-oscillation amplitude of spin-wave edge modes, consistent with our micromagnetic modeling. This hybrid SHNO expands spintronic applications, including providing new means of coupling multiple SHNOs for neuromorphic computing and advancing magnonics.

Magnetic Damping Properties of Single-Crystalline Co55Mn18Ga27 and Co50Mn18Ga32 Films

We investigate the structural, static magnetic and damping properties in two Mn-deficient magnetic Weyl semimetal Co-Mn-Ga (CMG) alloy films, i.e., Co55Mn18Ga27 (CMG1) and Co50Mn18Ga32 (CMG2), which were epitaxially grown on MgO (001) substrates. CMG1 has a mixing phase of B 2 and L21, larger saturation magnetization (M s ∼ 760 emu/cm3), stronger in-plane magnetic anisotropy. CMG2 has an almost pure B2 phase, smaller M s (∼ 330 emu/cm3), negligible in-plane magnetic anisotropy. Time-resolved magneto-optical Kerr effect results unambiguously demonstrate an obvious perpendicular standing spin wave (PSSW) mode in addition to the Kittel mode for both of the CMG films. The intrinsic damping constant is about 0.0055 and 0.015 for CMG1 and CMG2, respectively, which are both significantly larger than that of the stoichiometric CMG (i.e., Co2MnGa) film reported previously. In combination with the first-principles calculations, the intrinsic damping properties of the Mn-deficient CMG films can be well explained by considering the increase of density of states at the Fermi level, reduction of M s, and excitation of the PSSW mode. These findings provide a new clue to tuning the magnetic damping of the magnetic Weyl semimetal film through slight off-stoichiometry.

Out-of-plane Ferromagnetic Resonance and Surface Spin Wave Modes in Ni80Fe20 Film on Ripple-Patterned Sapphire Substrate

The study of surface magnetic anisotropy of magnetic films is beneficial to understanding the behaviors of films at high frequencies and further promoting their high-frequency magnetic applications. We investigated the out-of-plane ferromagnetic resonance (FMR) and surface spin wave modes in 40-nm Ni80Fe20 (NiFe) films deposited on ripple-patterned sapphire substrate with periodicity and a flat sapphire substrate by broad-band FMR technique. When measuring the FMR of the film on ripple-patterned substrate, the in-plane angle (\U0001d711 H of the external applied magnetic field was along the direction of the ripples (\U0001d711 H = 90°) and perpendicular to the ripple direction (\U0001d711 H = 0°) respectively. The spin-wave resonance spectra consisting of up to two surface spin wave (SSW) modes were observed as the external magnetic field polar angle θH varied from “in-plane configuration” (θH = 90° ) to “out-of-plane configuration” (θH = 0°). As the decrease of θH , the two surface spin excitations disappeared in sequence and further only FMR mode was observed in the region θH which was smaller than the “critical angle” θc . The θc of \U0001d711 H = 90° is found to be different from that for \U0001d711 H = 0°. The dependences of field shift vs. out-of-plane angles θH for each SSW mode were analyzed by the surface inhomogeneity model. From the model, the surface anisotropy constants Ks of films were obtained. The results show that the values of surface anisotropy constants for the two SSW modes are different. Compared with the film sputtered on flat sapphire substrate, after introducing ripple-patterned substrate, the variation of Ks is only on the order of 0.01 erg/cm2 for the film of this thickness.

Control of spin wave propagation modes in the yttrium iron garnet waveguide by means of local laser heating

The results of micromagnetic modeling of the magnetic structure on the surface of a film of yttrium iron garnet (YIG) are presented, where a region of altered saturation magnetization was created by focused laser radiation. Based on the constructed amplitude-frequency characteristics of signal transmission through a magnon structure with a heating region, the possibility of implementing spin-wave signal filtering modes with a change in the diameter of the heated region on the YIG surface is shown.

Spin wave excitations in a nanowire spin Hall oscillator with perpendicular magnetic anisotropy

Spin torque oscillators (STOs) are emerging microwave devices that can potentially be used in spin-logic devices and the next-generation high-speed computing architecture. Thanks to their non-linear nature, STOs are easily tunable by the magnetic field and the dc current. Spin Hall nano-oscillators are promising types of STOs and most of the current studies focus on localized modes that can be easily excited. Here, we study using micromagnetic simulations, the nature of the spin-torque-induced excitations in nanowire devices made of perpendicular magnetic anisotropy (PMA) materials. Our results showed that, upon including PMA, the excitation of localized and propagating spin wave modes is feasible. We study the nature of the mode excitations as a function of the PMA strength (Ku) and the current. Indeed, we estimate a critical value of Ku to allow for the excitation of the propagating spin wave. We attribute this mode selectivity between localized and propagating modes to the magnitude and the change of the sign of the nonlinearity of the system from negative to positive at a non-zero Ku, which is supported by analytical calculations. Our results provide deep insight into engineering microwave devices for future magnonic and computational applications.

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.

A Brillouin light scattering study of the spin-wave magnetic field dependence in a magnetic hybrid system made of an artificial spin-ice structure and a film underlayer

We present a combined Brillouin light scattering (BLS) and micromagnetic simulation investigation of the magnetic-field-dependent spin-wave spectra in a hybrid structure made of permalloy (NiFe) artificial spin-ice (ASI) systems, composed of stadium-shaped nanoislands, deposited on the top of an unpatterned permalloy film with a nonmagnetic spacer layer. The thermal spin-wave spectra were recorded by BLS as a function of the magnetic field applied along the symmetry direction of the ASI sample. Magneto-optic Kerr effect magnetometry was used to measure the hysteresis loops in the same orientation as the BLS measurements. The frequency and the intensity of several spin-wave modes detected by BLS were measured as a function of the applied magnetic field. Micromagnetic simulations enabled us to identify the modes in terms of their frequency and spatial symmetry and to extract information about the existence and strength of the dynamic coupling, relevant only to a few modes of a given hybrid system. Using this approach, we suggest a way to understand if the dynamic coupling between ASI and film modes is present or not, with interesting implications for the development of future three-dimensional magnonic applications and devices.

Hybridization‐Induced Spin‐Wave Transmission Stop Band within a 1D Diffraction Grating

AbstractSpin wave propagation is studied through a diffraction grating in a 200 nm thick YIG film by using scanning time resolved magneto‐optic Kerr microscopy (TR‐MOKE) and supported by micromagnetic simulations. Caustic‐like spin wave emission and the hybridization of Damon Eshbach (DE) type spin wave modes within the grating region, depending on the magnetic field and the dimensions of the grating, are observed. Hybridization leads to an increased attenuation length for propagating spin waves and consequently to a transmission stop‐band for spin waves at the grating for a certain magnetic field range.

Curvature-induced stabilization and field-driven dynamics of magnetic hopfions in toroidal nanorings

Three dimensional magnetic textures are a cornerstone in magnetism research. In this work, we analyze the stabilization and dynamic response of a magnetic hopfion hosted in a toroidal nanoring with intrinsic Dzyaloshinskii–Moriya interaction simulating FeGe. Our results evidence that unlike their planar counterparts, where perpendicular magnetic anisotropies are necessary to stabilize hopfions, the shape anisotropy originated on the torus symmetry naturally yields the nucleation of these topological textures. We also analyze the magnetization dynamical response by applying a magnetic field pulse to differentiate among several magnetic patterns. Finally, to understand the nature of spin wave modes, we analyze the spatial distributions of the resonant mode amplitudes and phases and describe the differences among bulk and surface modes. Importantly, hopfions lying in toroidal nanorings present a non-circularly symmetric poloidal resonant mode, which is not observed in other systems hosting hopfions.

A hybrid model to calculate the spin wave excitations in ferromagnetic/non-magnetic multilayers

A theoretical work based on the second quantification of spin waves in ferromagnetic/non-magnetic multilayers has been presented in this paper. This theoretical approach intended to modelling the excitation modes of spin waves at low temperature. The effect of the characteristic parameters of the system on the spin wave dispersion modes has been investigated. This study shows that spin waves located at the interfaces are at the origin of the stability/instability of the magnetic state in the studied multilayers. It also shows that the dipolar interactions, the interface anisotropy and the exchange interactions have a major influence on the energy of these modes.

Inverse “Foldover” Resonance in an Yttrium Iron Garnet Film

Nonlinear magnetic resonance is studied in an in-plane magnetized yttrium iron garnet (YIG) film. For YIG films magnetized perpendicular to the plane, the effect referred to as the foldover resonance is well known. It arises because the precession frequency increases with the deviation of the magnetization. When the field is reduced, the frequency of the precession remains resonant because the demagnetizing field decreases with the deviation of the magnetization. The signal disappears when the radio frequency pump power is insufficient to maintain a nonequilibrium state of the system. In the in-plane magnetized yttrium iron garnet film, the precession frequency decreases with an increase in the pump amplitude. Accordingly, the foldover effect arises under an increase in the field. The fundamental difference is that the precession in the latter case should be unstable with respect to the decay into spin wave modes. The deviation angles of magnetization of about 10° are reached, and the rate of decay of the uniform precession into spin waves, which depends on the deviation angle of the magnetization, is measured. This study opens up another way of achieving the magnon density corresponding to the formation of its Bose–Einstein condensate.

Spin-wave-based tunable coupler between superconducting flux qubits

Quantum computing and simulation based on superconducting qubits have achieved significant progress and entered the noisy intermediate-scale quantum (NISQ) era recently. Using a third qubit or object as a tunable coupler between qubits is an important step in this process. In this article, we propose a hybrid system made of superconducting qubit and a yttrium iron garnet (YIG) system as an alternative way to realize this. YIG thin films have spin wave (magnon) modes with low dissipation and reliable control for quantum information processing. Here, we propose a scheme to achieve strong coherent coupling between superconducting (SC) flux qubits and magnon modes in YIG thin film. Unlike the direct $\sqrt{N}$ enhancement factor in coupling to the Kittel mode and other spin ensembles, with $N$ the total number of spins, an additional spatial-dependent phase factor needs to be considered when the qubits are magnetically coupled with the magnon modes of finite wavelength. To avoid undesirable cancellation of coupling caused by the symmetrical boundary condition, a CoFeB thin layer is added to one side of the YIG thin film to break the symmetry. Our numerical simulation demonstrates avoided crossing and coherent transfer of quantum information between the flux qubit and the standing spin waves in YIG thin films. We show that the YIG thin film can be used as a tunable coupler between two flux qubits, which have a modified shape with small direct inductive coupling between them. Our results manifest that by cancellation of direct inductive coupling and indirect spin-wave couple of flux qubits we can turn on and off the net coupling between qubits. This bring magnonic YIG thin film into the field of quantum information processing.

Nonreciprocal magnetoacoustic waves in synthetic antiferromagnets with Dzyaloshinskii-Moriya interaction

The interaction between surface acoustic waves (SAWs) and spin waves (SWs) in a piezoelectric/magnetic thin film heterostructure yields potential for the realization of novel microwave devices and applications in magnonics. In the present work, we investigate the SAW-SW interaction in a Pt/Co(2 nm)/Ru(0.85 nm)/Co(4 nm)/Pt synthetic antiferromagnet (SAF) composed of two ferromagnetic layers with different thicknesses separated by a thin nonmagnetic Ru spacer layer. Because of the combined presence of interfacial Dzyaloshinskii--Moriya interaction (iDMI) and interlayer dipolar coupling fields, the optical SW mode shows a large nondegenerate dispersion relation for oppositely propagating SWs. Due to SAW-SW interaction, we observe nonreciprocal SAW transmission in the piezoelectric/SAF hybrid device. The equilibrium magnetization directions of both Co layers are manipulated by an external magnetic field to set a ferromagnetic, canted, or antiferromagnetic configuration. This has a strong impact on the SW dispersion, its nonreciprocity, and SAW-SW interaction. The experimental results are in agreement with a phenomenological SAW-SW interaction model, which considers the interlayer exchange coupling, iDMI, and interlayer dipolar coupling fields of the SWs.

Coupling of terahertz light with nanometre-wavelength magnon modes via spin–orbit torque

Spin-based technologies can operate at terahertz frequencies but require manipulation techniques that work at ultrafast timescales to become practical. For instance, devices based on spin waves, also known as magnons, require efficient generation of high-energy exchange spin waves at nanometre wavelengths. To achieve this, a substantial coupling is needed between the magnon modes and an electro-magnetic stimulus such as a coherent terahertz field pulse. However, it has been difficult to excite non-uniform spin waves efficiently using terahertz light because of the large momentum mismatch between the submillimetre-wave radiation and the nanometre-sized spin waves. Here we improve the light–matter interaction by engineering thin films to exploit relativistic spin–orbit torques that are confined to the interfaces of heavy metal/ferromagnet heterostructures. We are able to excite spin-wave modes with frequencies of up to 0.6 THz and wavelengths as short as 6 nm using broadband terahertz radiation. Numerical simulations demonstrate that the coupling of terahertz light to exchange-dominated magnons originates solely from interfacial spin–orbit torques. Our results are of general applicability to other magnetic multilayered structures, and offer the prospect of nanoscale control of high-frequency signals.

Unveiling a Pump-Induced Magnon Mode via Its Strong Interaction with Walker Modes

We observe a power-dependent anticrossing of Walker spin-wave modes under microwave pumping when a ferrimagnet is placed in a microwave waveguide that does not support any discrete photon mode. We interpret this unexpected anticrossing as the generation of a pump-induced magnon mode that couples strongly to the Walker modes of the ferrimagnet. This anticrossing inherits an excellent tunability from the pump, which allows us to control the anticrossing via the pump power, frequency, and waveform. Further, we realize a remarkable functionality of this anticrossing, namely, a microwave frequency comb, in terms of the nonlinear interaction that mixes the pump and probe frequencies. Such a frequency comb originates from the magnetic dynamics and thereby does not suffer from the charge noise. The unveiled hybrid magnonics driven away from its equilibrium enriches the utilization of anticrossing for coherent information processing.

Nonlocal Detection of Interlayer Three-Magnon Coupling.

A leading nonlinear effect in magnonics is the interaction that splits a high-frequency magnon into two low-frequency magnons with conserved linear momentum. Here, we report experimental observation of nonlocal three-magnon scattering between spatially separated magnetic systems, viz. a CoFeB nanowire and a yttrium iron garnet (YIG) thin film. Above a certain threshold power of an applied microwave field, a CoFeB Kittel magnon splits into a pair of counterpropagating YIG magnons that induce voltage signals in Pt electrodes on each side, in excellent agreement with model calculations based on the interlayer dipolar interaction. The excited YIG magnon pairs reside mainly in the first excited (n=1) perpendicular standing spin-wave mode. With increasing power, the n=1 magnons successively scatter into nodeless (n=0) magnons through a four-magnon process. Our results demonstrate nonlocal detection of two separately propagating magnons emerging from one common source that may enable quantum entanglement between distant magnons for quantum information applications.