Perpendicular Standing Spin Wave Research Articles

Manipulation of high-frequency spin waves in ferromagnetic thin films via magnetic torques induced by ultrafast demagnetization

Spin-based technologies demand the effective excitation and control of high-frequency spin waves in order to increase the operational speed of magnonic logic circuits. An available option for the high-frequency spin wave is the perpendicular standing spin waves (PSSWs) in ferromagnetic thin films. However, the practical utilization of a PSSW is still challenging due to a few unsolved critical issues such as its relatively low amplitude and simultaneous excitation of other PSSW modes. Here, efficient excitation and control of a first-order PSSW mode are demonstrated in Ni80Fe20 thin films using a double-laser-pulse scheme. Based upon our experimental and theoretical investigations, it is found that the precession amplitudes of the Kittel and PSSW modes show strong dependence on equivalent torques (i.e., the averaged torques during fast relaxation process after the second pulse excitation) applied to these two modes. Thus, selective excitation and amplification of the first-order PSSW mode can be realized by manipulating the equivalent torque, i.e., introducing a second laser pulse with an appropriate arrival time and laser fluence. Moreover, the spectral tuning of this single PSSW mode can be achieved by proportionately adjusting the laser fluence of two pump pulses. These findings may pave the way for the realization and construction of future high-performance spintronic devices.

Interlayer coupling of the Kittel mode and the perpendicular standing spin wave in magnetic multilayers

Magnetic/nonmagnetic multilayers are complex and fascinating systems with immense potential for various technological applications. To meet the requirements of spintronic devices, it is essential to comprehend their magneto-dynamic behaviour and interlayer coupling mechanisms. Here, we systematically study the static and dynamic coupling of different spin precession modes, including the Kittel mode and the perpendicular standing spin wave (PSSW) mode, between permalloy (Py) layers with variable thicknesses. Our main focus centers around three distinct types of magnetic multilayers featuring different spacers (Ta, Pt, Ru). According to the ferromagnetic resonance results, we find that the nonmagnetic layers inside these structures display distinct magnetic static and dynamic characteristics over varying ranges of magnetic layer thickness. When the thickness of the Py layer is 10 nm, it demonstrates a ferromagnetic exchange coupling between the Py layers via the Ta and Pt layers. Conversely, when the spacer layer is composed of Ru, a clear antiferromagnetic coupling is detected. All of the multilayers, however, exhibit increased ferromagnetic exchange coupling as the thickness of the Py layer increases. Furthermore, it is found that the Pt spacer layer still plays a crucial role in dynamic interlayer coupling in the uniform precession mode, while the Py/Ru multilayer exhibits a stronger coupling in the non-uniform precession mode.

Excitation and modulation of exchange spin waves in CoFeB films

Spin waves in nanostructures have great potential to be future spintronic information carriers. Here, we report the excitation and modulation of exchange spin waves in Co20Fe60B20 (CoFeB) films by varying magnetic anisotropy. In a 50 nm-thick CoFeB film, the effective excitation of perpendicular standing spin waves (PSSWs) is achieved due to the uniaxial anisotropy induced by oblique sputtering. Additionally, patterning the films into a periodic array of rectangles enables the excitation of both exchange-dominated surface spin waves and PSSWs, with the modulation of spin waves achievable by altering the length–width ratio of the rectangle. It is worth noting that PSSWs are present in the easy axis, whereas surface spin waves are observed in the hard axis, emphasizing the significant influence of shape anisotropy on spin waves. Furthermore, we demonstrate the existence of PSSW in a CoFeB/Pb(Mg1/3Nb2/3)O3-Pb0.7Ti0.3O3 (PMN-PT) multiferroic heterostructure. The resonance field of PSSW can be shifted by applying electric fields, which originates from the strain anisotropy driven by the piezoelectric effect. These findings are expected to provide valuable insights for the development of energy-efficient spintronic devices and high-frequency data processing systems.

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.

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.

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.

Exchange stiffness constant determination using multiple-mode FMR perpendicular standing spin waves

The exchange stiffness constant is recognized as one of the fundamental properties of magnetic materials, though its accurate experimental determination remains a particular challenge. In thin films, resonance measurements exploiting perpendicular standing spin waves (PSSWs) are increasingly used to extract this parameter, typically through a determination of the first-order PSSW mode. Here, we present a systematic study of multiple PSSW modes in NiFe films, where both the sample thickness and the cap layer material are varied. The results show that a simple analysis based on the Kittel rigid pinning model yields an exchange stiffness constant that varies with thickness, mode number, and capping layer material. This finding is clearly inconsistent with physical expectation that the exchange stiffness constant of a material is single valued for a particular set of thermodynamic conditions. Using a more general exchange boundary condition, we show, through a comprehensive set of micromagnetic simulations, that a dynamic pinning mechanism originally proposed by Wigen is able to reproduce the experimental results using a single value of Aex. Our findings support the utility of short wavelength, higher order PSSWs to determine the Aex of thin films and show that the value of Aex obtained has a weak dependency on the material immediately adjacent to the magnetic layer.

Magnetization dynamics affected by phonon pumping

"Pumping" of phonons by a dynamic magnetization promises to extend the range and functionality of magnonic devices. We explore the impact of phonon pumping on room-temperature ferromagnetic resonance (FMR) spectra of bilayers of thin yttrium iron garnet (YIG) films on thick gadolinium gallium garnet substrates over a wide frequency range. At low frequencies the Kittel mode hybridizes coherently with standing ultrasound waves of a bulk acoustic resonator to form magnon polarons that induce rapid oscillations of the magnetic susceptibility, as reported before. At higher frequencies, the phonon resonances overlap, merging into a conventional FMR line, but with an increased line width. The frequency dependence of the increased line broadening follows the predictions from phonon pumping theory in the thick substrate limit. In addition, we find substantial magnon-phonon coupling of a perpendicular standing spin wave (PSSW) mode. This evidences the importance of the mode overlap between the acoustic and magnetic modes, and provides a route towards engineering the magnetoelastic mode coupling.

Curvilinear spin-wave dynamics beyond the thin-shell approximation: Magnetic nanotubes as a case study

Surface curvature of magnetic systems can lead to many static and dynamic effects which are not present in flat systems of the same material. These emergent magnetochiral effects can lead to frequency nonreciprocity of spin waves, which has been shown to be a bulk effect of dipolar origin and is related to a curvature-induced symmetry breaking in the magnetic volume charges. So far, such effects have been investigated theoretically mostly for thin shells, where the spatial profiles of the spin waves can be assumed to be homogeneous along the thickness. Here, using a finite-element dynamic-matrix approach, we investigate the transition of the spin-wave spectrum from thin to thick curvilinear shells, at the example of magnetic nanotubes in the vortex state. With increasing thickness, we observe the appearance of higher-order radial modes which are strongly hybridized and resemble the perpendicular-standing spin waves (PSSWs) in flat films. Along with an increasing dispersion asymmetry, we uncover the curvature-induced nonreciprocity of the mode profiles. This is explained in a very simple, general picture for thick curvilinear shells, considering the inhomogeneity of the emergent geometric volume charges along the thickness of the shell. Such curvature-induced mode-profile asymmetry also leads to nonreciprocal hybridization, which can facilitate unidirectional spin-wave propagation. With that, we also show how curvature allows for nonlinear three-wave splitting of a higher-order radial mode into secondary modes which can also propagate unidirectionally. We believe that our study provides a significant contribution to the understanding of the spin-wave dynamics in curvilinear magnetic systems, and also advertises these for novel magnonic applications.

Experimental observation of interlayer perpendicular standing spin wave mode with low damping in skyrmion-hosting [Pt/Co/Ta]10 multilayer

An interlayer perpendicular standing spin wave mode is observed in the skyrmion-hosting [Pt/Co/Ta]10 multilayer by measuring the time-resolved magneto-optical Kerr effect. The observed interlayer mode depends on the interlayer spin-pumping and spin transfer torque among the neighboring Co layers. This mode shows monotonically increasing frequency-field dependence which is similar to the ferromagnetic resonance mode, but within higher frequency range. Besides, the damping of the interlayer mode is found to be a relatively low constant value of 0.027 which is independent of the external field. This work expounds the potential application of the [heavy-metal/ferromagnetic-metal] n multilayers to skyrmion-based magnonic devices which can provide multiple magnon modes, relatively low damping, and skyrmion states, simultaneously.

Exchange spin waves in thin films with gradient composition

We report investigation of ferromagnetic resonance phenomenon in ferromagnetic thin films with essentially non-uniform composition. Epitaxial Pd-Fe thin film with linear distribution of Fe content across the thickness is used as the model material. Anomalous perpendicular standing spin waves are observed and quantified using the collective dynamic equation. Numerical analysis yields the exchange stiffness constant for diluted Pd-Fe alloy $D=2A/\mu_0M_s=15$~T$\cdot$nm$^2$ and the ratio of the effective magnetization to the saturation magnetization $M_{eff}/M_s=1.16$. It is demonstrated that, overall, engineering of thin films with non-uniform composition across the thickness can be used for high-frequency or low-field magnonic operations using exchange spin waves.

Hybrid Magnonics for Short-Wavelength Spin Waves Facilitated by a Magnetic Heterostructure

Recent research on hybrid magnonics has been restricted by the long magnon wavelengths of the ferromagnetic resonance modes. We present an experiment on the hybridization of 250-nm-wavelength magnons with microwave photons in a multimode magnonic system consisting of a planar cavity and a magnetic bilayer. The coupling between magnon modes in the two magnetic layers, i.e., the uniform mode in Permalloy and the perpendicular standing spin waves (PSSWs) in yttrium iron garnet, serves as an effective means for exciting short-wavelength PSSWs, which is further hybridized with the photon mode of the microwave resonator. The demonstrated magnon-photon coupling approaches the superstrong coupling regime, and can even be achieved near zero bias field.

Femtosecond laser comb driven perpendicular standing spin waves

We study femtosecond laser comb driven sustained and coherent spin wave (SW) generation in Permalloy films over a thickness range of d = 40–100 nm. A simple rapid demagnetization model describes the dependence of the observed SW intensity on laser power for all film thicknesses. In the thicker films, we observe laser comb excited perpendicular standing spin waves up to the third order and to 18 multiples of the 1 GHz laser repetition rate. Our results demonstrate the versatility of femtosecond combs as contact-less SW point sources over a wide range of film thickness and type of SW modes.

Magnetic polarization selective spectroscopy of magnetic thin films probed by wideband crossed microstrip circuit in GHz regime.

We have developed a method to obtain wideband magnetic polarization selective spectra of magnetic thin films by using circularly polarized microwaves. The combination of an over-coupled crossed microstrip resonator and a hybrid coupler enables broadband and accurate control of circularly polarized microwaves. The performance of the present method was demonstrated with an yttrium iron garnet thin film, and we detected the magnetic polarization dependence of a Kittel mode and a perpendicular standing spin wave mode in the range of 3-20GHz. In addition, three types of crossed microstrip resonators were systematically studied with experiments and simulations. As a result, we achieved the polarization efficiency of 80% and found how to optimize the crossed microstrip resonator depending on the desired sensitivity, bandwidth, or sample size.

Effective exchange interaction for terahertz spin waves in iron layers

The exchange stiffness is a central material parameter of all ferromagnetic materials. Its value controls the Curie temperature as well as the dynamic properties of spin waves to a large extent. Using ultrashort spin current pulses we excite perpendicular standing spin waves (PSSW) in ultrathin epitaxial iron layers at frequencies of up to 2.4 THz. Our analysis shows that for the PSSWs the observed exchange stiffness of iron is about 20% smaller compared to the established iron bulk value. In addition, we find an interface-related reduction of the effective exchange stiffness for layers with the thickness below 10 nm. To understand and discuss the possible mechanisms of the exchange stiffness reduction we develop an analytical one-dimensional model. In doing so we find that the interface induced reduction of the exchange stiffness is mode dependent.

Measuring spin wave resonance in Ni100 x Fe x films: compositional and temperature dependence

We study the composition and temperature dependence of the spin wave resonance in NiFe films, where, x is 40% or below, with a thickness of 100 nm using a temperature variable broadband ferromagnetic resonance (FMR) spectroscopy. From the uniform FMR mode, the saturation magnetization and the Gilbert damping are measured, and using the first perpendicular standing spin wave mode, the exchange stiffness constant is determined. At lower temperatures, we measure an increase of both and A, while α shows a very weak temperature dependence. We find that follows perfectly Bloch’s law, while A is best described by a T 2 law. Additionally, we measure a linear increase in and A with the increase of Fe content in films, while α strongly decreases. The compositional variation of α and A can be ascribed to the increase of in Fe-rich films. Furthermore, we estimate the exchange length () in NiFe films. We find that is temperature independent, however, a strong decrease of is measured in Fe-rich films. This reduction is inversely proportional to .

Noncollinear Remanent Textures Induced by Surface Spin Flop in Synthetic Antiferromagnets with Perpendicular Anisotropy

The surface spin flop, observed in synthetic antiferromagnets (SAFs) with uniaxial anisotropy and strong antiferromagnetic (AF) interlayer exchange coupling, can be considered as a laterally homogeneous, vertical AF domain wall pushed into the SAF from either the top or the bottom in the presence of a strong external vertical magnetic field. As a result, the AF domain wall can be described as a one-dimensional entity. In this work, we present a concept to stabilize laterally homogeneous vertical AF domain walls by local variation of the perpendicular magnetic anisotropy in $\mathrm{Co}/\mathrm{Pt}$-based SAFs. Our approach not only allows the stabilization of the vertical AF domain wall in the absence of any external magnetic field, but furthermore enables a deterministic selection among four different remanent states, each one stable within a broad external magnetic field range of almost one tesla. We also demonstrate an extension to our concept by stabilizing two coexisting vertical AF domain walls, thus yielding a system with a total of six different selectable (and reprogrammable) remanent states. The controlled stabilization of noncollinear AF textures in the form of vertical AF domain walls at remanence could be used as an infrastructure for propagating spin waves within the AF domain wall itself, as well as for tuning the dynamic behavior of perpendicular standing spin wave modes existing vertically across the SAF.

Multiple order spin-wave resonance in composition gradient sputtering FeCoB thin films

FeCoB films with different B doping contents and different thicknesses were deposited by composition gradient sputtering. The results show that in-plane anisotropy fields and exchange constants change with the increasing B contents and increasing thickness, respectively. Both results of the composition-gradient films and the thickness-dependent films and the micromagnetic simulation indicate that multiple order spin-wave resonances are easy to obtain in the films with the large in-plane anisotropy field. We observed four resonance peaks including three perpendicular standing spin waves. The hysteresis loop and magnetic domain results indicate that such films also have good magnetic softness and an in-plane homogeneous domain structure.

One-dimensional optomagnonic microcavities for selective excitation of perpendicular standing spin waves

Here we propose a method of the excitation of perpendicular standing spin waves (PSSWs) of different orders in an optomagnonic microcavity by ultrashort laser pulses. The microcavity is formed by a magnetic dielectric film surrounded by dielectric non-magnetic Bragg mirrors. Optical cavity modes in the magnetic layer provide concentration and strongly non-uniform distribution of the optical power over the layer thickness and therefore induce the effective field of the inverse Faraday effect also spatially non-uniform. It results in excitation of PSSWs. PSSWs whose wavevector is closest to the wavevector characterizing distribution of the inverse Faraday effect field are excited most efficiently. Consequently, a key advantage of this approach is a selectivity of the PSSW excitation which allows to launch PSSWs of required orders only. All-optical operation of the optomagnonic cavities opens new possibilities for their applications for quantum technologies.

Selective and Tunable Excitation of Standing Spin Waves in a Magnetic Dielectric Film by Optical Guided Modes

We propose an approach for wavelength-selective excitation of perpendicular standing spin waves by optical guided modes in a magnetic dielectric film. TM-polarized guided waves with elliptical polarization induce an effective magnetic field due to the inverse transverse magneto-optical Kerr effect (ITMOKE). The ITMOKE is similar to the inverse Faraday effect, except for the induced magnetic field direction that is oriented in the film plane perpendicular to guided-mode propagation. Switching between different guided modes by tuning the wavelength or angle of the laser pulse significantly modifies the spatial distribution of the induced ITMOKE field and, therefore, selectively launches the standing spin-wave modes of different orders. Consequently, one may perform a tunable optical excitation of a certain spin-wave mode via a femtosecond laser pulse of the corresponding wavelength. The proposed approach broadens the spin-wave manipulation capabilities via optical means.