Coupled Spin Waves Research Articles

Strongly Coupled Spin Waves and Surface Acoustic Waves at Room Temperature.

Here, we report the observation of strong coupling between magnons and surface acoustic wave (SAW) phonons in a thin CoFeB film constructed in an on-chip SAW resonator by analyzing SAW phonon dispersion anticrossings. We employ a nanostructured SAW resonator design that, in contrast to conventional SAW resonators, allows us to enhance shear-horizontal strain. Crucially, this type of strain couples strongly to magnons. Our device design provides the tunability of the film thickness with a fixed phonon wavelength, which is a departure from the conventional approach in strong magnon-phonon coupling research. We detect a monotonic increase in the coupling strength by expanding the film thickness, which agrees with our theoretical model. Our work offers a significant way to advance fundamental research and the development of devices based on magnon-phonon hybrid quasiparticles.

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.

Spin-wave dynamics controlled by tunable ac magnonic crystal

The magnonic crystal, which has a spatial modulation wave vector $q$, couples the spin wave with wave vector $k$ to the one with wave vector $k\ensuremath{-}q$. For a conventional magnonic crystal with direct current (dc) supply, the spin waves around $q/2$ are resonantly coupled to the waves near $\ensuremath{-}q/2$, and a band gap is opened at $k=\ifmmode\pm\else\textpm\fi{}q/2$. If instead of the dc current the magnonic crystal is supplied with an alternating current (ac), then the band gap is shifted to $k$ satisfying $|{\ensuremath{\omega}}_{s}(k)\ensuremath{-}{\ensuremath{\omega}}_{s}(k\ensuremath{-}q)|={\ensuremath{\omega}}_{\mathrm{ac}}$; here ${\ensuremath{\omega}}_{s}(k)$ is the dispersion of the spin wave, while ${\ensuremath{\omega}}_{\mathrm{ac}}$ is the frequency of the ac modulation. The resulting gap in the case of the ac magnonic crystal is the half of the one caused by the dc with the same amplitude of modulation. The time evolution of the resonantly coupled spin waves controlled by properly suited ac pulses can be well interpreted as the motion on a Bloch sphere. The tunability of the ac magnonic crystal broadens the perspective of spin-wave computing.

Reconfigurable Spin-Wave Coupler Based on Domain-Wall Channels

In functional magnonic devices, spin-wave couplers serve a key role in controlling the spin-wave transmission across different magnonic units. Here we study a reconfigurable spin-wave coupler based on domain-wall channels. The design relies on the dipolar interaction between spin waves propagating in neighboring domain walls. The dipolar-coupled spin-wave modes and their propagation in domain walls are analyzed using micromagnetic simulations and analytical calculations. The distance between domain walls and thus the spin-wave coupling strength can be tuned dynamically. Such a feature results in a dynamically manipulatable spin-wave coupler that enables full control over the propagation properties of coupled spin waves. The spin-wave coupler based on domain-wall channels can be achieved in a single magnetic film, avoiding complex nanofabrication, and enabling possibilities in reconfigurable magnonic functional devices.

Coupled spin waves and crystalline electric field levels in candidate multiferroic ErFeO3

We report an inelastic neutron scattering study of candidate multiferroic ErFeO3, a compound that has been previously reported to have three different magnetic states and undergoes signatures of Fe3+−Er3+ cooperative coupling. The spectrum at low energy transfer is dominated by excitations of the Er3+ character, even above the Er3+ antiferromagnetic ordering temperature of 4.5 K. In addition, a crystalline electric field excitation at 6 meV exhibits additional energy splitting upon cooling through 4.5 K with mode-dependent polarization. This indicates different moment directions for these modes, an interesting consequence of Cy ordering of the Er3+ moments.

Multimode unidirectional spin-wave coupling in an array of non-identical magnonic crystals near band gap frequencies

Using Brillouin light spectroscopy and micromagnetic simulation methods, we show how the intermodal coupling between two magnonic crystals (MCs) affects signals spatial selection with frequency separation during spin-wave transport. We have experimentally demonstrated control of the intermodal coupling of spin waves (SWs) propagating in non-identical magnonic-crystal microwaveguides near the band gap frequency. We show that the spin-wave propagation direction within the MCs of different width can be controlled by the lateral coupling between SWs. Our findings provide an alternative method for signal filtering and separation within magnonic networks for the implementation of magnonic demultiplexers, power dividers, couplers and microwave signal processing devices. based on the lateral array of non-identical MCs.

Spin waves in unsaturated single- and double-layered ferromagnetic nanorings

A theoretical analysis is described for the spin waves in single- and double-layered nanorings using a microscopic, or Hamiltonian-based, formalism. The calculations, which yield the frequencies and spatially-dependent intensities of the quantized spin waves, are applied to the vortex and onion (bi-domain) states in a single nanoring, as well as to the field-induced switching. In the case of asymmetric double-layered nanorings (with a nonmagnetic spacer) there are coupled spin waves controlled by varying the spacer thickness to change the strength of the inter-ring dipolar interactions. The different possible magnetic states, depending on the applied magnetic field, may involve vortex states (with the same or opposite chirality) in both layers, a vortex state in one layer and onion state in the other, or onion states in both layers. Numerical applications are made to permalloy nanorings with realistic dimensions and magnetic parameter values.

Управляемая электрическим полем спин-волновая связь в латеральных ансамблях магнитных микроструктур

In this work, using numerical and experimental studies, we have demonstrated the possibility of controlling the dipole spin-wave coupling in a lateral array of ferromagnetic stripes using local deformations. As an experimental demonstration of the investigated physical processes, a configuration of a magnonic structure with a piezoelectric layer and structured electrodes on its surface is proposed, and the technique of laser ablation with spatial resolution is used to structure the piezoelectric layer. The mechanisms for controlling the dipole coupling of spin waves by creating elastic deformations localized in the region of the maximums of the electric field are revealed. From an applied point of view, the results obtained can be used to create a class of information processing devices, such as demultiplexing systems with frequency-space selectivity, controlled simultaneously by an electric and magnetic field.

Strain reconfigurable spin-wave transport in the lateral system of magnonic stripes

We demonstrate the possibility of controlling dipole spin-wave coupling in the lateral array of ferromagnetic stripes using local strains. Lateral system of magnonic stripes with a piezoelectric layer is fabricated and tested with microwave and Brillouin light scattering spectroscopy. The mechanisms of controlling the dipole coupling of spin waves by elastic strains localized in the region of maximums of the electric field strength are revealed. It is shown that when the absolute value and sign of the electric field are changed, it is possible to effectively control the properties of the propagating spin waves and the spatial distribution of the intensity of the dynamic magnetization in the lateral structure. We emphasize that the spin-wave intermodal coupling can be tuned with the external electric field in the adjacent magnonic stripes. Formation of channel for spin-wave edge mode propagation is observed experimentally in the vicinity of the gap between adjacent stripes. Effective control of the spin-wave coupling by changing the gap is demonstrated. From an applied point of view, the results can be used in information processing devices with electric and magnetic field tunability.

Spin-wave coupling to electromagnetic cavity fields in dysposium ferrite

Coupling of spin-waves with electromagnetic cavity field is demonstrated in an antiferromagnet, dysprosium ferrite (DyFeO3). By measuring transmission at 0.2-0.35 THz and sweeping sample temperature, magnon-photon coupling signatures were found at crossings of spin-wave resonances with Fabry-Perot cavity modes formed in samples. The obtained spectra are explained in terms of classical electrodynamics and a microscopic model.

Controlled Spin-Wave Transport in a Magnon-Crystal Structure with a One-Dimensional Array of Holes

Spin-wave transport in a lateral system of microwaveguides coupled to each other through a magnonic crystal structure with a one-dimensional array of holes has been analyzed. Mechanisms of controlling a spin-wave signal at the tangential magnetization of the structure have been studied by the micromagnetic simulation and Brillouin spectroscopy. It has been shown that the anisotropy of the shape in region of coupling of spin waves propagating through isolated channels can be effectively changed under the variation of the magnetization angle of the structure, which allows controlling spatial and frequency selective regimes of spin-wave transport. The proposed structure can be used as a functional element of interconnections in planar topologies of magnonic networks and devices for parallel processing of a signal based on them.

Magnetic resonance in defect spins mediated by spin waves

In search of two level quantum systems that implement a qubit, the nitrogen-vacancy (NV) center in diamond has been intensively studied for years. Despite favorable properties such as remarkable defect spin coherence times, the addressability of NV centers raises some technical issues. The coupling of a single NV center to an external driving field is limited to short distances, since an efficient coupling requires the NV to be separated by only a few microns away from the source. As a way to overcome this problem, an enhancement of coherent coupling between NV centers and a microwave field has recently been experimentally demonstrated using spin waves propagating in an adjacent yttrium iron garnet (YIG) film [1]. In this paper we analyze the optically detected magnetic resonance spectra that arise when an NV center is placed on top of a YIG film for a geometry similar to the one in the experiment. We analytically calculate the oscillating magnetic field of the spin wave on top of the YIG surface to determine the coupling of spin waves to the NV center. We compare this coupling to the case when the spin waves are absent and the NV center is driven only with the antenna field and show that the calculated coupling enhancement is dramatic and agrees well with the one obtained in the recent experiment.

Temperature-dependent relaxation of dipole-exchange magnons in yttrium iron garnet films

Low energy consumption enabled by charge-free information transport, which is free from ohmic heating, and the ability to process phase-encoded data by nanometer-sized interference devices at GHz and THz frequencies are just a few benefits of spin-wave-based technologies. Moreover, when approaching cryogenic temperatures, quantum phenomena in spin-wave systems pave the path towards quantum information processing. In view of these applications, the lifetime of magnons$-$spin-wave quanta$-$is of high relevance for the fields of magnonics, magnon spintronics and quantum computing. Here, the relaxation behavior of parametrically excited magnons having wavenumbers from zero up to $6\cdot 10^5 \mathrm{rad~cm}^{-1}$ was experimentally investigated in the temperature range from 20 K to 340 K in single crystal yttrium iron garnet (YIG) films epitaxially grown on gallium gadolinium garnet (GGG) substrates as well as in a bulk YIG crystal$-$the magnonic materials featuring the lowest magnetic damping known so far. As opposed to the bulk YIG crystal in YIG films we have found a significant increase in the magnon relaxation rate below 150 K$-$up to 10.5 times the reference value at 340 K$-$in the entire range of probed wavenumbers. This increase is associated with rare-earth impurities contaminating the YIG samples with a slight contribution caused by coupling of spin waves to the spin system of the paramagnetic GGG substrate at the lowest temperatures.

Nonlinear Spin Wave Effects in the System of Lateral Magnonic Structures

The spin-wave dynamics in the system of lateral magnetic microstructures have been studied experimentally and numerically. Regimes of the propagation of coupled spin waves have been investigated by Brillouin spectroscopy measurement and numerical experiment. A phenomenological model has been proposed to describe the properties of spin waves in a lateral structure. It has been shown that the length of the coupling between spin waves can be governed by varying the power of the signal. The results can be used to fabricate magnetic waveguides of spin-wave demultiplexers, power splitters, and microwave couplers based on the lateral system.

Coupled spin waves in magnetic waveguides induced by elastic deformations in YIG–piezoelectric structures

The numerical simulation and Brillouin spectroscopy measurement have demonstrated the possibility of controlling the properties of coupled spin waves propagating in a transversely limited layered YIG–piezoelectric structure. It has been shown that an electric field applied to the piezoelectric layer induces an inhomogeneous distribution of an internal magnetic field in the ferromagnetic layer, which results in the formation of waveguide channels for spin magnetostatic waves. In this case, the properties of coupled spin waves can be efficiently controlled by varying the magnetization angle of the structure. The results demonstrate the possibility of integration of straintronics and magnonics to fabricate electric- and magnetic-field-controlled power splitters, multiplexers, and microwave couplers.

Magnon-photon coupling in antiferromagnets

Magnon-photon coupling in antiferromagnets has many attractive features that do not exist in ferro- or ferrimagnets. We show quantum-mechanically that, in the absence of an external field, one of the two degenerated spin wave bands couples with photons, while the other does not. The photon mode anticrosses with the coupled spin waves when their frequencies are close to each other. Similar to its ferromagnetic counterpart, the magnon-photon coupling strength is proportional to the square root of the number of spins N in antiferromagnets. An external field removes the spin wave degeneracy, and both spin wave bands couple to the photons, resulting in two anticrossings between the magnons and photons. Two transmission peaks were observed near the anticrossing frequency. The maximum damping that allows clear discrimination of the two transmission peaks is proportional to N, and it is well below the damping of antiferromagnetic insulators. Therefore, the strong magnon-photon coupling can be realized in antiferromagnets and the coherent information transfer between the photons and magnons is possible.

Nonlinear spin wave coupling in adjacent magnonic crystals

We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.

Spin-wave nonreciprocity based on interband magnonic transitions

We theoretically demonstrate linear spin-wave nonreciprocity in a Ni80Fe20 nanostripe waveguide, based on interband magnonic transitions induced by a time-reversal and spatial-inversion symmetry breaking magnetic field. An analytical coupled-mode theory of spin waves, developed to describe the transitions which are accompanied by simultaneous frequency and wavevector shifts of the coupled spin waves, is well corroborated by numerical simulations. Our findings could pave the way for the realization of spin-wave isolation and the dynamic control of spin-wave propagation in nanoscale magnonic integrated circuits via an applied magnetic field.

Coupled spin waves in trilayer films and nanostripes of permalloy separated by nonmagnetic spacers: Brillouin light scattering and theory

We present a combined experimental and theoretical study of the di-exchange spin waves in layered structures constituted by permalloy(30 nm)/Cu(10 nm)/permalloy ($d$)/Cu(10 nm)/permalloy (30 nm), which differ by the variable thickness $d$ of the middle permalloy film (with $d=15$, 30, 60 nm). Both the plane layered films and two sets of stripes having widths of 150 and 400 nm were studied. The spin-wave dispersions (frequency vs wave vector) were measured by Brillouin light scattering and the experimental data interpreted using a microscopic (Hamiltonian-based) theory that takes into account the magnetic dipole-dipole and exchange interactions within each stripe and the dipole-dipole coupling between stripes of the stack. Overall, good agreement is found, showing that modes of the layered films constituted by surface dipolar and exchange-dominated waves give rise to complicated spectra in the case of layered stripes because of the lateral confinement. The role of the middle-layer thickness $d$ in the determination of the perpendicular profile of the spin modes is analyzed in detail.

Coupled spin, elastic, and electromagnetic waves in the magnetic of a ferromagnetic spiral phase

The spectrum of coupled spin, elastic, and electromagnetic waves in the magnetic of a ferromagnetic spiral phase is investigated. The frequency dependences of the reflection coefficient of electromagnetic waves from the surface of a semi-infinite magnet for different angles of the spiral are obtained. An acoustic analog of the Faraday effect in the magnetics of a ferromagnetic spiral phase is considered.