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Magnonic crystals are structures with periodically varied magnetic properties that are used to control collective spin-wave excitations. With micromagnetic simulations, we study spin-wave spectra in a 2D antidot lattice based on a multilayered thin film with perpendicular magnetic anisotropy (PMA). We show that the modification of the PMA near the antidot edges introduces interesting changes to the spin-wave spectra, even in a fully saturated state. In particular, the spectra split into two types of excitations: bulk modes with amplitude concentrated in a homogeneous part of the antidot lattice and edge modes with an amplitude localized in the rims of reduced PMA at the antidot edges. Their dependence on the geometrical or material parameters is distinct, but at resonance conditions fulfilled, we found strong hybridization between bulk and radial edge modes. Interestingly, the hybridization between the fundamental modes in bulk and rim is of magnetostatic origin, but the exchange interactions determine the coupling between higher-order radial rim modes and the fundamental bulk mode of the antidot lattice. [ABSTRACT FROM AUTHOR]

With the development of new nanofabrication technologies and measurement techniques, the interest of researchers is moving toward 3D structures and 3D magnetization textures. Special attention is paid to the topological magnetization textures, particularly hopfions. In this paper, we investigate the magnetization dynamics of the hopfion through the numerical solution of the eigenvalue problem. We show that the spectrum of spin-wave modes of the hopfion is much richer than those attainable in ferromagnetic resonance experiments or time-domain simulations reported so far. We identified four groups of modes that differ in the character of oscillations (clockwise or counter-clockwise rotation sense), the position of an average amplitude localization along the radial direction, and different oscillations in the vertical cross section. The knowledge of the full spin-wave spectrum shall help in hopfion identification, understanding of the interaction between spin waves and hopfion dynamics as well as the development of the potential of hopfion in spintronic and magnonic applications. [ABSTRACT FROM AUTHOR]

We have investigated multifunctional periodic structures in which electromagnetic waves and spin waves can be confined in the same areas. Such simultaneous localization of both sorts of excitations can potentially enhance the interaction between electromagnetic waves and spin waves. The system we considered has a form of one dimensional photonic-magnonic crystal with two types of magnetic layers (thicker and thinner ones) separated by sections of the dielectric photonic crystals. We focused on the electromagnetic defect modes localized in the magnetic layers (areas where spin waves can be excited) and decaying in the sections of conventional (nonmagnetic) photonic crystals. We showed how the change of relative thickness of two types of the magnetic layers can influence on the spectrum of spin waves and electromagnetic defect modes, both localized in magnetic parts of the system. [ABSTRACT FROM AUTHOR]

We investigate the properties of a photonic-magnonic crystal, a complex multifunctional one-dimensional structure with magnonic and photonic band gaps in the GHz and PHz frequency ranges for spin waves and light, respectively. The system consists of periodically distributed dielectric magnetic slabs of yttrium iron garnet and nonmagnetic spacers with an internal structure of alternating TiO2 and SiO2 layers which form finite-size dielectric photonic crystals. We show that the spin-wave coupling between the magnetic layers, and thus the formation of the magnonic band structure, necessitates a nonzero in-plane component of the spin-wave wave vector. A more complex structure perceived by light is evidenced by the photonic miniband structure and the transmission spectra in which we have observed transmission peaks related to the repetition of the magnetic slabs in the frequency ranges corresponding to the photonic band gaps of the TiO2/SiO2 stack. Moreover, we show that these modes split to very high sharp (a few THz wide) subpeaks in the transmittance spectra. The proposed novel multifunctional artificial crystals can have interesting applications and be used for creating common resonant cavities for spin waves and light to enhance the mutual influence between them. [ABSTRACT FROM AUTHOR]

We study the effect of one-side metallization of a uniform ferromagnetic thin film on its spin-wave dispersion relation in the Damon-Eshbach geometry. Due to the finite conductivity of the metallic cover layer on the ferromagnetic film, the spin-wave dispersion relation may be nonreciprocal only in a limited wave-vector range. We provide an approximate analytical solution for the spin-wave frequency, discuss its validity, and compare it with numerical results. The dispersion is analyzed systematically by varying the parameters of the ferromagnetic film, the metal cover layer and the value of the external magnetic field. The conclusions drawn from this analysis allow us to define a structure based on a 30 nm thick CoFeB film with an experimentally accessible nonreciprocal dispersion relation in a relatively wide wave-vector range. [ABSTRACT FROM AUTHOR]

We present the observation of a complete bandgap and collective spin wave excitation in two-dimensional magnonic crystals comprised of arrays of nanoscale antidots and nanodots, respectively. Considering that the frequencies dealt with here fall in the microwave band, these findings can be used for the development of suitable magnonic metamaterials and spin wave based signal processing. We also present the application of a numerical procedure, to compute the dispersion relations of spin waves for any high symmetry direction in the first Brillouin zone. The results obtained from this procedure have been reproduced and verified by the well established plane wave method for an antidot lattice, when magnetization dynamics at antidot boundaries are pinned. The micromagnetic simulation based method can also be used to obtain iso-frequency contours of spin waves. Iso-frequency contours are analogous of the Fermi surfaces and hence, they have the potential to radicalize our understanding of spin wave dynamics. The physical origin of bands, partial and full magnonic bandgaps have been explained by plotting the spatial distribution of spin wave energy spectral density. Although, unfettered by rigid assumptions and approximations, which afflict most analytical methods used in the study of spin wave dynamics, micromagnetic simulations tend to be computationally demanding. Thus, the observation of collective spin wave excitation in the case of nanodot arrays, which can obviate the need to perform simulations, may also prove to be valuable. [ABSTRACT FROM AUTHOR]

We investigate spin waves in two-dimensional superlattices in the form of an infinite ferromagnetic slab of finite thickness with periodically embedded ferromagnetic inclusions. One of the reasons of the interest in magnonic superlattices is the possibility of tailoring their spectrum to produce magnonic gaps, crucial for the prospective applications. The objective of this study is to find the optimal values of structural parameters for which low-frequency magnonic gaps will occur and have a maximum width. We provide some guidelines for designing superlattices with a desired spectrum. We focus on the role of the symmetry of the lattice versus other geometrical factors, including the filling fraction and the superlattice constant. We compare the spectra of superlattices with inclusions of circular, hexagonal, and square cross sections. [ABSTRACT FROM AUTHOR]

We present the results of plane wave method-based calculations adopted to magnonic band structures for exchange spin waves propagating in three-dimensional magnonic crystals (MCs) composed of two ferromagnetic metals. The crystals under consideration consist of a system of ferromagnetic spheres arranged in sites of a hexagonal lattice and embedded in a ferromagnetic material. Having analyzed all the possible combinations of magnonic crystal component materials from: Co, Ni, Fe, and Py (for spheres and matrix), we find material configurations for which either absolute or partial magnonic gaps occur in the spin-wave spectrum of the MC. We also demonstrate that the opening of a magnonic gap necessitates a sufficiently large contrast of magnetic parameters, and find the exchange length contrast to be the best measure of the capacity of the MC to produce a magnonic gap. Wider magnonic gaps are obtained in MCs in which the exchange length in the sphere material is larger than in the matrix. Among the MCs considered in this study, an absolute magnonic gap is obtained in a crystal with Ni spheres embedded in Fe. [ABSTRACT FROM AUTHOR]

We have investigated theoretically band structure of spin waves in magnonic crystals with periodicity in one- (1D), two- (2D) and three-dimensions (3D). We have solved Landau-Lifshitz equation with the use of plane wave method, finite element method in frequency domain and micromagnetic simulations in time domain to find the dynamics of spin waves and spectrum of their eigenmodes. The spin wave spectra were calculated in linear approximation. In this paper we show usefulness of these methods in calculations of various types of spin waves. We demonstrate the surface character of the Damon-Eshbach spin wave in 1D magnonic crystals and change of its surface localization with the band number and wavenumber in the first Brillouin zone. The surface property of the spin wave excitation is further exploited by covering plate of the magnonic crystal with conductor. The band structure in 2D magnonic crystals is complex due to additional spatial inhomogeneity introduced by the demagnetizing field. This modifies spin wave dispersion, makes the band structure of magnonic crystals strongly dependent on shape of the inclusions and type of the lattice. The inhomogeneity of the internal magnetic field becomes unimportant for magnonic crystals with small lattice constant, where exchange interactions dominate. For 3D magnonic crystals, characterized by small lattice constant, wide magnonic band gap is found. We show that the spatial distribution of different materials in magnonic crystals can be explored for tailored effective damping of spin waves. [ABSTRACT FROM AUTHOR]

Excitation of bulk spin waves by acoustic wave localized on the elastic planar defect in the bulk ferromagnet was analytically and numerically investigated. We showed that besides magnetic oscillations forced by acoustic wave strain the resonance between Kosevich wave and bulk spin wave can occurs. For the frequency of the Kosevich wave far below the resonance frequency the amplitude of dynamic magnetization is negligible. For the frequency above the resonance the acoustic wave excites bulk spin wave of the same frequency but different absolute value of the wave vector. [ABSTRACT FROM AUTHOR]

In this paper, we show analytically and numerically, that the ultrathin metallic layer up to few monatomic layers separating two ferromagnetic media, which are exchange coupled, can effectively change the phase of the reflected or transmitted spin waves. Taking into account ground states with parallel orientations of the magnetization vectors, we developed the analytical model, which shows the possibility of spin-wave phase control by varying the exchange coupling strength between two ferromagnets. Moreover, we demonstrate with micromagnetic simulations that the effect still exists for the spin waves propagating in thin ferromagnetic film during the reflection or transmission from the interface, where interlayer exchange interactions are present. [ABSTRACT FROM AUTHOR]

For magnon spintronic applications, the detailed knowledge of spin wave (SW) beam dispersion, transmission (reflection) of SWs passing through (reflected from) interfaces, or borders or the scattering of SWs by inhomogeneities is crucial. These wave properties are decisive factors on the usefulness of a particular device. Here, we demonstrate, using micromagnetic simulations supported by an analytical model, that the Goos-Hänchen (GH) shift exists for SW reflecting from thin film edge and that with the effect becomes observable. We show that this effect will exist for a broad range of frequencies in the dipole-exchange range, with the magnetization degree of pinning at the film edge as the crucial parameter, whatever its nature. Moreover, we have also found that the GH effect can be accompanied or even dominating by a bending of the SW beam due to the inhomogeneity of the internal magnetic field. This inhomogeneity, created by demagnetizing field taking place at the film edge, causes gradual change of SWs refractive index. The refraction of the SW beams by the non-uniformity of the magnetic field enables the exploration of graded index magnonics and metamaterial properties for the transmission and processing of information at nanoscale. [ABSTRACT FROM AUTHOR]

We present an all-optical time-resolved measurement of spin wave (SW) dynamics in a series of antidot lattices based on [Co(0.75nm)/Pd(0.9nm)]8 multilayer (ML) systems with perpendicular magnetic anisotropy. The spectra depend significantly on the areal density of the antidots. The observed SW modes are qualitatively reproduced by the plane wave method. The interesting results found in our measurements and calculations at small lattice constants can be attributed to the increase of areal density of the shells with modified magnetic properties probably due to distortion of the regular ML structure by the Ga ion bombardment and to increased coupling between localized modes. We propose and discuss the possible mechanisms for this coupling including exchange interaction, tunnelling, and dipolar interactions. [ABSTRACT FROM AUTHOR]

We use a microscopic theory taking into account the dipolar and nearest-neighbour exchange interactions for exploring spin-wave excitations in two-dimensional magnetic dots in the vortex state. Normal modes of different profiles are observed: azimuthal and radial modes, as well as fundamental (quasiuniform) and highly localized modes. We examine the dependence of the frequencies and profiles of these modes on the dipolar-to-exchange interaction ratio and the size of the dot. Special attention is paid to some particular modes, including the lowest mode in the spectrum and the evolution of its profile, and the fundamental mode, the frequency of which proves almost independent of the dipolar-to-exchange interaction ratio. We also provide a selective overview of the experimental, analytical and numerical results from the literature, where different profiles of the lowest mode are reported. We attribute this diversity to the competition between the dipolar and exchange interactions. Finally, we study the hybridization of the modes, show the multi-mode hybridization and explain the selection rules. [ABSTRACT FROM AUTHOR]

We investigate the magnonic band structure of in-plane magnetized two-dimensional magnonic crystals composed of cobalt dots embedded into a permalloy antidot lattice. Our analysis is based on the results of numerical calculations carried out by the plane wave method. The complex magnonic band structure found in square-lattice magnonic crystals is explained on the basis of the spin wave dispersion relations calculated in the empty lattice model. We show that four principal effects influence the formation of a magnonic band structure in planar two-dimensional bi-component magnonic crystals: a folding effect, Bragg scattering, hybridization between various spin wave modes, and a demagnetizing field. While the first two effects are found for other types of waves in periodic composites, the third one exists in an anisotropic medium and the last one is specific to spin waves propagating in magnonic crystals with magnetization in the film plane. The strong anisotropy in the dispersion relation of spin waves in thin ferromagnetic films results in the crossing and anti-crossing of the fast, Damon–Eshbach-like mode with a number of other spin waves folded to the first Brillouin zone. The demagnetizing field can induce the formation of channels for spin waves which are propagating perpendicular to the external magnetic field direction, but this property exists only in the limiting range of the thicknesses and the lattice constants of the bi-component magnonic crystals. Based on the model analysis we propose a modification of the magnonic crystal structure by changing its thickness, lattice constant and aspect ratio along the direction of the applied magnetic field to significantly modify the magnonic band structure and obtain partial magnonic band gaps. [ABSTRACT FROM AUTHOR]

The nonreciprocal properties of spin waves in metallized one-dimensional bi-component magnonic crystal composed of two materials with different magnetizations are investigated numerically. Nonreciprocity leads to the appearance of indirect magnonic band gaps for magnonic crystals with both low and high magnetization contrast. Specific features of the nonreciprocity in low contrast magnonic crystals lead to the appearance of several magnonic band gaps located within the first Brillouin zone for waves propagating along the metallized surface. Analysis of the spatial distribution of dynamic magnetization amplitudes explains the mechanism of dispersion band formation and hybridization between magnonic bands in magnonic crystals with metallization. [ABSTRACT FROM AUTHOR]

We theoretically study the spin-wave spectra in magnonic waveguides periodically patterned with nanoscale square antidots. We show that structural changes breaking the mirror symmetry of the waveguide can close the magnonic bandgap. The effect of these intrinsic symmetry breaking can be compensated by adjusted asymmetric external bias magnetic field, i.e., by an extrinsic factor. This allows for the recovery of the magnonic bandgaps. The described methods can be used for developing parallel models for recovering bandgaps closed due to a fabrication defect. The model developed here is particular to magnonics, an emerging field combining spin dynamics and spintronics. However, the underlying principle of this development is squarely based upon the translational and mirror symmetries, thus, we believe that this idea of correcting an intrinsic defect by extrinsic means, should be applicable to spin-waves in both exchange and dipolar interaction regimes, as well as to other waves in general. [ABSTRACT FROM AUTHOR]

The dispersion of spin waves in a Permalloy binary antidot array constituted by two alternated antidot sublattices with different diameters of the circular holes has been investigated. The diameters of the holes are D1=300 nm and D2=150 nm with a holes center-to-center spacing of 425 nm. The spin wave frequency has been measured with Brillouin light scattering applying a magnetic field along the edge of the square unit cell of the lattice and sweeping the spin-wave wave vector along the perpendicular direction. The measured dispersion has been compared with calculations performed by the plane wave method, achieving a good agreement with the experimental results over the whole wave vector range. [ABSTRACT FROM AUTHOR]

In this paper, we propose a standard micromagnetic problem, of a nanostripe of permalloy. We study the magnetization dynamics and describe methods of extracting features from simulations. Spin wave dispersion curves, relating frequency and wave vector, are obtained for wave propagation in different directions relative to the axis of the waveguide and the external applied field. Simulation results using both finite element (Nmag) and finite difference (OOMMF) methods are compared against analytic results, for different ranges of the wave vector. [ABSTRACT FROM AUTHOR]

We investigate the magnonic properties of thin slabs of one-dimensional magnonic crystals with the aim of obtaining a structure that possesses negative permeability at high frequencies. Metamaterials of this kind could be used within devices based on the negative refractive index phenomenon. We calculate the relative excitation strengths of different spin-wave modes in one-dimensional magnonic crystals. We find that the coupling between light and high-order magnonic modes can be significant for the specific design of the magnonic structure. These results suggest that magnonic crystals are therefore promising candidates for the negative refractive index metamaterials. [ABSTRACT FROM AUTHOR]

The calculation of the magnonic spectra using the plane-wave method has limitations, the origin of which lies in the formulation of the effective magnetic field term in the equation of motion (the Landau-Lifshitz equation) for composite media. According to ideas of the plane-wave method the system dynamics is described in terms of plane waves (a superposition of a number of plane waves), which are continuous functions and propagate throughout the medium. Since in magnonic crystals the sought-for superposition of plane waves represents the dynamic magnetization, the magnetic boundary conditions on the interfaces between constituent materials should be inherent in the Landau-Lifshitz equations. In this paper we present the derivation of the two expressions for the exchange field known from the literature. We start from the Heisenberg model and use a linear approximation and take into account the spacial dependence of saturation magnetization and exchange constant present in magnetic composites. We discuss the magnetic boundary conditions included in the presented formulations of the exchange field and elucidate their effect on spin-wave modes and their spectra in one- and two-dimensional planar magnonic crystals from plane-wave calculations. [ABSTRACT FROM AUTHOR]

The plane-wave method is used to determine the spin-wave spectra in nanoscale one-dimensional magnonic crystals formed by a periodic lattice of ferromagnetic stripes. The dynamic demagnetizing field in a new formulation is used in these calculations. The calculated spectra of spin waves are compared with experimental data taken from literature and a good agreement is obtained. The dependence of the spin-wave spectra on magnetic material parameters consisting of magnetic stripes is systematically studied. We proved that the experimentally found magnonic band structure with two magnonic gaps is of magnetostatic nature. [ABSTRACT FROM AUTHOR]

The aim of this study is to analyse the stability of the single in-plane vortex state in two-dimensional magnetic nanodots with a nonmagnetic impurity (single-spin defect) at the centre. Small square and circular dots including up to a few thousand of spins are studied by means of a microscopic theory with nearest-neighbour exchange interactions and dipolar interactions fully taken into account. We calculate the spin-wave frequencies versus the dipolar-to-exchange interaction ratio d to find the values of d for which the assumed state is stable. Transitions to other states and their dependence on d and the vortex size are investigated as well, with two types of transition found: vortex core formation for small d values (strong exchange interactions), and in-plane reorientation of spins for large d values (strong dipolar interactions). Various types of localized spin waves responsible for these transitions are identified. [ABSTRACT FROM AUTHOR]

Abstract: We show that magnetostatic modes with amplitude localized in different regions of the sample along the direction of the magnetic field occur in ferromagnetic stripes: bulk-dead modes, with amplitude localized in two regions and comb modes localized in its central part. We also demonstrate these localization properties can be studied by Brillouin light scattering techniques and applied in practice. Having established that the localization of these modes varies with their frequency, we use this finding as the basis of a trial reinterpretation of experimental results obtained by Demidov et al. [Appl. Phys. Lett. 92 (2008) 232503]. [Copyright &y& Elsevier]

Spin wave resonance (SWR) spectra in composite ferromagnetic trilayer [A|B|A] are calculated by means of a transfer matrix method. Both the resonance spectra and the respective spin wave mode profiles are found to be sensitive to exchange and magnetization contrasts between the constituents A and B; thorough calculations are performed for two specific trilayer systems, [iron|nickel|iron] and [permalloy|nickel|permalloy] systems. We found that some remote lines of the trilayer SWR spectra may have higher intensity than the first ones. This high intensity of remote resonance lines is explained as an effect originating in the spin wave mode “localization” in the outer sublayers A; this is why the intensity of these “amplified” resonance lines are found to vary with the filling fraction (the width ratio of sublayers A and B). Depending on the surface spin pinning conditions this filling fraction effect may involve (for surface spins unpinned) resonance intensity changes alone or (for surface spins pinned) with an additional shift of the corresponding resonance lines. This property offers a possibility of a simple qualitative SWR determination of the surface pinning conditions in ferromagnetic trilayers. [Copyright &y& Elsevier]

The features of standing spin waves (SWs) excited during ferromagnetic resonance in three different one-dimensional magnonic crystals (MC) are intensively studied. The investigated magnonic crystals were: an array of air-spaced cobalt stripes, an array of air-spaced permalloy (Py) stripes, and a bi-component MC composed of alternating Co and Py stripes. All MC structures were made by etching technique from Co and Py thin films deposited onto Si substrates. Two configurations are considered with the in-plane external magnetic field applied parallel or perpendicular to the stripes. The supporting calculations are performed by the finite element method in the frequency domain. A number of intensive SW modes occurred in periodic structures under ferromagnetic resonance conditions as a consequence of standing spin waves excitation. These modes were analyzed theoretically in order to explain the origins of SW excitations. With the support of numerical calculations, we analyze also the possible scenarios for the occurrence of standing SWs in the investigated structures. It is demonstrated that the SW propagation length is an important factor conditioning the standing SW formation in MCs. [ABSTRACT FROM AUTHOR]

We use a microscopic theory taking into account dipolar and nearest-neighbour exchange interactions to explore spin-wave excitations in two-dimensional square-shaped magnetic nanorings with the Landau state assumed as a magnetic state. From the spin-wave spectra, we determine the range of the dipolar-to-exchange interaction ratio in which the assumed state is stable. Various types of localized spin waves prove responsible for the transition to a new magnetic configuration. We found the transition forced by predominating exchange interactions size-independent in a wide range of both external and internal size of the ring. [ABSTRACT FROM AUTHOR]

We present an all-optical time-resolved measurement of dipole-exchange spin wave spectra in a series of CoO capped [Co(t)/Pt(7 Å)]n-1 Co(t) multilayer systems, where the total Co moment (n × t) is constant. In general, the spectra consist of two intense peaks and additional lower intensity peaks. The observed spin wave modes are modeled by a discrete dipole approximation. The frequency of the spin wave bands depends significantly upon the magnetic anisotropy and the lattice spacing between planes. Both symmetric and anti-symmetric modes are observed from the calculation of the spin-wave profiles across the multilayer in the out-of-plane direction. [ABSTRACT FROM AUTHOR]

Planar one-dimensional magnonic crystals of nanoscale lattice constant having different types of overlayers, dielectric and metallic, are studied. The dynamics of magnetization is described by the Landau-Lifshitz equation, which is solved using the plane-wave method. The calculations are performed with the nonuniform dynamic dipolar field. At the same time, the finite thickness of the studied structures is taken into account. New possibilities for shaping dispersion relations of spin waves and magnonic bandgaps in planar magnonic crystals by adding metallic/dielectric overlayers on the top of it are found. [ABSTRACT FROM AUTHOR]

In the emerging field of magnon-spintronics, spin waves are exploited to encode, carry and process information in materials with periodic modulation of their magnetic properties, named magnonic crystals. These enable the redesign of the spin wave dispersion, thanks to its dependence on the geometric and magnetic parameters, resulting in the appearance of allowed and forbidden band gaps for specific propagation directions. In this work, we analyze the spin waves band structure of two-dimensional magnonic crystals consisting of permalloy square antidot lattices with different geometrical parameters. We show that the frequency of the most intense spin-wave modes, measured by Brillouin light scattering, exhibits a universal dependence on the aspect ratio (thickness over width) of the effective nanowire enclosed between adjacent rows of holes. A similar dependence also applies to both the frequency position and the width of the main band gap of the fundamental (dispersive) mode at the edge of the first Brillouin zone. These experimental findings are successfully explained by calculations based on the plane-wave method. Therefore, a unified vision of the spin-waves characteristics in two-dimensional antidot lattices is provided, paving the way to the design of tailored nanoscale devices, such as tunable magnonic filters and phase-shifters, with predicted functionalities. [ABSTRACT FROM AUTHOR]

A possibility to observe huge lateral shift (Goos-Hänchen effect) of exchange spin wave reflected from the interface of two ferromagnetic materials is theoretically investigated. The strong dependence of this effect on the exchange coupling between two magnetic media as well as on the magnetic field is obtained. We show that nonzero interlayer exchange is necessary to observe the lateral shift of reflected spin-wave, and this shift can reach values up to a few hundreds of wavelengths. The observed effect can be a useful tool in investigation of the magnetic coupling between two magnetic materials also through nonmagnetic spacer. [ABSTRACT FROM AUTHOR]

We demonstrate that the magnonic band structure, including the band gap of a ferromagnetic antidote waveguide, can be significantly tuned by a relatively weak modulation of its structural parameters. We study the magnonic band structure in nanoscale spin-wave waveguides with periodically distributed small antidots along their central line by two independent computational methods, namely, a micromagnetic simulation and a plane-wave method. The calculations were performed with consideration of both the exchange and dipolar interactions. For the exchange dominated regime, we discuss, in details, the impact of the changes of the lattice constant, size, and shape of the antidots on the spin-wave spectra. We have shown that a precise choice of these parameters is crucial for achieving desired properties of antidot waveguides, i.e., a large group velocity and filtering properties due to existence of magnonic band gaps. We discuss different mechanisms of magnonic gap opening resulting from Bragg scattering or anticrossing of modes. We have shown that the dipolar interactions start to assert their role in the spin-wave spectrum when the waveguide is scaled up, but even for a period of few hundreds of nanometers, the magnonic band structure preserves qualitatively the properties found in the exchange dominating regime. The obtained results are important for future development of magnonic crystal based devices. [ABSTRACT FROM AUTHOR]

• Transmitted spin wave phase shift changes for π via the uniform exchange parameter. • Maximum transmittance is reached at low negative values of the exchange parameter. • Strongest variation of the phase shift is for small interlayer exchange coupling. • Transmittance and the phase shift are strongly depended on the magnetic field. With increasing demand for miniaturization in computational and communication technologies, the ability to control spin wave amplitude and phase attract considerable attention, due to prospect of magnonics for valuable decrease of consumed energy with increased functionality of devices. In our paper we theoretically investigate spin wave propagation in the system of two antiferromagnetically coupled magnetic media separated with an ultrathin nonmagnetic interface layer. We propose to use this specially designed interface to perform control over the phase and the intensity of the transmitted spin waves. Our results show, that the interface with varying exchange coupling parameter can be treated as a metasurface, which can offer a change of the spin wave phase between transmitted and incident waves in the range from - π / 2 to π / 2. In particular we show, that a positive shift correlates with the lower and the negative phase shift with higher transmittance. Moreover, we show that the phase shift can be controlled by the external magnetic field. [ABSTRACT FROM AUTHOR]

We study propagation of the Gaussian beam of spin waves and its reflection from the edge of thin yttrium-iron-garnet film with in-plane magnetization perpendicular to this edge. We have performed micromagnetic simulations supported by analytical calculations to investigate the influence of the surface magnetic anisotropy present at the film edge on the reflection, especially in the context of the Goos-Hänchen effect. We have shown the appearance of a negative lateral shift between reflected and incident spin wave beams' spots. This shift is particularly sensitive to the surface magnetic anisotropy value and is a result of the Goos-Hänchen shift which is sensitive to the magnitude of the anisotropy and of the bending of the spin wave beam. We have demonstrated that the demagnetizing field provided a graded increase of the refractive index for spin waves, which is responsible for the bending. [ABSTRACT FROM AUTHOR]

We studied a finite Fibonacci sequence of Co and Py stripes aligned side by side and in direct contact with each other. Calculations based on a continuous model, including exchange and dipole interactions, were performed for structures feasible for fabrication and characterization of the main properties of magnonic quasicrystals. We have shown the fractal structure of the magnonic spectrum with a number of magnonic gaps of different widths. Moreover, localization of spin waves in quasicrystals and the existence of surface spin waves in finite quaiscrystal structure is demonstrated. [ABSTRACT FROM AUTHOR]

Spin waves propagation in 1D magnonic crystals is investigated theoretically. Mathematical model based on plane wave expansion method is applied to different types of magnonic crystals, namely bi-component magnonic crystal with symmetric/asymmetric boundaries and ferromagnetic film with periodically corrugated top surface. It is shown that edge modes in magnonic crystals may exhibit nonreciprocal behaviour at much lower frequencies than in homogeneous films. [ABSTRACT FROM AUTHOR]

We present an experimental and theoretical study of magnonic band gaps in planar one-dimensional magnonic crystals of two types, with a periodic array of metallic stripes or a periodic array of grooves on an yttrium iron garnet film. Propagating magnetostatic surface spin waves are excited in the considered periodic magnetic structures and measured by microstripe transducers with a vector network analyzer and with a Brillouin light scattering spectroscopy. The properties of magnonic band gaps are explained and illustrated by finite element method calculations. We demonstrate a major influence of the nonreciprocal spin-wave dispersion properties induced by metallic stripes on the width of the magnonic band gap and its dependence on the external magnetic field. The indirect character of the band gap and the higher group velocity of spin waves in the metallic magnonic crystal are identified as the main causes of the wider band gap and steeper decrease in its width with increasing magnetic field in this structure as compared to the grooved magnonic crystal. Potential applications of both types of magnonic crystals and prospects for their miniaturization are discussed as well. [ABSTRACT FROM AUTHOR]

We study the spin-wave spectra in magnonic antidot waveguides (MAWs) for two limiting cases (strong and negligible) of the surface anisotropy at the ferromagnet/air interface. The MAWs under investigation have the form of a thin stripe of permalloy with a single row of periodically arranged antidots in the middle. The introduction of a magnetization pinning at the edges of the permalloy stripe and the edges of antidots is found to modify the spin-wave spectrum. This effect is shown to be necessary for magnonic gaps to open in the considered systems. Our study demonstrates that the surface anisotropy can be crucial in the practical applications of MAWs and related structures and in the interpretation of experimental results in one- and two-dimensional magnonic crystals. We used three different numerical methods, i.e., plane waves method (PWM), finite difference method, and finite element method to validate the results. We showed that PWM in the present formulation assumes pinned magnetization, while in micromagnetic simulations special care must be taken to introduce pinning. [ABSTRACT FROM AUTHOR]

The spin-wave band structure of a two-dimensional bicomponent magnonic crystal, consisting of Co nanodisks partially embedded in a Permalloy thin film, is experimentally investigated along a high-symmetry direction by Brillouin light scattering. The eigenfrequencies and scattering cross sections are interpreted using plane wave method calculations and micromagnetic simulations. At the boundary of both the first and the second Brillouin zones, we measure a forbidden frequency gap whose width depends on the magnetic contrast between the constituent materials. The modes above and below the gap exhibit resonant spin-precession amplitudes in the complementary regions of periodically varying magnetic parameters. Our findings are key to advance both the physics and the technology of band gap engineering in magnonics. [ABSTRACT FROM AUTHOR]

We report spin wave excitations in a nanopatterned antidot lattice fabricated from a 30-nm thick Nig0Fe2o film. The 250-nm-wide circular holes are arranged in a rhombic unit cell with a lattice constant of 400 nm. By Brillouin light scattering, we find that quantized spin wave modes transform to propagating ones and vice versa by changing the in-plane orientation of the applied magnetic field H by 30°. Spin waves of either negative or positive group velocity are found. In the latter case, they propagate in narrow channels exhibiting a width of below 100 nm. We use the plane wave method to calculate the spin wave dispersions for the two relevant orientations of H. The theory allows us to explain the wave-vector-dependent characteristics of the prominent modes. Allowed minibands are formed for selected modes only for specific orientations of H and wave vector. The results are important for applications such as spin wave filters and interconnected waveguides in the emerging field of magnonics where the control of spin wave propagation on the nanoscale is key. [ABSTRACT FROM AUTHOR]

All-electrical spin-wave spectroscopy and frequency-resolved magneto-optical Kerr-effect measurements are combined to study spin waves propagating through a magnetic antidot lattice nanopatterned from a Ni80Fe20 thin film. Spin waves are injected from a plain film into the antidot lattice and the transmission across the interface is explored in detail for different wavelengths. We find that spin waves with a wavelength much greater than the lattice periodicity are not described well by recently discussed approaches. Instead the spin-wave dispersion is consistent with an effective magnetization smaller than the saturation magnetization measured on the unstructured ferromagnetic material. Consistently, we find that the transmission coefficients are modeled well by assuming an effectively continuous metamaterial for spin waves characterized by the reduced magnetization. The experimental data and interpretation are substantiated theoretically using the plane-wave method and micromagnetic modeling. The results are interesting for the development of frequency-selective mirrors in magnonics through lateral nanopatterning. [ABSTRACT FROM AUTHOR]

An efficient way for control of the spin wave propagation in a magnetic medium is the use of periodic patterns known as magnonic crystals (MCs). However, the fabrication of MCs especially bicomponents, with periodicity in nanoscale, is a challenging task due to the requirement for sharp interfaces. An alternative method to circumvent this problem is to use homogeneous ferromagnetic film with a modified periodically surrounding. In this work we demonstrate that the magnonic band structure is formed in thin Py film due to dynamical magnetostatic coupling with the array of Ni stripes. We show that the band gap width can be systematically tuned by changing separation between film and stripes. We show also the effect of nonreciprocity, which is seen at the band gap edge which is shifted from the Brillouin zone boundary and also in nonreciprocal interaction of propagating spin waves in Py film with the standing waves in Ni stripes. Our findings open a possibility for further investigation and exploitation of the nonreciprocity and band structure in magnonic devices. [ABSTRACT FROM AUTHOR]

The main object of investigation in magnonics, spin waves (SWs) are promising information carriers. Presently, the most commonly studied are plane-wave-like SWs and SWs propagating in confined structures, such as waveguides. Here we consider a Gaussian SW beam obliquely incident on an ultranarrow interface between two identical ferromagnetic materials. We use an analytical model and micromagnetic simulations for an in-depth analysis of the influence of the interface properties, in particular the magnetic anisotropy, on the transmission of the SW beam. We derive analytical formulas for the reflectance, transmittance, phase shift, and Goos-Hänchen (GH) shift for beams reflected and refracted by an interface between two semi-infinite ferromagnetic media. The GH shifts in SW beam reflection and transmission are confirmed by micromagnetic simulations in the thin-film geometry. We demonstrate the dependence of the characteristic properties on the magnetic anisotropy at the interface, the angle of incidence, and the frequency of the SWs. We also propose a method for the excitation of high-quality SW beams in micromagnetic simulations. [ABSTRACT FROM AUTHOR]