Propagating Spin Waves Research Articles

Nonreciprocal transmission of magnetoacoustic waves in compensated synthetic antiferromagnets

We investigate the interaction between surface acoustic waves (SAWs) and spin waves (SWs) in a Pt/Co($2\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$)/Ru($0.85\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$)/Co($2\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$)/Pt compensated synthetic antiferromagnet (SAF) composed of two ferromagnetic layers with equal thicknesses separated by a thin nonmagnetic Ru spacer layer. Because of the combined presence of interlayer dipolar coupling fields and interfacial Dzyaloshinskii--Moriya interaction (iDMI), the optical SW mode shows a large nondegenerate dispersion relation for counter-propagating SWs. Due to resonant SAW-SW interaction, we observe a nonreciprocal SAW transmission in the prepared piezoelectric/SAF hybrid device. We demonstrate that the nonreciprocity of the SAW transmission in symmetric SAFs with equal thicknesses of the magnetic layers can show a substantially different characteristic behavior in comparison to asymmetric SAFs or magnetic single layers with iDMI. For the prepared SAF, the nonreciprocal shift of the magnetoacoustic resonance fields and the magnetoacoustic SW excitation efficiency depend on the external magnetic field sweep direction. For one magnetic field sweep direction and angle of the magnetic field, the resonance fields of the waves propagating in one direction are larger than for the waves propagating in the opposite direction. In addition, the magnitude of the nonreciprocal field shift is at minimum if the external magnetic field is aligned perpendicular to the SW propagation direction. The experimental results are in agreement with a phenomenological SAW-SW interaction model.

Surface properties of ferromagnetic films and spin wave modes

Ferromagnetic films are a fundamental platform in Magnonics, the area that studies spin wave propagation and its possible applications. These films have been studied for a long time experimentally and theoretically, either individually or as parts of multifilms structures. The present study delves into an issue of interest that remains to be studied in detail, which is the relation between the surface properties of these films and the spin wave propagation in them. The main idea of this work is that the frequencies of spin waves may be determined experimentally with precision and through their relation with surface properties one may theoretically validate and derive the main parameters of models that describe the behavior of the surfaces. Several parameters may be changed in the process of testing the relation between surface properties and spin waves, like an applied magnetic field orientation and strength, the angle of in-plane spin wave propagation, etc. This study uses a continuum micromagnetic model for the description of the magnetization dynamics, in this case, the surface properties enter through effective boundary conditions. Three models of surface properties are studied: uniaxial surface anisotropy, the latter combined with bulk uniaxial anisotropy, and surfaces with Dzyaloshinskii-Moriya interactions (DMI). In general, the boundary conditions affect the equilibrium magnetization in boundary layer regions close to the surfaces: an asymptotic analysis predicts their penetration lengths for reasonable surface anisotropies. For very thin films, this is quite relevant since the boundary layers are of the order of the film thickness, we propose this as a practical way to define what may be considered a very thin film. Effective physical parameters of thin films and very thin films clearly depend on the surface properties. The main effects of the surfaces on spin waves occur for angles of inclination of the applied magnetic field close to perpendicular to the plane, and they may be of significant magnitude. Several different numerical methods were used to solve for the spin waves, in the context of an orthogonality equation method.

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 selection in an ensemble of laterally and vertically coupled iron-yttrium garnet microwaveguides

Numerical micromagnetic modeling used to study the modes of propagation of spin waves and processes of power transfer in the considered arrays of microwaves in the configuration corresponding to excitation in two central channels of one of the layers of surface and inverse bulk magnetostatic spin waves is conducted. It is shown that the proposed structure performs the functions of spatial-frequency signal selection, the efficiency of which depends on the mutual orientation of the submagnetization field and the direction of wave propagation.

Resonant dynamics of three-dimensional skyrmionic textures in thin film multilayers

Skyrmions are topological magnetic solitons that exhibit a rich variety of dynamics, such as breathing and gyration, which can involve collective behavior in arrangements like skyrmion lattices. However, such localized excitations typically lie in the gap of the spin wave spectrum and do not couple to propagating modes. By combining magnetic force microscopy, broadband ferromagnetic resonance, and micromagnetics simulations, we show that in thin-film multilayers of [Pt/FeCoB/AlOx]20 a high-frequency (>12 GHz) mode accompanies the skyrmion lattice phase, which involves the coherent precession of the skyrmion cores that results in the generation of 50–80 nm wavelength spin waves flowing into the uniformly magnetized background. This observation is made possible by a Gilbert damping constant of ∼0.02, which is nearly an order of magnitude lower than in similar ultrathin materials. The simulations also reveal a complex three-dimensional spin structure of the skyrmion cores, which plays a key role for spin wave generation.

Reconfigurable Dipolar Spin-Wave Coupling in a Bilateral Yttrium Iron Garnet Structure

We report on the coupling of spin waves propagating as guided modes of yttrium iron garnet stripes. Three stripes are placed parallel to each other and separated by gaps that are small enough to provide nearest-neighbor coupling. We term this geometry ``bilateral stripes.'' The origin of the coupling is the long-ranging dynamic, stray (dipole) field of the precessing magnetization vector. We propose controlling characteristics of this coupling through variation of the static magnetization angle with respect to the main axes of the geometry. We verified the functionality of the proposed magnonic coupler with a micromagnetic simulation of spin-wave propagation along the bilateral stripes. The micromagnetic numerical simulation yielded spectra of transmission of spin waves through the device prototype. Analysis of those spectra revealed that the bilateral stripes can be used as a functional unit in planar magnonic networks---they can be employed as a directional coupler, spin-wave multiplexer, or microwave power divider. Using Brillouin light scattering spectroscopy, we experimentally demonstrated spin-wave transport along the bilateral stripes. We were able to control the spin-wave routing between the stripes (``magnetic channels'') by varying the angle of the bias magnetic field.

Identifying and Constructing Complex Magnon Band Topology.

Magnetically ordered materials tend to support bands of coherent propagating spin wave, or magnon, excitations. Topologically protected surface states of magnons offer a new path toward coherent spin transport for spintronics applications. In this work we explore the variety of topological magnon band structures and provide insight into how to efficiently identify topological magnon bands in materials. We do this by adapting the topological quantum chemistry approach that has used constraints imposed by time reversal and crystalline symmetries to enumerate a large class of topological electronic bands. We show how to identify physically relevant models of gapped magnon band topology by using so-called decomposable elementary band representations, and in turn discuss how to use symmetry data to infer the presence of exotic symmetry enforced nodal topology.

Spin wavepackets in the Kagome ferromagnet Fe3Sn2: Propagation and precursors

The propagation of spin waves in magnetically ordered systems has emerged as a potential means to shuttle quantum information over large distances. Conventionally, the arrival time of a spin wavepacket at a distance, d, is assumed to be determined by its group velocity, vg. Here, we report time-resolved optical measurements of wavepacket propagation in the Kagome ferromagnet Fe3Sn2 that demonstrate the arrival of spin information at times significantly less than d/vg. We show that this spin wave "precursor" originates from the interaction of light with the unusual spectrum of magnetostatic modes in Fe3Sn2. Related effects may have far-reaching consequences toward realizing long-range, ultrafast spin wave transport in both ferromagnetic and antiferromagnetic systems.

Self-Oscillations in a Nanogap Spin Hall Nano-Oscillator with a Perpendicularly Magnetized External Film

We study spin-current-induced magnetodynamics in a planar nanogap spin Hall nano-oscillator (SHNO) based on $\mathrm{Pt}/[\mathrm{Co}/\mathrm{Ni}{]}_{4}$ with a large perpendicular magnetic anisotropy (PMA) at in-plane field geometry. Two distinct dynamic modes are observed in the spin-torque ferromagnetic resonance (FMR) and the generated microwave spectra. The primary mode has a frequency above the FMR frequency and a significant blueshift of the frequency with the increasing current $I$, consistent with the propagating spin-wave mode. The secondary higher-frequency mode with a much weaker power intensity, discrete frequency jump, and a slight redshift of frequency is only observed at low fields below the saturation field of 2 kOe, suggesting that it is likely related to the emerged domain region with in-plane magnetization due to grain-boundary defects, which is further supported by the frequency enhancement with reducing temperature. The primary propagating mode decreases its frequency and broadens its minimum linewidth by reducing the temperature, indicating that the frequency-drift instability dominates its dynamical decoherence due to the boundary-pinning effect. Furthermore, the micromagnetic simulation reproduces the experimentally observed propagating spin-wave and in-plane domain modes, and provides their spatial characteristics. Our demonstrated propagating spin waves in a SHNO with an out-of-plane magnetization extended bilayer can facilitate long-distance mutual synchronization in the SHNO network arrays for enhancing coherence and power as spin-wave sources in magnon-based devices or spin-based neuromorphic computing.

Between waves and patterns: Spin wave freezing in films with Dzyaloshinskii-Moriya interaction

The relationship between waves and static pattern formation is an intriguing effect and remains unexplained in many areas of physics, including magnetism. We study the spin-wave-mediated spin reorientation transition (SRT) in magnetic films with uniaxial magnetic anisotropy and Dzyaloshinskii-Moriya interaction (DMI). In particular, we show that propagating spin waves can freeze in the SRT, causing periodic magnetic domains to arise, which is reminiscent of the wave amplitude distribution. This process can take place under the influence of a change in the magnetic field, but also of other parameters. Interestingly, at the SRT, DMI nonreciprocity leads to the emergence of flowing magnetization patterns, which suggests a spontaneous breaking of translational symmetry, and the formation of magnonic space-time crystals. The described phenomena are general and should take place in a large family of magnetic materials. Therefore, the results should be of great importance for the further development of spintronics and magnonics.

Propagating spin-wave spectroscopy in a liquid-phase epitaxial nanometer-thick YIG film at millikelvin temperatures

Performing propagating spin-wave spectroscopy of thin films at millikelvin temperatures is the next step toward the realization of large-scale integrated magnonic circuits for quantum applications. Here, we demonstrate spin-wave propagation in a 100 nm-thick yttrium-iron-garnet (YIG) film at temperatures down to 45 mK, using stripline nanoantennas deposited on YIG surface for electrical excitation and detection. The clear transmission characteristics over the distance of 10 μ m are measured and the extracted spin-wave group velocity and the YIG saturation magnetization agree well with the theoretical values. We show that the gadolinium-gallium-garnet (GGG) substrate influences the spin-wave propagation characteristics only for the applied magnetic fields beyond 75 mT, originating from a GGG magnetization up to 62 kA / m at 45 mK. Our results show that the developed fabrication and measurement methodologies enable the realization of integrated magnonic quantum nanotechnologies at millikelvin temperatures.

Micromagnetic study of inertial spin waves in ferromagnetic nanodots

Here we report the possibility to excite ultra-short spin waves in ferromagnetic thin-films by using time-harmonic electromagnetic fields with terahertz frequency. Such ultra-fast excitation requires to include inertial effects in the description of magnetization dynamics. In this respect, we consider the inertial Landau-Lifshitz-Gilbert (iLLG) equation and develop analytical theory for exchange-dominated inertial spin waves. The theory predicts a finite limit for inertial spin wave propagation velocity, as well as spin wave spatial decay and lifetime as function of material parameters. Then, guided by the theory, we perform numerical micromagnetic simulations that demonstrate the excitation of ultra-short inertial spin waves (20 nm long) propagating at finite speed in a confined magnetic nanodot. The results are in agreement with the theory and provide the order of magnitude of quantities observable in realistic ultra-fast dynamics experiments.

Theory of optical generation and detection of propagating magnons in an antiferromagnet

We report a theory of optical generation and detection of the propagating spin waves in antiferromagnetic materials relevant for ultrafast pump-probe experiments. We derive and solve the equations of motion for antiferromagnetic spins in response to the light-induced effective magnetic field in the linear regime. Different forms of the excitation and the properties of the generated spin waves are analyzed. We theoretically show the selective detection of the spin waves by the magneto-optical Kerr effect. The developed formalism is readily applicable to inform future experiments on antiferromagnetic optomagnonics.

Spin-wave nonreciprocity at the spin-flop transition region in synthetic antiferromagnets

We investigate the frequency nonreciprocity in CoFeB/Ru/CoFeB synthetic antiferromagnets near the spin-flop transition region, where the magnetic moments in the two ferromagnetic layers are noncollinear. Using conventional Brillouin light scattering, we perform systematic measurements of the frequency nonreciprocity as a function of an external magnetic field. At near zero magnetic field, where the antiparallel alignment of the magnetic moments in the two layers is established, we observe a significant frequency nonreciprocity of up to a few GHz, which vanishes when the relative magnetization orientation switches into the parallel configuration at a large magnetic field. For the intermediate values of the magnetic field, where the system transitions from the antiparallel to the parallel orientation, a nonmonotonous dependence of the frequency nonreciprocity is found, with a maximum frequency shift around the spin-flop critical point. This nontrivial dependence of the nonreciprocity versus field is attributed to the nonmonotonous dependence of the dynamic dipolar interaction, which is the main factor that causes asymmetry in the dispersion relation. Furthermore, we found that the sign of the frequency shift changes even without switching the polarity of the bias field. These results show that one can precisely control the nonreciprocal propagation of spin waves via field-driven magnetization reorientation.

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.

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.

Controlling the Modes of Spin Wave Propagation in an Yttrium Iron Garnet Waveguide by Local Laser Heating

Controlling the Modes of Spin Wave Propagation in an Yttrium Iron Garnet Waveguide by Local Laser Heating

Unidirectional Propagation of Spin Waves Excited by Femtosecond Laser Pulses in a Planar Waveguide

Low-energy magnonic logic circuits are an actively developing field of modern magnetism. The potential benefits of magnonics for data processing are vitally dependent on units based on non-reciprocal propagation of spin waves in analogy to semiconductor diodes and transistors in electronics. In this article, we suggest the approach to realize non-reciprocal propagation of spin waves in a ferromagnetic metallic waveguide by exciting them with femtosecond laser pulse. Using micromagnetic modeling, we show that the combination of an external magnetic field and the position of the excitation laser spot across the waveguide leads to unidirectional propagation of the excited spin-wave packet. The results are crucial for the design of hybrid magnonic-photonic circuits in future generations of data processing 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.

Hybridized Propagation of Spin Waves and Surface Acoustic Waves in a Multiferroic-Ferromagnetic Heterostructure

Coherent coupling in magnon-based hybrid systems has many potential applications in quantum information processing. Magnons can propagate in magnetically ordered materials without any motion of electrons, offering a unique method to build low-power-consumption devices and information channels free of heat dissipation. In this paper, we demonstrate the coherent propagation of hybridized modes between spin waves and Love surface acoustic waves in a multiferroic ${\mathrm{Bi}\mathrm{Fe}\mathrm{O}}_{3}$ and ferromagnetic ${\mathrm{La}}_{0.67}{\mathrm{Sr}}_{0.33}{\mathrm{Mn}\mathrm{O}}_{3}$-based heterostructure. The magnetoelastic coupling enables a giant enhancement of the strength of the hybridized mode by a factor of 26 compared to that of the pure spin waves. A short wavelength down to 250 nm is demonstrated for the hybridized mode, which is desirable for nanoscale acoustomagnonic applications. Our combined experimental and theoretical analyses represent a step towards the coherent control in hybrid magnonics, which may inspire the study of magnon-phonon hybrid systems for coherent information processing and manipulation.