Here, we present a study investigating the effects of spin-wave coupling in a structure composed of parallel-oriented magnonic stripes fabricated from thin films of yttrium-iron garnet. The structure consists of two parallel stripes separated by a sufficiently small gap to enable dipolar coupling, while a third stripe is positioned atop the lateral system, forming an asymmetric three-dimensional (3D) coupler geometry. Through the utilization of Brillouin light-scattering spectroscopy, we experimentally demonstrate the transport of spin waves along the asymmetric 3D coupler. Additionally, by employing experimental techniques, we explore the nonreciprocal propagation of spin waves in the considered structure by reversing the polarity of the external magnetic field. To gain further insights, we employ micromagnetic modeling and the finite-element method to obtain the eigenmode spectra of the asymmetric 3D coupler. Our results show that reversing the polarity of the external magnetic field induces coupling between the magnetic stripes. We elucidate the characteristics of lateral and vertical spin-wave transport, as well as nonreciprocal spin-wave propagation within the investigated structure. Notably, in the asymmetric 3D coupler, the coupling length diminishes, offering the potential to enhance the density of functional elements in the design of three-dimensional magnonic networks.

Purpose. Investigation of the joint manifestation of the effects of anisotropic signal propagation, coupling, and nonlinear power dependence of the medium parameters in a lattice of laterally and vertically coupled spin-wave (SW) microwaveguides. Consideration of the case of the influence of the rotation of the magnetization angle and the change of the lateral gap between microwaveguides located on the same substrate on the transverse profile of the spin-wave beam and the spatial localization of the SW amplitude. Methods. The method of micromagnetic modeling based on the numerical solution of the Landau–Lifshitz–Hilbert equation shows the possibility of controlling the direction of propagation of SW in an ensemble of laterally and vertically coupled iron yttrium garnet (YIG) microwaveguides by changing the magnetization angle. By the method of numerical integration of the system of coupled discrete nonlinear Schrodinger equations, the possibility of changing the transverse profile of the spin-wave beam by changing the level of the initial signal amplitude is shown. Results. The spatial distributions of the components of the dynamic magnetization of the SW excited in two microwaveguides located on the same substrate obtained in micromagnetic simulations indicate a change in the character of localization of the SW power in the output sections of the microwaveguides. At variation of the lattice magnetization angle, a shift of the threshold power value is observed, at which a characteristic curbing of the transverse width of the spin-wave beam in the nonlinear mode appears. Conclusion. When excitation of surface magnetostatic SW in a lattice of laterally and vertically coupled microwaveguides, a transformation of the transverse profile of the wave is observed at a deviation of the magnetization angle of the structure by 15º , which is manifested in the change of the SW length and its localization in each of the microwaveguides. The combined effects of dipole coupling, gyrotropy, and nonlinearity of the medium make it possible to control the value of the threshold power of the SW, at which the mode of diffractionless propagation of the spin-wave beam is realized in a single layer of the structure.

Here, we report the results of strain-controlled spin-wave propagation regimes in a double-period multiferroic structure. It consists of an alligator-type magnonic crystal with a period of 250 μm and a piezoelectric layer, featuring a periodic counter-pin-type electrode system with a period of 125 μm. Employing microwave measurements, we acquired the transmission and dispersion of spin waves under various external electric field configurations applied to the piezoelectric layer. The formation of bandgaps in the magnon spectrum and the variation of the spin-wave transmission when altering the configurations of the external electric field are demonstrated. A finite element method reveals that the combination of the non-uniformity in the initial internal magnetic field of the magnonic crystal, which is caused by the presence of periodic alligator-type regions, together with elastic deformations, heightens the amplitude of the modulation of the internal magnetic field. Micromagnetic modeling has demonstrated that this modulation enhancement results in the variation of the spin-wave transmission at the frequency of the magnonic bandgap center of the magnonic crystal. The proposed design of the reconfigurable magnonic crystal creates a condition for the nucleation of the spin-wave bandgap, with further enhancement of the spin-wave reflection from the periodic grating induced by strain. We demonstrate the potential use of the proposed device as a multi-band NAND/NXOR spin-wave based logic gate.

Using experimental and numerical investigation, we demonstrate laser-controlled propagation and interaction of spin waves in an irregular magnetic structure in the geometry of the Mach–Zehnder interferometer. It is shown that the use of laser radiation for heating one of the interferometer arms leads to controlled interference of a spin-wave signal in the output section. The yttrium–iron garnet film heating under the action of laser radiation is measured experimentally. Using micromagnetic modeling, the evolution of the spin-wave interference pattern under the action of laser heating of one of the interferometer arm is demonstrated. The results of this study ensure a simple solution for developing tunable spin-wave interferometers for the paradigm of the magnonic logics.

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.

Here, we report on the experimental study of spin-wave propagation and interaction in the double-branched Mach–Zehnder interferometer (MZI) scheme. We show that the use of a piezoelectric plate (PP) with separated electrodes connected to each branch of the MZI leads to the tunable interference of the spin-wave signal at the output section. Using a finite element method, we carry out a physical investigation of the mechanisms of the impact of distributed deformations on the magnetic properties of YIG film. Micromagnetic simulations and finite-element modelling can explain the evolution of spin-wave interference patterns under strain induced via the application of an electric field to PP electrodes. We show how the multimode regime of spin-wave propagation is used in the interferometry scheme and how scaling to the nanometer size represents an important step towards a single-mode regime. Our findings provide a simple solution for the creation of tunable spin-wave interferometers for the magnonic logic paradigm.

In this work, we will reveal the regularities in the control of the dipole spin-wava spectra of in lateral heterostructures formed from two magnonic crystals with a piezoelectric layer placed on one of them. The electric field control of the spatial and transfer characteristics of dipole spin waves in lateral heterostructures is shown. Based on the finite element method, the influence of distributed elastic deformations on the magnitudes of internal magnetic fields in magnonic crystals is evaluated. Based on the results of numerical simulations, a physical interpretation of the transformation of the eigenmode spectrum of coupled magnon crystals is given. Keywords: spin waves, magnonics, straintronics, lateral structures.

In this work, we will reveal the regularities in the control of the dipole spin-wava spectra of in lateral heterostructures formed from two magnonic crystals with a piezoelectric layer placed on one of them. The electric field control of the spatial and transfer characteristics of dipole spin waves in lateral heterostructures is shown. Based on the finite element method, the influence of distributed elastic deformations on the magnitudes of internal magnetic fields in magnonic crystals is evaluated. Based on the results of numerical simulations, a physical interpretation of the transformation of the eigenmode spectrum of coupled magnon crystals is given.

Here, we present the results of an experimental and numerical study of controllable spin-wave propagation in the yttrium iron garnet stripe with an Fe-Rh slab. The transformation of spin-wave dispersion and transmission are observed by the focusing laser light on top of the Fe-Rh slab. It was shown that the geometry variation and design of the Fe-Rh slab significantly affect spin-wave propagation. The static internal magnetic field profile in the yttrium iron garnet is subject to position and the geometric parameters of the Fe-Rh slab. Additionally, the possibility of width mode filtering was shown for a surface magnetostatic spin wave by the means of micromagnetic simulation. The qualitative correspondence between the behavior of spin waves in the numerical simulation and microwave spectroscopy data was observed. The proposed structure can be used as a functional unit with the simultaneous frequency selective and spin-wave mode filtration regime in planar magnonic networks.

In this article, we report on the Fano resonance characteristics tunability in a coupled system of magnonic stripes and resonators by variating the geometric parameters, the magnitude of the coupling between them, and the intensity of spin waves (SWs). Using numerical integration of the coupled-wave equation system, we calculated the transfer characteristics of the considered system and the parameters of Fano resonance considering the cubic nonlinearity of magnetic media. We demonstrate the features of constructive and destructive interference of SWs at Fano resonance. Our results reveal the mechanism of the SW spectra control of the nonlinear Fano resonance (asymmetry coefficient and resonance frequency shifts) via the intensity of SW.

We demonstrate that properties of spin-wave propagation in the adjacent magnonic crystal stripes with one of them in contact with a piezoelectric layer can be controlled by an external electric field. We perform microwave spectroscopy and employ a theoretical approach based on the analysis of the set of coupled wave equations. By considering incident and reflected waves in the first Brillouin zone, we calculate the reflection coefficients of the magnonic structure. Two narrow magnon bands are observed in the experiment, and their behavior with the variation of the electric field applied to the piezoelectric layer was shown. The finite-element calculations of the self-consistent eigenvalue problem elucidate how the influence of the piezoelectric layer can be modeled as a localized strain-induced internal magnetic field and its variation affects the spin-wave dispersion. Both the frequency shift and closing of a magnon band are detected in our measurements and confirmed by the simulations and the analytical approach. Therefore, we demonstrate the electric field control of the magnonic bands. Our results reveal the mechanism of the spin-wave spectra control in the coupled magnonic crystals. The results pave the way for the implementation of frequency selective magnonic devices based on a straintronic approach.

We report here on dipolar coupling of spin waves propagating as guided modes of adjacent 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. The origin of the coupling is the dipole field of the precessing magnetization vector. The micromagnetic numerical simulation, yielded spectra of spin waves through the magnonic structure. Analysis of those spectra revealed that the lateral structure can be used as a functional unit in planar magnonic networks – they can be utilized as a directional coupler, spin-wave multiplexer, or microwave power divider. Using Brillouin light scattering spectroscopy, we experimentally demonstrated spin-wave transport along the lateral stripes. We were able to control the spin-wave routing between the stripes by varying the bias angle of the magnetic field.

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.

The purpose of research is to study of characteristics of the Fano resonance in a coupled system of nonlinear microwave-guides and resonators depending on geometric parameters of the systems, magnitude of the coupling between them, and the intensity of spin waves. Methods. Linear and nonlinear spin-wave excitations in lateral systems of irregular microwave-guides and resonators based on films of yttrium iron garnet are considered. Using micromagnetic simulation of spin-wave excitations and numerical integration of the coupled wave equation system, the transfer characteristics of the "microwave-guide - resonator" system and the Fano resonance parameters are calculated taking into account the cubic nonlinearity of magnetic media. Results. Based on the numerical integration of the system of equations of coupled waves that take into account the cubic nonlinearity of the magnetic media, theoretical studies have been carried out of the dependences of the transfer and phase characteristics of the "microwave-guide - resonator" system on the intensity of surface spin waves. Features of the demonstration of constructive and destructive interference of spin waves at Fano resonance are studied. Dependences of characteristics of the parameters of the Fano nonlinear resonance (asymmetry coefficient, resonance frequency shifts) on the intensity of spin-wave excitations are established. Conclusion. Results can be used to create spin-wave demultiplexers, power dividers and microwave couplers based on the lateral system of magnetic waveguides as a threshold element for neuromorphic networks, etc.

The results of numerical and experimental studies have been used to demonstrate the possibility of controlling the dipole spin-wave coupling in a lateral array of ferrite stripes by means of local deformations. A configuration of a magnonic structure with a piezoelectric layer and structured electrodes on its surface is proposed to use as an experimental demonstration of the studied physical processes, and a laser ablation technique with spatial resolution is used to arrange the piezoelectric layer into a structure. It is shown that local elastic strains can be used to induce a waveguide channel for propagating spin-wave edge modes. From the point of view practical applications, the obtained results can be used to create a class of information processing devices, such as demultiplexing systems with frequency–space selectivity that are controlled simultaneously by an electric and magnetic field.

Magnonics is a budding research field in nanomagnetism and nanoscience that addresses the use of spin waves (magnons) to transmit, store, and process information. The rapid advancements of this field during last one decade in terms of upsurge in research papers, review articles, citations, proposals of devices as well as introduction of new sub-topics prompted us to present the first roadmap on magnonics. This is a collection of 22 sections written by leading experts in this field who review and discuss the current status besides presenting their vision of future perspectives. Today, the principal challenges in applied magnonics are the excitation of sub-100 nm wavelength magnons, their manipulation on the nanoscale and the creation of sub-micrometre devices using low-Gilbert damping magnetic materials and its interconnections to standard electronics. To this end, magnonics offers lower energy consumption, easier integrability and compatibility with CMOS structure, reprogrammability, shorter wavelength, smaller device features, anisotropic properties, negative group velocity, non-reciprocity and efficient tunability by various external stimuli to name a few. Hence, despite being a young research field, magnonics has come a long way since its early inception. This roadmap asserts a milestone for future emerging research directions in magnonics, and hopefully, it will inspire a series of exciting new articles on the same topic in the coming years.

The traditional approach in semiconductor microelectronics is based on the use of a charge of current carriers, at the same time, the use of elementary quanta of magnetic excitations and spin waves as carriers of information signals allows the creation of a new generation of electronic devices magnonics, reducing the magnitude of thermal fission and size, as well as increasing their functionality [1]. Magnonics devices have advanced capabilities due to the control of the properties of spin waves through various influences (for example, changes in the external magnetic field, electric field, heating, etc.), in contrast to vacuum and semiconductor microwave devices. It should be noted that magnon devices can easily be combined with a sufficiently large number of semiconductor integrated technologies. The use of multilayer magnetic microstructures based on films of yttrium iron garnet having a record low damping of spin waves seems to be important for the development of basic elements of magnonics and their formation in the so-called "magnonic networks" [2-3]. Using numerical studies based on the finite element method and micromagnetic simulation, we studied the propagation dynamics of surface magneto-static waves in a system of lateral YIG waveguides. Structure is consisting of parallel-oriented magnetic stripes obtained using the laser scribing method from a YIG film 10 μm thick located on a gallium-gadolinium garnet substrate. The distance between magnetic microwaves is 40 μm. The length along the long side of the waveguides was 8 mm. Spin waves were excited using a microstrip antenna 1 μm thick and 30 μm wide. The structure is placed in an external static magnetic field, H = 1200 Oe, changing at an angle φ. To demonstrate the control modes of the intensity of the spin-wave signal with a change in the magnetization angle, a numerical simulation was performed based on the solution of the Landau – Lifshitz equation. References: [1] A.V. Sadovnikov, A.A. Grachev, S.E. Sheshukova, Yu.P. Sharaevskii, A.A. Serdobintsev, D.M. Mitin, S A. Nikitov,Physical Review Lettetrs 120, (2018) [2] A.V. Sadovnikov, A.A. Grachev, E.N. Beginin, S.E. Sheshukova, Yu.P. Sharaevskii, and S.A. Nikitov, Physical Review Applied 7, (2017) [3] A.V. Sadovnikov, A.A. Grachev, E.N. Beginin, S.E. Sheshukova, Yu.P. Sharaevskii, A.A. Serdobintsev, D.M. Mitin, S.A. Nikitov, IEEE Transactions on Magnetics 53, (2017)

Here we report about the strain-tuned dipolar spin-wave coupling in the adjacent system of yttrium iron garnet stripes, which were strain-coupled with the patterned piezoelectric layer. Spatially-resolved laser ablation technique was used for structuring the surface of the piezoelectric layer and electrodes on top of it. Using a phenomenological model based on coupled modes equation, we demonstrate a voltage-controlled intermodal coupling in lateral magnonic stripes. The features of the tunable spin-wave coupling by changing the geometric parameters and the type of magnetization is demonstrated.

A numerical study of the features of the propagation of spin waves in a waveguide made of yttrium-ron garnet (YIG) and Fe-Rh alloy in the form of a plate, located on top of the central part of the YIG, has been carried out. Based on the simulation results, the possibilities of controlling the dynamics of spin waves in the structure under study were also revealed. Micromagnetic numerical simulation was used to study the transfer of a spin-wave signal in a multimode mode by numerically solving the Landau – Lifshitz – Hilbert equation. Transformation of the transmission spectra of spin waves shows that the proposed structure will make it possible to control the propagation of spin-wave modes due to a sharp change in the Fe-Rh magnetization in the region of the magnetic phase transition temperature close to room temperature. In addition, the spin wave signal can be controlled by a small temperature change in the Fe-Rh plate generated by laser radiation. The two-layer structure of YIG/Fe-Rh, from an applied point of view, can be used as a functional unit in planar magnon networks performing space-frequency demultiplexing and filtering of spin-wave modes.