Damon-Eshbach Mode Research Articles

Nonlinear three-magnon scattering in low-damping La0.67Sr0.33MnO3 thin films

Abstract Three-magnon scattering, a nonlinear process in which a high-energy magnon splits into two low-energy magnons with energy and momentum conservation, have been widely studied in magnonics community. Here, we report experimental observation of nonlinear three-magnon scattering in La0.67Sr0.33MnO3 thin films with low magnetic damping (~10-4) by all-electric and angle-resolved spin wave spectroscopy. The reflection spectra of the spin wave resonance with high excitation at Damon–Eshbach configuration demonstrate a scattering regime with gradual signal disappearance, where a magnon of Damon–Eshbach mode decays into two magnons of volume mode above threshold power (-10 dBm) of injected microwave. The nonlinear scattering is only allowed at low-field regime and calculated dispersions of dipole-exchange spin wave claim the mechanism of allowed and forbidden three-magnon scattering. The films and heterostructures of La0.67Sr0.33MnO3havebeenalready demonstrated with rich physical phenomena and great versatility, and the nonlinear magnetic dynamics of La0.67Sr0.33MnO3 thin films is revealed in this work, which offer more possibility of applications to oxide magnonics and nonlinear magnonic devices.

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.

Dipolar spin waves in uniaxial easy-axis antiferromagnets: A natural topological nodal-line semimetal

The existence of the magnetostatic surface spin waves in ferromagnets, known as Damon-Eshbach mode, was recently demonstrated to originate from the topology of the dipole-dipole interaction. In this work, we study the topological characteristics of magnons in easy-axis antiferromagnets with uniaxial anisotropy. The dipolar spin waves are found to be, driven by the dipole-dipole interaction, in a topological nodal-line semimetal phase, which hosts Damon-Eshbach-type surface modes due to the bulk-edge correspondence. The long wavelength character of dipolar spin waves makes our proposal valid for any natural uniaxial easy-axis antiferromagnet, and thus enriches the candidates of topological magnonic materials. In contrast to the nonreciprocal property in ferromagnetic case, the surface modes with opposite momentum coexist at each surface, but with different chiralities. Such a chirality-momentum or spin-momentum locking, similar to that of electronic surface states in topological insulators, offers the opportunity to design novel chirality-based magnonic devices in antiferromagnets.

Photovoltage detection of spin excitation of a ferromagnetic stripe and disk at low temperature

Photovoltage spectroscopy is a beneficial technique to investigate the dynamic properties of the spin excitations of ferromagnetic elements fabricated at the surface of a GaAs/Al0.33Ga0.67As heterojunction. This method is of particular interest for probing localized spin wave modes. The high sensitivity of the photovoltage technique arises from the high electron mobility of 2D electrons μ = 1.5 × 106 cm2 · V−1 · S−1 which enables efficient rectification of magnetic moment oscillations through the Hall effect. We report on the discrete structure of spin wave eigenmodes as a function of magnetic field orientation, the shape of Co ferromagnets, and the geometry of nanomagnets. We indicated bonding–antibonding spin waves when the static magnetic field, is parallel to the short side of the stripe at different microwave frequencies at 4 K. We also observed Damon–Eshbach modes when is parallel to the stripe. Micromagnetic simulations confirm the experimental results. We observe the discrete structure of the photovoltage for individual dots. We also investigate the effect of the magnetocrystalline anisotropy field of Co on ferromagnetic resonance. Our results demonstrate that photovoltage measurements in hybrid semiconductor-ferromagnetic structures provide a sensitive and extended tool for probing the spin waves of small magnets with a size of 80 nm.

Nanoscale X-ray imaging of spin dynamics in yttrium iron garnet

Time-resolved scanning transmission x-ray microscopy has been used for the direct imaging of spin-wave dynamics in a thin film yttrium iron garnet (YIG) with sub-200 nm spatial resolution. Application of this x-ray transmission technique to single-crystalline garnet films was achieved by extracting a lamella (13×5×0.185 μm3) of the liquid phase epitaxy grown YIG thin film out of a gadolinium gallium garnet substrate. Spin waves in the sample were measured along the Damon-Eshbach and backward volume directions of propagation at gigahertz frequencies and with wavelengths in a range between 200 nm and 10 μm. The results were compared to theoretical models. Here, the widely used approximate dispersion equation for dipole-exchange spin waves proved to be insufficient for describing the observed Damon-Eshbach type modes. For achieving an accurate description, we made use of the full analytical theory taking mode-hybridization effects into account.

Optical heterodyne imaging of magnetostatic modes in one-dimensional magnonic crystals

We demonstrate a real-space imaging of a heterodyne signal of light that is produced as a result of the Brillouin light scattering by coherently driven magnons in magnetostatic modes. With this imaging technique, we characterize surface magnetostatic modes (Damon-Eshbach modes) in a one-dimensional magnonic crystal, which is formed by patterned aluminum strips deposited on the ferromagnetic film. The modified band structures of the magnonic crystal are deduced from the Fourier transforms of the real-space images. The heterodyne imaging provides a simple and powerful method to probe magnons in structured ferromagnetic films, paving a way to investigate more complex phenomena, such as Anderson localization and topological transport with magnons.

Phase detection of spin waves in yttrium iron garnet and metal induced nonreciprocity

We report experiments which characterize spin wave propagation in a thin (111) yttrium iron garnet film for arbitrary angles between the in-plane magnetic field and the mode wavevectors. By measuring the magnetic field evolution of the phase of the wave traveling across the film, we deduce the frequency dependence of the wavevector, the dispersion relation, from which the mode velocity follows. Additionally, we observe multiple nodes in the regime of the propagating Damon-Eshbach mode; these arise from avoided crossings associated with the higher, exchange split, standing wave modes along the film normal, the positions of which correlate with the direct absorption measurements of their positions. This information allows a determination of the exchange parameter. Using this technique, we examine the nonreciprocity in spin wave propagation that results from an adjacent metal layer.

Spin-wave-induced lateral temperature gradient in a YIG thin film/GGG system excited in an ESR cavity

The lateral thermal gradient of an yttrium iron garnet (YIG) film under microwave application in the cavity of the electron spin resonance system (ESR) was measured at room temperature by fabricating a Cu/Sb thermocouple onto it. To date, thermal transport in YIG films caused by the Damon-Eshbach mode (DEM)—the unidirectional spin-wave heat conveyer effect—was demonstrated only by the excitation using coplanar waveguides. Here, we show that the effect exists even under YIG excitation using the ESR cavity—a tool often employed to realize spin pumping. The temperature difference observed around the ferromagnetic resonance field under 4 mW microwave power peaked at 13 mK. The observed thermoelectric signal indicates the imbalance of the population between the DEMs that propagate near the top and bottom surfaces of the YIG film. We attribute the DEM population imbalance to different magnetic dampings near the top and bottom YIG surfaces. Additionally, the spin wave dynamics of the system were investigated using the micromagnetic simulations. The micromagnetic simulations confirmed the existence of the DEM imbalance in the system with increased Gilbert damping at one of the YIG interfaces. The reported results are indispensable to the quantitative estimation of the electromotive force in the spin-charge conversion experiments using ESR cavities.

Measurements of long-wavelength spin waves for the magnetic field in the Damon-Eshbach, backward-volume and forward-volume geometries of an yttrium iron garnet film

We report systematic measurements of the dispersion of long wavelength spin waves for a wide range of wave vectors for the magnetic field along the three principal directions defining the forward volume, backward volume and Damon-Eshbach modes of a 9.72 μm thick film of an yttrium iron garnet obtained using lithographically patterned, multi-element, spatially resonant, antennas. Overall good agreement is found between the experimental data for the backward volume and Damon-Eshbach modes and the magnetostatic theory of Damon and Eshbach. Also, good agreement is found between the experimental data for the forward volume mode and the theory of Damon and van de Vaart.

Propagation of magnetostatic spin waves in an yttrium iron garnet film for out-of-plane magnetic fields

We have observed the propagation of spin waves across a thin yttrium iron garnet film on (1 1 1) gadolinium gallium garnet for magnetic fields inclined with respect to the film plane. Two principle planes were studied: that for H in the plane defined by the wave vector k and the plane normal, n, with limiting forms corresponding to the Backward Volume and Forward Volume modes, and that for H in the plane perpendicular to k, with limiting forms corresponding to the Damon-Eshbach and Forward Volume modes. By exciting the wave at one edge of the film and observing the field dependence of the phase of the received signal at the opposing edge we determined the frequency vs. wavevector relation, ω = ω (k), of various propagating modes in the film. Avoided crossings are observed in the Damon-Eshbach and Forward Volume regimes when the propagating mode intersects the higher, exchange split, volume modes, leading to an extinction of the propagating mode; analysis of the resulting behavior allows a determination of the exchange parameter. The experimental results are compared with theoretical simulations.

Excitation of the three principal spin waves in yttrium iron garnet using a wavelength-specific multi-element antenna

We report systematic measurements of the dispersion of long wavelength spin waves for the magnetic field along the three principal directions (supporting the forward volume, backward volume and Damon-Eshbach modes) of a 3.05 μm thick yttrium iron garnet film on a lattice-matched (111) gadolinium gallium garnet substrate obtained using a lithographically patterned, multi-element, 50 μm spatially-resonant, antenna.

Computation of Two-Port Parameters in Magnonic Devices Through Circuit-Field Coupling

This paper presents a model for the computation of two-port parameters from the configuration of a typical Magnonic device involving two coplanar waveguides. A Permalloy thin film is saturated using an appropriate dc field. The first waveguide then performs the function of excitation of spin waves by superposition of an RF field. The second waveguide detects the excited wave vector in Damon–Eshbach mode at resonance frequency. The model is solved using the generalized mean residual method for a linearized approximation of the Landau–Lifshitz–Gilbert equation coupled with Maxwell equations. Complex impedance matrices from the two-port network are extracted for both uniformly saturated and non-uniform initial ground states. Findings report low absorption potential and shift in resonance frequency for highly non-uniform ground states. Validation of the model for uniformly saturated ground states is performed against experimental and semi-analytical findings, showing good agreement.

Observation of spin-wave Doppler shift in Co90Fe10/Ru micro-strips for evaluating spin polarization

The current-induced spin-wave Doppler shift has been investigated for Co90Fe10 films, with and without under- and overlayers of Ru, aiming to obtain quantitative insights into the value of spin polarization of the diffusive electrical currents flowing in this material. This extends the use of spin-wave Doppler shift spectroscopy beyond the study of permalloy to other soft magnetic materials suitable for use in spintronic applications such as racetrack memories. The Damon-Eshbach spin-wave mode was employed, and a control experiment of permalloy yielded a value of spin polarization of P = 0.44 ± 0.03 for that material. An extended method to properly evaluate spin-wave Doppler shifts is developed that takes account of the non-negligible Oersted fields that are generated by the current density asymmetry caused by conducting under- or overlayers. The values of spin polarization for various Co90Fe10-based structures are found to lie in the range of 0.3–0.35, only slightly less than in permalloy.

Investigation of the unidirectional spin heat conveyer effect in a 200 nm thin Yttrium Iron Garnet film.

We have investigated the unidirectional spin wave heat conveyer effect in sub-micron thick yttrium iron garnet (YIG) films using lock-in thermography (LIT). Although the effect is small in thin layers this technique allows us to observe asymmetric heat transport by magnons which leads to asymmetric temperature profiles differing by several mK on both sides of the exciting antenna, respectively. Comparison of Damon-Eshbach and backward volume modes shows that the unidirectional heat flow is indeed due to non-reciprocal spin-waves. Because of the finite linewidth, small asymmetries can still be observed when only the uniform mode of ferromagnetic resonance is excited. The latter is of extreme importance for example when measuring the inverse spin-Hall effect because the temperature differences can result in thermovoltages at the contacts. Because of the non-reciprocity these thermovoltages reverse their sign with a reversal of the magnetic field which is typically deemed the signature of the inverse spin-Hall voltage.

Direct observation of isolated Damon-Eshbach and backward volume spin-wave packets in ferromagnetic microstripes.

The analysis of isolated spin-wave packets is crucial for the understanding of magnetic transport phenomena and is particularly interesting for applications in spintronic and magnonic devices, where isolated spin-wave packets implement an information processing scheme with negligible residual heat loss. We have captured microscale magnetization dynamics of single spin-wave packets in metallic ferromagnets in space and time. Using an optically driven high-current picosecond pulse source in combination with time-resolved scanning Kerr microscopy probed by femtosecond laser pulses, we demonstrate phase-sensitive real-space observation of spin-wave packets in confined permalloy (Ni80Fe20) microstripes. Impulsive excitation permits extraction of the dynamical parameters, i.e. phase- and group velocities, frequencies and wave vectors. In addition to well-established Damon-Eshbach modes our study reveals waves with counterpropagating group- and phase-velocities. Such unusual spin-wave motion is expected for backward volume modes where the phase fronts approach the excitation volume rather than emerging out of it due to the negative slope of the dispersion relation. These modes are difficult to excite and observe directly but feature analogies to negative refractive index materials, thus enabling model studies of wave propagation inside metamaterials.

Tailoring dynamic magnetic characteristics ofFe60Al40films through ion irradiation

Magnetization dynamics in $\mathrm{F}{\mathrm{e}}_{60}\mathrm{A}{\mathrm{l}}_{40}$ thin films possessing depth-varying saturation magnetization (${M}_{\mathrm{S}}$) have been studied experimentally and theoretically. Variation in ${M}_{\mathrm{S}}$ was achieved by irradiation of 40 nm thick, chemically ordered (B2 phase) $\mathrm{F}{\mathrm{e}}_{60}\mathrm{A}{\mathrm{l}}_{40}$ films with $\mathrm{N}{\mathrm{e}}^{+}$ ions with energies between 0--30 keV. The initial B2 phase is paramagnetic, and as the penetrating ions cause chemical disordering, the ion-affected region transforms to the ferromagnetic A2 phase. The effective ferromagnetic thickness and the depth of the A2/B2 phase boundary depend on the ion energy ($E$); the effective thicknesses are 8.5 and 40 nm, respectively, for $E=2.5$ and 30 keV. Thermally excited spin waves in films with varying effective ferromagnetic thicknesses were analyzed by employing Brillouin light scattering and vector network analyzer ferromagnetic resonance spectroscopy. The analytical calculations are in good agreement with the experimental values and show that the observed spin-wave modes are directly related to the effective ferromagnetic thickness; films irradiated with $E\phantom{\rule{0.28em}{0ex}}<\phantom{\rule{0.28em}{0ex}}15\phantom{\rule{0.28em}{0ex}}\mathrm{keV}$ only show the Damon-Eshbach mode, whereas for $15\phantom{\rule{0.28em}{0ex}}\ensuremath{\le} E\phantom{\rule{0.28em}{0ex}}<\phantom{\rule{0.28em}{0ex}}20\phantom{\rule{0.28em}{0ex}}\mathrm{keV}$, an additional lower frequency standing spin-wave mode is observed. In films irradiated with $E \ensuremath{\ge}\phantom{\rule{0.28em}{0ex}}20\phantom{\rule{0.28em}{0ex}}\mathrm{keV}$, the Damon-Eshbach mode is observed to lie between two standing spin-wave modes. Furthermore, the A2/B2 phase boundary can be shown to act as an asymmetric pinning site. Controlling the depth of the phase boundary by varying the ion energy can be a path to manipulate spin-wave propagation in materials displaying the phenomenon of disorder induced ferromagnetism.

A scenario for magnonic spin-wave traps.

Spatially resolved measurements of the magnetization dynamics on a thin CoFeB film induced by an intense laser pump-pulse reveal that the frequencies of resulting spin-wave modes depend strongly on the distance to the pump center. This can be attributed to a laser generated temperature profile. We determine a shift of 0.5 GHz in the spin-wave frequency due to the spatial thermal profile induced by the femtosecond pump pulse that persists for up to one nanosecond. Similar experiments are presented for a magnonic crystal composed of a CoFeB-film based antidot lattice with a Damon Eshbach mode at the Brillouin zone boundary and its consequences are discussed.

Spin pumping and the inverse spin-hall effect via magnetostatic surface spin-wave modes in Yttrium-Iron garnet/platinum bilayers

Spin pumping at a boundary between a yttriumiron garnet (YIG) film and a thin platinum (Pt) layer is studied under conditions in which a magnetostatic surface spin wave (MSSW, or DamonEshbach mode) is excited in YIG by a narrow strip-line antenna. It is shown that the voltage created by the inverse spin-Hall effect (ISHE) in Pt is strongly dependent on the wavevector of the excited MSSW. For YIG film thicknesses of 41 and 0.9m, the maximum ISHE voltage corresponds to the maximum of efficiently excited MSSW wavevectors and does not coincide with the maximum of absorbed microwave power. For a thinner (0.175m) YIG film, the maximum of the ISHE voltage moves closer to the ferromagnetic resonance and almost coincides with the region of the maximum microwave absorption. We show that the effect is related to the change in the thickness profile and the wavenumber spectrum of the excited MSSW taking place when the YIG film thickness is increased.

Magnetoelastic wave tunneling via a gap between ferroelectric crystals with relative longitudinal displacement

The tunneling of a plane monochromatic acoustic wave via a gap between two ferromagnetic crystals exhibiting relative longitudinal displacement has been studied. It is shown that, at a gap width comparable with the wavelength, the acoustic wave can exhibit complete transmission at the Damon-Eshbach mode frequency. If the gap width is much smaller than the wavelength, the complete transmission takes place at two resonance frequencies. Allowance for the longitudinal displacement of one crystal leads in all cases to violation of the resonance conditions, which results in a significant decrease in the transmission coefficient. The greater the velocity of crystal displacement, the stronger the decrease in the acoustic wave transmission though the gap between ferromagnetic crystals.

Spin wave quantization in continuous film with stripe domains

We investigated the spin wave dynamics of CoFeSiB film, which has a stripe domain structure at a low magnetic field region (<1 kOe). We measured the spin wave excitation spectra by employing Brillouin light scattering. Abnormal field dependence and dispersion relations were observed, and they are similar to spin wave quantization in laterally confined magnetic structures such as arrays of magnetic nanowires. The observed spin wave excitation spectra must be interpreted with spin wave quantization such as Damon–Eshbach mode separation. It was found that the spin wave quantization is related to the stripe magnetic domain structure in continuous film. The physical origin of the quantization is the partial reflection of the propagating spin wave at the periodic stripe domain boundaries.