Spin-wave Frequency Research Articles

Influence of local Dzyaloshinskii–Moriya interaction on spin waves in symmetrical heavy metal/ferromagnet/heavy metal multilayer

Abstract In a heavy metal/ferromagnet/heavy metal multilayer with inversion symmetry, the total interlayer Dzyaloshinskii–Moriya interaction (iDMI) is expected to be absent while the local iDMI constants for the top and bottom FM atomic layers can still be nonzero. This study investigates the influence of local iDMI on spin waves in this structure, in which the FM medium consists of two atomic layers with opposite local iDMI at the bottom HM/FM interface and the top FM/HM interface. Theoretical analysis and simulations are conducted to examine the spin-wave dynamics and propagation in the symmetrical sandwich structure. The results show that the local iDMI decreases the characteristic frequency of spin waves, indicating a regulation of spin wave propagation by iDMI and shows the asymmetry of spin-wave propagation between the two FM atomic layers due to iDMI. This work paves the way for deep exploration of spin waves in such structures and offers valuable insights for subtle magnetic interactions in other symmetrical multilayers.

Spin-wave resonance frequency and quantum fluctuation of the (anti)ferri-(anti)ferrimagnetic double-layer superlattice

The Hamiltonian of a four-sublattice simple cubic superlattice was solved by applying the linear spin-wave theory and the retarded Green's function technique. This study focused on the spin-wave resonance frequency, energy gap, sublattice magnetization, and quantum fluctuations of the system. The results show that the spin quantum number, interlayer (intralayer) exchange couplings, and intralayer anisotropy have a significant influence. In the ground state, the magnetizations of the sublattices are smaller than their spin quantum numbers, indicating the existence of quantum zero-point vibrations in the (anti)ferrimagnetic-(anti)ferrimagnetic bilayer system.

Real-time observation of coherent spin wave handedness

Magnonics, a crucial domain in information science and technology, utilizes spin waves in magnets as efficient information carriers. While antiferromagnets have been suggested for versatile magnonic platform because of the coexistence of right- and left-handed spin waves, their energetic degeneracy poses challenges for observation through spectral measurements, limiting their applicability. Recent observations of distinct spin wave handedness within the gigahertz regime have reported but, are yet to be demonstrated in terahertz (THz) frequencies of antiferromagnetic spin waves. Most of all, the coherence of spin waves is a key aspect of quantum information. Here, employing THz time-domain spectroscopy—a direct, precise, and easy probe for monitoring coherent spin wave dynamics—we discern chiral antiferromagnetic spin waves of opposite phase windings in the time domain, noting their handedness reversal across the angular momentum compensation temperature in ferrimagnets. We establish a principle for directly measuring the handedness of coherent antiferromagnetic spin waves in ferrimagnets with net magnetic moment M ≠ 0 but angular momentum L = 0. Our multidimensional access in the time and spectral domain enables the accurate determination of critical temperature and the dynamic observation of coherent chiral spin waves simultaneously in a single experiment, with potential applications in exploring other quantum chiral entities.

Collective spin waves in RKKY interlayer-coupled Ni80Fe20/Ru/Ni80Fe20 nanowire arrays

We report on a comprehensive investigation of collective spin waves in Ruderman–Kittel–Kasuya–Yosida (RKKY) interlayer-coupled Ni80Fe20 (10 nm)/Ru(1.0 nm)/ Ni80Fe20 (10 nm) nanowire (NW) arrays. We employed Brillouin light scattering to probe the field- and wavevector-dependences of the spin-wave frequency spectra. The acquired data were subsequently analyzed and interpreted within the framework of a microscopic Hamiltonian-based method, enabling a detailed understanding of the observed spin-wave behavior. We observed the propagation of Bloch-type collective spin waves within the arrays, characterized by distinct magnonic bandwidths that stem from the combined influence of RKKY interlayer and inter-NW dynamical dipolar interactions.

A spin-wave frequency demultiplexer based on YIG nanowaveguides intersecting at a small angle

We experimentally demonstrate a simple design for a spin-wave frequency demultiplexer based on submicrometer-width yttrium iron garnet waveguides intersecting at an angle of 30°. We show that, depending on the frequency, spin waves excited in the input arm of the device are predominantly directed to one of the two output arms. This spin-wave routing is characterized by a large extinction ratio of about 10. The frequency response of the demultiplexer can be efficiently controlled by changing the static magnetic field and the geometry of the device. Due to the small intersection angle and symmetry of the device, its operation does not require conversion between different types of spin-wave modes. This results in a high efficiency of the device and allows its facile integration into magnonic networks for complex signal processing and computing with spin waves.

Magnetoelectric coupling in Ba:Pb(Zr,Ti)O3/Co40Fe40B20 nanoscale waveguides studied by propagating spin-wave spectroscopy

In this study, we report on the characterization of the magnetoelectric coupling coefficient in Ba-substituted Pb(Zr, Ti)O3/Co40Fe40B20 (BPZT/CoFeB) nanoscaled waveguides with lateral dimensions of 700 nm using propagating spin-wave spectroscopy. The characterization was conducted in a Damon–Eshbach configuration to maximize the magnetoelastic coupling strength, as predicted by strain distribution calculations using finite element simulations. The spin-wave resonance frequency is controlled by applying bias voltages on the magnetoelectric waveguide. The magnitude of the frequency shift was correlated with the strength of the magnetoelastic field, which reached a maximum value of 5.71 mT in our experiments. In addition, the results demonstrated that the coupling coefficient behavior is associated with the hysteretic ferroelectric nature of BPZT, reaching a maximum value of 1.69 mT/V.

Left-handed polarized spin waves induced by spin polarized electric currents in ferromagnetic domain walls

Polarization refers to the orientation of the wave oscillation which is a fundamental property of wave. It has been used widely to encode information in photonics and phononics. In magnonics, spin wave also has been used for transmitting and processing information. However, exploiting the spin wave polarization to design devices has not been achieved yet in ferromagnets as only the right-handed polarized spin waves can be accommodated in ferromagnets. Our eariler study suggests that the left-handed polarized spin waves can be introduced into ferromagnets by appling a spin-polarized electric current, thus making it possible to design spin wave devices with polarization encoding. But the critical current needed to induce left-handed polarized spin wave in a uniformly magnetized ferromagnet is too high to be realized experimentally. Magnetic domain wall can serve as spin wave guide, and the cutoff frequency of spin wave in a domain wall approaches zero. In this work, the dispersion relationship and propagation characteristics of spin wave in a Bloch domain wall are studied based on the Landau-Lifshitz equation in the presence of a spin-polarized electrical current. It is found that the stable left-handed spin wave can be generated in the domain wall with only a small current density. Micromagnetic simulations confirm the theoretical analysis results. In addition, due to the different excitation efficiencies and spin transfer torque induced propagating nonreciprocity of left- and right-handed polarized spin wave, it is possible to excite selectively the left- and right-handed polarized spin wave, as well as nearly linearly polarized spin waves. This study provides a practical and feasible solution for designing spin wave devices based on the polarization coding technique.

The influence of the demagnetizing field on the concentration of spin wave energy in two-dimensional magnonic crystals

We use the Plane Wave Method to theoretically study thin-film magnonic crystals (MCs) composed of two very common magnetic materials: cobalt and permalloy. In both cases, we consider Co inclusions in the Py matrix and Py inclusions in the Co matrix. An external magnetic field is applied in the plane of the structure, leading to the formation of a demagnetizing field at the interface between the inclusions and matrix. Previous studies have shown that this field strongly affects the spectrum of spin waves, including the position and width of bandgaps. In this study, we exploit the in-plane squeezing of the MC structure to enhance the demagnetizing field. This results in the transfer of low-frequency spin waves from Py to Co, affecting the energy distribution (i.e., the spin-wave profile). The change in the concentration of spin-wave profiles leads to certain peculiarities in the spin-wave frequency spectrum. These include modes repulsion caused by hybridization, which in turn leads to the reordering of modes in the spectrum.

Verification of spinwave excitation in coaxial gyromagnetic nonlinear transmission lines.

The knowledge of physical mechanism of microwave generation in coaxial gyromagnetic nonlinear transmission lines (GNLTLs) is not complete up until now, especially the action of spinwave excitation during this process. In this paper, control experiments on different groups of GNLTLs with a single variable of NiZn ferrite material spinwave linewidth ΔHk are proposed as an indirect way to demonstrate this microscopic process. Comparative analyses of different groups of GNLTL experimental results are conducted to clarify the existence and effect of spinwave excitation. Theoretical treatment of conditions of spinwave excitation in GNLTLs is derived to explain the experimental results. It is illustrated that spinwave can be excited when the synchronism condition between the working frequency of GNLTL and the spinwave frequency spectrum is satisfied. The unstable spinwave excitation will consume the RF energy of GNLTLs heavily and cause a rapid decrease in RF oscillation.

High-resolution Brillouin light scattering study on Ti/Au/Co/Ni multilayer

The topic of this paper addresses the Brillouin light scattering (BLS) study of the spin-wave and surface acoustic wave dynamics in the multilayer consisting of Ti/Au/Co/Ni deposited on Si substrate. We make the quantitative analysis of spin-wave frequency under a range of wave vectors to determine the dispersion relation and to study the effect of the magnetic field. These findings were correlated with theoretical models to determine the magnetic system parameters, such as magnetization, Lande g factor, exchange stiffness constant etc. In addition to this, we have conducted finite element method based simulations to understand the nature of surface phonons and to determine the elastic tensor parameters for the Ti/Au/Co/Ni layer from the fitting of simulation results with the experiment data points.

Learning Trajectories from Spin-Wave Dynamics

The efficacy of a physical reservoir computer model based on traveling spin waves in a spin-wave delay-line active-ring resonator was demonstrated recently. In the present work, we investigate how this neuromorphic device can be adapted for sensing applications. In this ``reservoir computing for sensing'' framework, we exploit strong coupling of the physical reservoir to its environment to utilize the reservoir as a sensing element. The dynamics of traveling spin waves in delay-line active rings are strongly dependent on the magnetic field and carrier frequency of those spin waves. Treating the spin-wave frequency as an environmental variable, we excite the active ring into different dynamical states by modulating the carrier frequency of a drive signal of microwave pulses injected into the ring. Training a linear regression on the time-multiplexed output from the ring allows the periodic amplitude patterns of the spin waves to be mapped reproducibly onto two-dimensional trajectories, representing periodic ``behavioral'' targets. Our work demonstrates the versatility of a magnonic resonator as a multipurpose computing and sensing device.

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.

Spin Wave Spectra in Pseudoperovskite Manganites with Superexchange Interaction Competition

In compounds La1/3Ca2/3MnO3 and BiMnO3, a calculation of spin-wave dispersion dependences along pseudoperovskite directions of reciprocal space is made. The model includes orbitally dependent superexchange interaction and single-ion anisotropy. Considered compounds present competing exchange interactions within magnetic unit cell because of orbital or charge-orbital ordering. The nearest neighbor superexchange interaction is taken into account. The magnetic structure and dispersion dependences of spin waves frequencies are calculated within the framework of regular multi-sublattice model. The peculiarities of frustrated magnetic spin-wave spectra are found. It is shown, that crossing and splitting of spin-waves branches in non-symmetric points of magnetic Brillouin zone is a common feature of the spectra due to exchange competition. The band structure of Г-point spectra for both compounds are predicted.

Magnonic Interconnections: Spin-Wave Propagation across Two-Dimensional and Three-Dimensional Junctions between Yttrium Iron Garnet Magnonic Stripes

Spin-wave transport across multidimensional networks of magnonic waveguides represents a crucial and necessary aspect of prospective densely packed three-dimensional spin-wave architectures. Here, we report the results of investigations of spin-wave propagation through magnonic waveguides extending along and bending across two and three dimensions. We consider three designs of in-plane two-dimensional bends, namely with right-angled, diagonal, and curved geometries. Our numerical and experimental results show that such bends facilitate the conversion of spin-wave types, with the output modal number depending on the spin-wave frequency. At the same time, variation of the width of lateral magnonic bends enables the spin-wave wavelength to be modified. When propagating across three-dimensional waveguide bends in the form of out-of-plane junctions, the spin-wave wavelength can similarly be tuned by adjusting the stripe's thickness. Our results show that magnonic waveguides can serve not only as passive conduits but also as active elements in modifying the properties of the transmitted spin wave in three-dimensional magnonic networks.

Shaping the spin wave spectra of planar 1D magnonic crystals by the geometrical constraints

We present experimental and numerical studies demonstrating the influence of geometrical parameters on the fundamental spin-wave mode in planar 1D magnonic crystals. The investigated magnonic crystals consist of flat stripes separated by air gaps. The adjustment of geometrical parameters allows tailoring of the spin-wave frequencies. The width of stripes and the width of gaps between them affect spin-wave frequencies in two ways. First, directly by geometrical constraints confining the spin waves inside the stripes. Second, indirectly by spin-wave pinning, freeing the spin waves to a different extent on the edges of stripes. Experimentally, the fundamental spin-wave mode frequencies are measured using an all-optical pump-probe time-resolved magneto-optical Kerr-effect setup. Our studies address the problem of spin-wave confinement and spin-wave dipolar pinning in an array of coupled stripes. We show that the frequency of fundamental mode can be tuned to a large extent by adjusting the width of the stripes and the width of gaps between them.

Oxide magnonics: Spin waves in functional magnetic oxides

Spin waves or their quanta magnons are collective excitations in magnetically ordered materials. Magnonics have recently attracted tremendous interest for building next-generation nanoscale devices and circuits with low-power consumption. Oxide materials provide an excellent platform for achieving highly efficient spin-wave excitation and transmission for magnonic applications with versatile functionalities. In this article, we review some recent advances for oxide-based magnonics, including both magnetic oxides for hosting spin waves and non-magnetic oxides for manipulating spin waves. First, we introduce recent development on coherent propagation and incoherent transport of magnons in thin-film iron garnets, low-damping ferrimagnetic oxides widely used in magnonics. Then, we discuss spin-wave chirality due to the inversion symmetry broken in magnetic oxides. Magnonics in antiferromagnetic oxides is also presented, where the spin-wave resonance frequency enters THz regime. Nanoscale spin textures, such as magnetic skyrmions, can be stabilized in magnetic oxides, and provide additional versatilities by coupling their dynamics with spin waves. Last but not the least, we highlight the electrical control of spin waves based on multiferroic oxides toward applications for hybrid magnonics.

Dipole-exchange spin waves in unsaturated ferromagnetic nanorings with interfacial Dzyaloshinski–Moriya interactions

A theoretical analysis is made for the quantized spin waves in single-layered ferromagnetic nanorings with the added effect of interfacial Dzyaloshinski–Moriya interactions (DMI). A microscopic, or Hamiltonian-based, formalism is employed that includes competing terms for the symmetric (bilinear) exchange interactions, the antisymmetric DMI, the magnetic dipole–dipole interactions, and applied magnetic field. It is found that, in our model, the transition field value between vortex and onion states is shifted by the inclusion of DMI effects. Significantly, the spin-wave frequencies are also modified with the effects being largest in the onion state close to the transition field. We present combined analytical and numerical results obtained for the static and dynamical magnetization, including the frequencies and amplitudes (with relative phase) of the spin waves when interfacial DMI is present.

Inverse design of magnonic filter

Monochromatic spin wave (SW) is the substrates for the realizing the practical function of magnonic devices, however the generating perfect monochromatic SW is still a unsolved but fundamental problems. In our latest work (Xing et al., 2022), the resonant tunneling effect was found in a magnonic crystals (MCs), which demonstrates a similar effect of Fabry–Pérot interferometer, and shows a promising application of band-pass magnonic filter (MF) for generating perfect monochromatic SW. The optimization of such MF is a complex problem, due to that the natural nonlinearity of spin-wave scattering behavior enhances sensitivity to device parameters. In this work, the inverse design (ID) approach is developed for designing the magnonic filters (MFs). To determine the optimizable variables, the fundamental properties of antiferromagnetically coupled heterojunction based MCs were theoretically investigated. The particle swarm algorithms (PSA) is used for automatically finding MFs which meet the inputting requirements. Here, the input of algorithms is a vector of SW frequency and output is a vector of parameters of MFs. Besides, the PSA is further optimized to be self-adapting to required accuracies, showing a higher computing efficiency than the convectional one. Finally, the output data of predicted MFs with various filtering characteristics are briefly summarized in a table as an alternative proposal for the future experimental design. These encouraging results show high potential of using ID approach in magnetism and boosting optimization of magnetic multilayer heterojunction devices, such as magnon transistor and magnon space–time crystals.

Spin-wave frequency combs

We experimentally demonstrate the generation of spin-wave frequency combs based on the nonlinear interaction of propagating spin waves in a microstructured waveguide. By means of time- and space-resolved Brillouin light scattering spectroscopy, we show that the simultaneous excitation of spin waves with different frequencies leads to a cascade of four-magnon scattering events, which ultimately results in well-defined frequency combs. Their spectral weight can be tuned by the choice of amplitude and frequency of the input signals. Furthermore, we introduce a model for stimulated four-magnon scattering, which describes the formation of spin-wave frequency combs in the frequency and time domain.

Simulation on spin wave transmission and domain wall dynamics in a permalloy nanostrip

Spin waves (SWs), the magnons, can potentially be used for fast and energy efficient information processing and the interaction of SWs with a magnetic domain wall (DW), which is quite complex, can play a key role in the development of magnonic devices. Manipulation of SW amplitude and phase is the key step in realization of spin wave devices. The SW transmission through DW is strongly dependent on the magnetization angle inside the DW and spatial movement of DW is coupled to this interaction. Magnonic spin transfer torque and linear momentum transfer of SW, collectively, control the motion of the DW and the rotation of magnetization inside the DW. In the present work, micromagnetic simulations were performed considering a ferromagnetic permalloy nanostrip with perpendicular magnetic anisotropy (PMA) using mumax3 platform to study SW transmission through DW. The correlation between rotation in magnetization tilt angle (δϕ) inside an initially Néel-type DW and SW-transmission ratio (TD) was investigated at different SW-frequencies ranging from 18 GHz to 28 GHz. Applied SW amplitude at each frequency was sufficiently large for transverse DW to show oscillatory motion along the length of the strip. The results showed that the dependence of TD on rotation in magnetization angle (δϕ) decreases as the frequency of SW is increased and it approaches a nearly isotropic behavior at higher frequencies.