Using a method based on mathematical operations with Maxwell’s equations in vector form, it is proved that electromagnetic waves propagating in an arbitrary direction in a bi-gyrotropic medium are always characterized by the collinear orientations of the Poynting vector and the group velocity vector. It is shown that the corresponding Cartesian components of these vectors are proportional to each other, which confirms the collinearity of these vectors. It is found that for all types of electromagnetic waves propagating in an unbounded ferromagnetic medium (which is a special case of a bi-gyrotropic medium), these vectors are always codirected.

The spatial-frequency distributions of spin waves in a magnon crystal and their dispersion characteristics were experimentally investigated. In spite of the weak energy contrast of the crystal, the formation of a number of Brillouin zones and the existence of two types of wave nonreciprocity were detected. Of the two types, one is due to the asymmetry of dispersion dependences with respect to the direction of wave propagation, and the other is due to the difference between the spatial distributions of the waves propagating in opposite directions. The magnon crystal made it possible to detect and measure these types of nonreciprocity.

Here we present the nonreciprocal propagation of caustic beams and channeling of the backward volume spin wave in an yttrium-iron-garnet structure with the longitudinal symmetry axis and broken translational symmetry. The experimental method of Brillouin spectroscopy and the numerical micromagnetic methods are used to study the mechanisms of control of the nonreciprocal spin-wave signal propagation in a Tshaped junction with a partially metallized surface. It is shown that the partial metallization of the surface together with the reversal of the magnetic field direction can serve as a way to control the propagation of spin-wave beams. The formation of the spin-wave channel between the metal stripe and the edge of the magnetic film is observed experimentally and demonstrated by numerical solution of the Landau-LifshitzGilbert equation and Maxwell's equations. The proposed theoretical analysis explains the experimental results and provides useful technical information for the fabrication of reconfigurable magnonic devices, which utilize the spin-wave beam formation in the region of the junction of the magnonic waveguides with different widths. The proposed structure can be used as a functional element of signal branching and/or power division in magnonic networks and signal-processing devices based on them.

Maxwell’s equations without using the magnetostatic approximation were used to derive a dispersion equation for spin waves in a tangentially magnetized ferrite plate one of the surfaces of which adjoins a perfect magnetic wall, and the isofrequency dependences of these waves were calculated. It was found that the wave distribution along the plate thickness is described by two wavenumbers, and the isofrequency dependences of different modes of spin waves smoothly pass one into another and have sections corresponding to the volume–volume, volume–surface, and surface–surface wave distributions.

The collinearity of the Poynting vector P and the group velocity vector U of electromagnetic waves in a bihyrotropic medium characterized by second rank Hermitian tensors of dielectric and magnetic permittivities is theoretically proved. It is shown that these vectors will be collinear in any anisotropic medium having either Hermitian or symmetric dielectric and magnetic permittivities tensors.

The possibility of intense excitation of exchange spin waves in a tangentially magnetized two-layer epitaxial film of iron yttrium garnet is demonstrated. The waves are excited in a thin transition layer at the interface between the ferrite layers, propagate into the doped layer with reduced magnetization, and reflect from its opposite surface. In continuous excitation mode, they can be observed as a series of spin wave resonance peaks. Mathematical processing of the measured frequencies of resonance peaks allows for the calculation of the magnetization profile of the doped layer and the modeling of the excitation and propagation processes of exchange spin waves. The proposed methodology of mathematical processing can be applied for non-destructive control of the layered structure of epitaxial ferrite structures.

The problem of arbitrary propagation of electromagnetic waves in a tangentially magnetized one-side metallized bigyrotropic layer is solved without using the magnetostatic approximation. It is shown that, in this problem, Maxwell’s equations are reduced to a differential equation corresponding to a biquadratic characteristic equation with four roots kx21, ‒kx21, kx22, and –kx22 describing the distribution of the wave in the layer cross section. A dispersion equation for describing waves with real kx21 and kx22 values is obtained. Using this equation, the characteristics of spin waves in a one-side metallized ferrite plate (a special case of a bigyrotropic layer) are calculated for the frequencies above the ferromagnetic resonance frequency. It is found for these waves that quantity kx21 can take both real and imaginary values, while quantity kx22, only real ones. It is found that, at a certain frequency, the spin wave has an isofrequency curve almost identical to a straight line.

A study is performed of the general nonreciprocal characteristics of a surface spin wave and a backward spin wave in a tangentially magnetized plane-parallel ferrite plate. The rule governing the interdependence between the localization of a spin wave across the thickness of the ferrite plate and directions of its group and phase velocities is established.

The possibility of frequency-selective propagation of spin waves in a magnonic microwave guide with a magnonic crystal consisting of two layers with different values of the saturation magnetization in the layers is demonstrated. It is shown that multimode propagation of spin waves can occur inside a two-layer structure in two frequency ranges, while the presence of a magnonic crystal on the surface of the structure leads to the manifestation of a band gap in one of the frequency ranges. At the same time, the process of propagation of a spin-wave signal is accompanied by a strong nonreciprocity, which manifests itself in a change in the amplitude-frequency characteristics when the direction of the external magnetic field is reversed, while the frequency range of the band gap differs depending on the direction of the field. The proposed concept of a two-layer spin-wave waveguide can underlie the manufacture of multichannel filters or magnonic logic devices. Keywords: magnonics, nonlinearity, nonlinear systems, multilayer systems, spin waves.

Analytically, without magnetostatic approximation, the problem of electromagnetic wave propagation along arbitrary direction in a tangentially magnetized bihyrotropic layer has been solved. It is found that one can bring the Maxwell equations for this problem to the fourth order differential equation and the obtained biquadratic characteristic equation determines two different wave numbers kx21 and kx22 describing the wave distribution over the layer thickness. The dispersion equation describing wave propagation in the bihyrotropic layer was obtained for the case of real kx21 and kx22 values. It is shown that in a ferrite plate, which is a special case of a bihyrotropic layer, three types of wave distribution over the plate thickness can take place: surface-surface (when kx21 and kx22 are real numbers), volume-surface (kx21 is imaginary and kx22 is real) and volume-volume distribution (kx21 and kx22 are imaginary numbers). Characteristics of the surface spin wave in ferrite plate are investigated. It is found that dependences of the wave numbers kx21 and kx22 on the wave vector orientation are significantly different from the similar magnetostatic dependence for a large part of the wave spectrum.

Purpose of this paper is to give an overview of various experimental methods for investigation of spin waves characteristics. Methods. The paper presents a description of a number of experimental techniques, such as the probing method, the phase shift method, the method of measure of equiphase dependences, the method of intersecting wave beams, and the use of Fourier analysis of the complex transfer coefficient of spin waves to determine their spatial spectrum. The conditions for using the listed methods and the characteristics of spin waves that one can measure by means of these methods are discussed in detail. Results. The paper presents a number of fundamental results that have been obtained on the basis of described methods. For example, the probing method was successfully used to visualize the amplitude and phase distribution of spin waves in the ferrite film plane and, in particular, it was used to experimentally confirm the previously predicted appearance of super-directed propagation of surface and backward volume spin wave beams. The phase-shift measurement method made it possible to measure the dispersion dependence of spin waves in ferrite structures such as ferrite – metal and ferrite – dielectric – metal, where measurements cannot be made by the probing method. The method of measuring equiphase dependences of spin waves made it possible, in particular, to measure for the first time with great accuracy the value of an external magnetic field magnetizing an yttrium iron garnet film to saturation in various crystallographic directions. The method of intersecting wave beams has made it possible to clarify the mechanism of parametric instability of surface spin waves. Fourier analysis of the complex transfer coefficient of spin waves allowed to determine the spatial spectrum of these waves; in particular, dispersion dependences of higher modes of the backward volume spin wave were first measured using this method. Conclusion. The methods described in this paper may continue to be successfully used for investigations of spin waves characteristics in various magnon crystals, ferrite structures and meta-structures.

Objectives. Nonreciprocal spin wave effects can manifest themselves in metalized films of ferrite garnets. By studying the dynamics of spin waves in micro- and nano-scale magnetic films, the possibility of using multilayer dielectric films of yttrium iron garnet (YIG) to ensure the manifestation of the nonreciprocity effect is demonstrated. This approach offers advantages compared to the use of a layered YIG/metal structure due to significantly lower spin-wave losses in the two-layer YIG film consisting of layers with different values of magnetization. Such films can be used in logical elements to create controllable Mach-Zehnder interferometers based on magnonic principles. The purpose of this work is to reconcile the concept of nonreciprocal spin-wave propagation of a signal with the simultaneous manifestation of the effects arising from the propagation of spin waves in microwave guides formed by finite-width YIG films.Methods. We used an experimental microwave spectroscopy method based on a vector network analyzer along with a finite difference method to perform a numerical simulation of the dispersion characteristics of spin waves in two-layer magnonic microwave guides. An analytical model was also used to obtain a dispersion equation based on the magnetostatic approximation.Results. Based on measurements of the amplitude and phase responses, the possible coexistence of two frequency ranges for the propagation of a spin-wave signal in a two-layer magnon microwave guide based on a YIG film formed by two layers with different values of saturation magnetization was demonstrated. Regimes of nonreciprocal propagation of a spin-wave signal were revealed. A numerical model was using to study the formation mechanisms of spin wave modes in the spectrum of a two-layer structure formed due to the finite dimensions of the microwave guide. An analytical model was used to evaluate the transformation of the mode spectrum. The experimental data are in good agreement with the results of the proposed numerical and analytical models.Conclusions. The possibility of frequency-selective propagation of spin waves in a magnon microwaveguide consisting of two layers with different saturation magnetization values is demonstrated. Multimode propagation of spin waves can occur inside a two-layer structure in two frequency ranges. At the same time, this process is accompanied by a strong nonreciprocity of spin-wave signal propagation, which manifests itself in a change in the amplitude and phase responses when the direction of the external magnetic field is reversed. The proposed two-layer spin-wave waveguide concept can be used in the manufacture of magnon interconnects and magnon interferometers with the support of multiband regimes of operation.

Here we present the frequency-selective spin-wave propagation in the magnonic waveguide consisting of two layers with different magnetization saturation. We show that the multimode spin-wave propagation can be performed inside the bilayer structure within two separate frequency range. At the same time this process is accompanied by strong nonreciprocity in spin-wave behavior with the relation to direction of the spin-wave propagation and bias magnetic field. Using the microwave spectroscopy we demonstrate the coexistence of two frequency range in the two samples of pure/modified yttrium iron garnet bilayers with the different orientation of layers with the respect of the substrate. Using the numerical model based on the magnetostatic dispersion relation for spin waves in the bilayer the nonreciprocal behavior of spin-waves was elucidated and its properties for the confined magnonic bilayer stripe was obtained. In particular, it was shown that the narrowing of the stripe leads to the pronounced variation of the nonreciprocity effect for the separate modes in the spin-wave spectra. The experimental data are in good agreement with the predicted by the proposed theoretical model. The proposed concept of bilayer spin-wave waveguide can underlie the fabrication of the magnonic interconnection bus with the support of multiple frequency band operational regimes.

Diffraction of a backward volume spin wave on a through hole in a ferrite plate is investigated experimentally and theoretically for when the length of the spin wave is greater than the diameter of the hole and the linear transducer exciting the wave is perpendicular to an external uniform magnetic field. It is found that in one direction of the possible super-directional propagation of the wave, a distinct shadow of the hole is observed at a considerable distance from the latter. Good agreement between the experimental and theoretical results is obtained.

The influence of the boundary conditions of “perfect metal” and “perfect magnetic wall” being established in various combinations near or on every surface of a tangentially magnetized ferrite plate, on the possibility of undistorted transmission of useful signal through the use of surface spin waves in this structure, is theoretically studied. It was found that, depending on parameters of the structure and boundary conditions, the quasi-linear regions occupying the range of frequencies with a width from 75 to 220 MHz and the range of wave numbers width from 40 to 200 cm –1 can occur in the dispersion characteristic of spin waves. It was demonstrated that, for undistorted transmission of the useful signal modulating the spin wave, using of the spin waves that parameters correspond to the mentioned quasi-linear regions is necessary.

Basing on the measurement of spatial spectra (spectra of wavenumbers), the dispersion characteristics of the first three modes of backward volume spin wave, propagating along the direction of a constant uniform magnetic field in a tangentially magnetized ferrite film, were visualized firstly. The study was carried out by microwave probing of spin waves with subsequent use of spatial Fourier analysis of the complex wave amplitude for a series of frequencies. It was found that experimental spatial spectrum of the backward volume spin wave modes has a fine structure and every m-th mode splits into n closely located satellite modes appearing due to the existence of layers with similar magnetic parameters in ferrite film. It was found that satellites of the first mode of this wave are excited most effectively, while satellites of the third mode - least effectively, and the effectiveness of satellites excitation decreases as the number n increases. It is found that the theoretical dispersion dependencies of the first three modes of the wave coincide well with the experimental dispersion dependencies of the satellite modes that are excited most effectively.

A magnetic system is developed to generate a stationary uniform magnetic field in a relatively large region between the poles of a magnet that is used in a setup for the study of characteristics of spin waves. The calculations and subsequent measurements show that the application of ring terminals with certain parameters in the magnet allows a several-fold increase in the size of the region with a high uniformity of the magnetic field. The Fourier analysis of the distribution of the amplitude of spin waves is used to show that improvement of the uniformity of the magnetic field in the system due to the application of the ring terminals leads to a several-fold increase in the accuracy of measurement of the wave number. It is found that the first mode of the backward volume spin wave is split into satellite modes that are excited in the ferrite film due to the presence of several layers with similar magnetic parameters.

Analytical formulas are obtained for all components of the high-frequency field, Poynting vector $$\overrightarrow P $$ , and group velocity vector $$\overrightarrow U $$ of electromagnetic waves propagating in an arbitrary direction in an unbounded bi-gyrotropic medium described by the Hermitian permittivity and permeability tensors. It is proven that the corresponding components of vectors $$\overrightarrow P $$ and $$\overrightarrow U $$ are proportional to each other (therefore, these vectors are parallel) and the ratio between these components is the volume density of the wave energy. The change in the absolute value and orientation of vector $$\overrightarrow U $$ and orientation of vector $$\overrightarrow P $$ depending on the orientation of the wave vector for different types of electromagnetic waves propagating in a ferromagnetic medium (a particular case of a bi-gyrotropic medium) is calculated. It is found that vectors $$\overrightarrow U $$ and $$\overrightarrow P $$ are always identically oriented for waves of all types in a ferromagnetic medium.

The orientations of the Poynting and group velocity vectors are calculated, depending on the orientation of the wave vector for different types of electromagnetic waves propagating in an infinite ferromagnetic medium. The Poynting and group velocity vectors are found to be codirectional for all the types of waves in this medium.

A magnetic system is developed for creating a stationary highly uniform magnetic field in a long domain between the poles of a C-magnet. Based on calculations of the constant magnetic field distribution and subsequent measurements, it is shown that using a magnet with ring tips that have certain parameters can greatly increase the spatial domain with high uniformity of the magnetic field.