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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 modifications to the spin-wave spectra, even in a fully saturated state. In particular, the spectra split in two types of excitations, bulk modes with amplitude concentrated in a homogeneous part of 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., Comment: 11 pages, 4 figure

The increasing demand for ultrahigh data storage densities requires development of 3D magnetic nanostructures. In this regard, focused electron beam induced deposition (FEBID) is a technique of choice for direct-writing of various complex nano-architectures. However, intrinsic properties of nanomagnets are often poorly known and can hardly be assessed by local optical probe techniques. Here, we demonstrate spatially resolved spin-wave spectroscopy of individual circular magnetic elements with radii down to 100 nm. The key component of the setup is a microwave antenna whose microsized central part is placed over a movable substrate with well-separated CoFe-FEBID nanodisks. The circular symmetry of the disks gives rise to standing spin-wave resonances and allows for the deduction of the saturation magnetization and the exchange stiffness of the material using an analytical theory. The presented approach is especially valuable for the characterization of direct-write elements opening new horizons for 3D nanomagnetism and magnonics., Comment: 10 pages, 5 figures

The Talbot effect has been known in optics since XIX century and found various technological applications. In this paper, we demonstrate with the help of micromagnetic simulations this self-imaging phenomenon for spin waves propagating in a thin ferromagnetic film magnetized out-of-plane. We show that the main features of the obtained Talbot carpets for spin waves can be described, to a large extent, by the approximate analytical formulas yielded by the general analysis of the wave phenomena. Our results indicate a route to a feasible experimental realisation of the Talbot effect at low and high frequencies and offer interesting effects and possible applications in magnonics., Comment: 10 pages, 10 figures

A mgnetic bimeron is an in-plane topological counterpart of a magnetic skyrmion. Despite the topological equivalence, their statics and dynamics could be distinct, making them attractive from the perspectives of both physics and spintronic applications. In this work, we investigate an antiferromagnetic (AFM) thin film with interfacial Dzyaloshinskii-Moriya interaction (DMI), and introduce the AFM bimeron cluster as a new form of topological quasi-particle. Bimerons demonstrate high current-driven mobility as generic AFM solitons, while featuring anisotropic and relativistic dynamics excited by currents with in-plane and out-of-plane polarizations, respectively. Moreover, these spin textures can absorb other bimeron solitons or clusters along the translational direction to acquire a wide range of N\'eel topological numbers. The clustering involves the rearrangement of topological structures, and gives rise to remarkable changes in static and dynamical properties. The merits of AFM bimeron clusters reveal a potential path to unify multi-bit data creation, transmission, storage and even topology-based computation within the same material system, and may stimulate innovative spintronic devices enabling new paradigms of data manipulations., Comment: 10 pages

Magnetic skyrmions are particle-like chiral spin textures found in a magnetic film with out-of-planeanisotropy and are considered to be potential candidates as information carriers in next generationdata storage devices. Despite intense research into the nature of skyrmions and their dynamic prop-erties, there are several key challenges that still need to be addressed. In particular, the outstandingissues are the reproducible generation, stabilization and confinement of skyrmions at room tempera-ture. Here, we present a method for the capture of nanometer sized magnetic skyrmions in an arrayof magnetic topological defects in the form of an antidot lattice. With micromagnetic simulations,we elucidate the skyrmion formation in the antidot lattice and show that the capture is dependenton the antidot lattice parameters. This behavior is confirmed with scanning transmission x-ray mi-croscopy measurements. This demonstration that a magnetic antidot lattice can be implemented asa host to capture skyrmions provides a new platform for experimental investigations of skyrmionsand skyrmion based devices.

We study the spin-wave dynamics in nanoscale antidot lattices based on Co/Pd multilayers with perpendicular magnetic anisotropy. Using time-resolved magneto-optical Kerr effect measurements we demonstrate that the variation of the antidot shape introduces significant change in the spin-wave spectra, especially in the lower frequency range. By employing micromagnetic simulations we show that additional peaks observed in the measured spectra are related to narrow shell regions around the antidots, where the magnetic anisotropy is reduced due to the Ga+ ion irradiation during the focused ion beam milling process of the antidot fabrication. The results point at new possibilities for exploitation of localized spin waves in out-of-plane magnetized thin films, which are easily tunable and suitable for magnonics applications., Comment: 12 pages, 6 figures

By means of the plane wave method, we study nonuniform, i.e., mode- and k-dependent, effects in the spin-wave spectrum of a two-dimensional bicomponent magnonic crystal. We use the crystal based on a hexagonal lattice squeezed in the direction of the external magnetic field wherein the squeezing applies to the lattice and the shape of inclusions. The squeezing changes both the demagnetizing field and the spatial confinement of the excitation, which may lead to the occurrence of an omnidirectional magnonic band gaps. In particular, we study the role played by propagational effects, which allows us to explain the k-dependent softening of modes. The effects we found enabled us not only to design the width and position of magnonic band gaps, but also to plan their response to a change in the external magnetic field magnitude. This allows the reversible tuning of magnonic band gaps, and it shows that the studied structures are promising candidates for designing magnonic devices that are tunable during operation., Comment: Final version

The one-dimensional planar magnonic crystals are usually fabricated as a sequence of stripes intentionally or accidentally separated by non-magnetic spacers. The influence of spacers on shaping the spin wave spectra is complex and still not completely clarified. We performed the detailed numerical studies of the one-dimensional single- and bi-component magnonic crystals comprised of a periodic array of thin ferromagnetic stripes separated by non-magnetic spacers. We showed that the dynamic dipolar interactions between the stripes mediated by non-magnetic spacer, even ultra-narrow, significantly shift up the frequency of the ferromagnetic resonance and simultaneously reduce the spin wave group velocity, which is manifested by the flattening of the magnonic band. We attributed these changes in the spectra to the modifications of dipolar pinning and shape anisotropy both dependent on the width of the spacers and the thickness of the stripes, as well as to the dynamical magnetic volume charges formed due to inhomogeneous spin wave amplitude.

The calculations of the inelastic spin wave scattering by flexure vibrations of the Bloch domain wall (Winters magnons) in thin magnetic films are presented. The approach is based on the interaction of the propagating spin waves with the dynamical emergent electromagnetic field generated by the moving inhomogeneous magnetization texture (domain wall). The probability of the spin wave scattering for the Winters magnon emission and absorption processes essentially rises with the spin wave scattering angle increase up to 900. The angular dependence of the scattering probability is essentially stronger for the magnon absorption processes that allow distinguishing these elementary emission/absorption processes experimentally., Comment: 12 pages, 3 figures

Spin waves are promising information carriers which can be used in modern magnonic devices, characterized by higher performance and lower energy consumption than presently used electronic circuits. However, before practical application of spin waves, the efficient control over spin wave amplitude and phase needs to be developed. We analyze analytically reflection and refraction of the spin waves at the interface between two ferromagnetic materials. In the model we consider the system consisting of two semi-infinite ferromagnetic media, separated by the ultra-narrow interface region with the magnetic anisotropy. We have found the Goos-Hanchen shift for spin waves in transmission and reflection, and performed detailed investigations of its dependence on the anisotropy at the interface and materials surrounding the interface. We have demonstrated possibility of obtaining Goos-Hanchen shift of several wavelengths in reflection for realistic material parameters. That proves the possibility for change of the spin waves phase in ferromagnetic materials at subwavelength distances, which can be regarded as a metasurface for magnonics., Comment: 6 pages, 3 figures

We investigated the lifetime of spin wave eigenmodes in periodic and quasiperiodic sequences of Py and Co wires. Those materials differ significantly in damping coefficients, therefore, the spatial distribution of the mode amplitude within the structure is important for the lifetime of collective spin wave excitations. Modes of the lower frequencies prefer to concentrate in Py wires, because of the lower FMR frequency for this material. This inhomogeneous distribution of amplitude of modes (with lower amplitude in material of higher damping and with higher amplitude in material of lower damping) is preferable for extending the lifetime of the collective excitations beyond the volume average of lifetimes for solid materials. We established the relation between the profile of the mode and its lifetime for periodic and quasiperiodic structures. We performed also the comparative studies in order to find the differences resulting from complexity of the structure and enhancement of localization in quasiperiodic system on the lifetime of spin waves., Comment: 16 pages, 8 figures

Local modification of magnetic properties of nanoelements is a key to design future-generation magnonic devices, in which information is carried and processed via spin waves. One of the biggest challenges here is to fabricate simple and miniature phase-controlling elements with broad tunability. Here, we successfully realize such spin-wave phase shifter upon a single nanogroove milled by focused ion beam in a Co-Fe microsized magnonic waveguide. By varying the groove depth and the in-plane bias magnetic field we continuously tune the spin-wave phase and experimentally evidence a complete phase inversion. The microscopic mechanism of the phase shift is based on the combined action of the nanogroove as a geometrical defect and the lower spin-wave group velocity in the waveguide under the groove where the magnetization is reduced due to the incorporation of Ga ions during the ion-beam milling. The proposed phase shifter can easily be on-chip integrated with spin-wave logic gates and other magnonic devices. Our findings are crucial for designing nano-magnonic circuits and for the development of spin-wave nano-optics., Comment: 8 pages, 6 figures

We present a theoretical investigation of the Goos-H\"anchen effect, i.e., the lateral shift of the light beam transmitted through one-dimensional biperiodic multilayered photonic systems consisting of equidistantmagnetic layers separated by finite size dielectric photonic crystals. We show that the increase of the number of periods in the photonic-magnonic structure leads to increase of the Goos-H\"anchen shift in the vicinity of the frequencies of defect modes located inside the photonic band gaps. Presence of the linear magnetoelectric coupling in the magnetic layers can result in a vanishing of the positive maxima of the cross-polarized contribution to the Goos-H\"anchen shift., Comment: 15 pages

By means of the plane wave method we study spin wave dynamics in two-dimensional bi-component magnonic crystals based on a squeezed hexagonal lattice and consist of a permalloy thin film with cobalt inclusions. We explore the dependence of a spin wave frequency on the external magnetic field, especially in weak fields where the mode softening takes place. For considered structures, the mode softening proves to be highly non-uniform on both the mode number and the wave vector. We found this effect to be responsible for the omnidirectional band gap opening. Moreover, we show that the enhancement of the demagnetizing field caused by the squeezing of the structure is of crucial importance for the non-uniform mode softening. This allows us to employ this mechanism to design magnonic gaps with different sensitivity for the tiny change of the external field. The effects we have found should be useful in designing and optimization of spin wave filters highly tunable by a small external magnetic field., Comment: Final version

We investigate experimentally and theoretically the magnetization reversal process in one-dimensional magnonic structures composed of permalloy nanowires of the two different widths and finite length arranged in a periodic and quasiperiodic order. The main features of the hysteresis loop are determined by different shape anisotropies of the component elements and the dipolar interactions between them. We showed, that the dipolar interactions between nanowires forming a ribbon can be controlled by change a distance between the neighboring ribbons. The quasiperiodic order can influence the hysteresis loop by introduction additional tiny switching steps when the dipolar interactions are sufficiently strong., Comment: 10 pages, 7 figures

Reversed structures of artificial spin-ice systems, where elongated holes with elliptical shape (antidots) are arranged into a square array with two orthogonal sublattices, are referred to as anti-squared spin-ice. Using Brillouin light scattering spectroscopy and plane wave method calculations, we investigate the spin wave propagation perpendicular to the applied field direction for two 20 nm thick Permalloy nanostructures which differ by the presence of single and double elliptical antidots. For the spin waves propagation along the principal antidot lattice axis, the spectrum consists of flat bands separated by several frequency gaps which are the effect of spin wave amplitude confinement in the regions between antidots. Contrarily, for propagation direction at 45 degrees with respect to the antidot symmetry axis, straight and narrow channels of propagation are formed, leading to broadening of bands and closing of the magnonics gaps. Interestingly, in this case, extra magnonic band gaps occur due to the additional periodicity along this direction. The width and the position of these gaps depend on the presence of single or double antidots. In this context, we discuss possibilities for the tuning of spin wave spectra in anti-squared spin ice structures.

Nanoscale magnetic systems have been studied extensively in various geometries, such as wires of different cross-sections, arrays of wires, dots, rings, etc. Such systems have interesting physical properties and promising applications in advanced magnetic devices. Uniform magnetic nanowires are the basic structures which were broadly investigated. However, some of their dynamical properties, like: (anti)crossing between the spin wave modes and impact of the magnetic field on spin wave spectrum, still need to be exploited. We continue this research by investigation of the spin wave dynamics in solid Ni nanowire of the circular cross-section. We use two approaches: semi-analytical calculations and numerical computations based on finite element method. We solve coupled Landau-Lifshitz and Maxwell equations and consider both magnetostatic and exchange interactions. We identify the dispersion brunches and its (anti)crossing by plotting the spatial profiles of spin wave amplitudes and magnetostatic potential. We also check how we can tune the spectrum of the modes by application of the external magnetic field and how it affects the modes and their dominating type of interaction., Comment: 21 pages, 5 figures

We study azimuthal spin-wave (SW) excitations in a circular ferromagnetic nanodot in different inhomogeneous, topologically non-trivial magnetization states, specifically, vortex, Bloch-type skyrmion and N\'eel-type skyrmion states. Continuous mapping of the SW spectrum between these states is realized with gradual change of the out-of-plane magnetic anisotropy and Dzyaloshinskii-Moriya exchange interaction (DMI). Our study shows lifting of the SW frequencies degeneracy and change in systematics of the frequency levels. The change is induced by a geometrical Berry phase, that is present for the dot-edge localized SWs in a vortex state and vanishes in skyrmion states. Furthermore, channeling of the azimuthal SWs localized at the skyrmion edge is present and induces large frequency splitting. This is attributed to DMI induced nonreciprocity, while coupling of the breathing and gyrotropic modes is related to soliton motion. Finally, an efficient coupling of the dynamic magnetization in the skyrmion state to uniform magnetic field in nanodots with non-circular symmetry is shown., Comment: 11 pages, 9 figures

We report the results of simulations of magnetic skyrmion stability in ultrathin magnetic multilayer nanodots with interfacial Dzyaloshinskii-Moriya exchange interaction (DMI). We found that in presence of the lateral confinement the magnetostatic energy significantly influences the skyrmion stability and leads to stabilization of large radius skyrmion even at low values of the DMI strength, in addition to small radius skyrmion stabilized by DMI. In particular, stabilization of the skyrmion state with two different radii (bi-stability) is found in dipolarly-coupled (Pt/Co/Ir)$_{n}$ circular nanodots with the number of repeats of the unit cell $n$ = 3 and 5. The bi-stability range is located at the DMI strength of 0.9-1.1 mJ/m$^2$ or at the total Co-layer thickness of 2.2-2.6 nm.

An efficient way for the control of spin wave propagation in a magnetic medium is the use of periodic patterns known as magnonic crystals (MCs). However, the fabrication of MCs especially bi-components, with periodicity on 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 modified periodically surrounding. The structure is also suitable for exploiting nonreciprocal properties of the surface spin waves. In this work, we demonstrate that the magnonic band structure forms in thin permalloy film due to dynamical magnetostatic coupling with Ni stripes near its surface. We show, that the band gap width can be systematically tuned by the changing interlayer thickness between film and stripes. We show also the effect of nonreciprocity, which is seen at the band gap edge shifted from the Brillouin zone boundary and also in nonreciprocal interaction of propagating spin waves in Py film with the standing spin waves in Ni stripes. Our findings open possibility for further investigation and exploitation of the nonreciprocity and band structure in magnonic devices., Comment: 12 pages, 5 figures

We study the effect of surface-induced Dzyaloshinskii-Moriya interaction (DMI) on the ferromagnetic resonance (FMR) spectrum of thickness-modulated one-dimensional magnonic crystals and isolated stripes. The DMI is found to substantially increases the intensity of absorption peaks and shifts the frequencies of the laterally quantized modes. The role of the DMI is determined by analyzing the amplitude and phase distributions of dynamic magnetic excitations calculated with frequency- and time-domain calculation methods. We propose experimentally realizable magnonic crystals and confined structures with multiple FMR absorption peaks. The frequency or magnetic field separation between FMR lines is exploited to propose a method for estimation of the DMI strength., Comment: 7 pages, 9 figures

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., Comment: 17 pages, 15 pages, EUs Horizon2020 research and innovation programme under the Marie Sklodowska-Curie GA No644348

In this paper, we theoretically study the influence of a non-magnetic spacer between ferromagnetic dots and ferromagnetic matrix on the frequency dispersion of the spin wave excitations in two-dimensional bi-component magnonic crystals. By means of the dynamical matrix method we investigate structures inhomogeneous across the thickness represented by square arrays of Cobalt or Permalloy dots in a Permalloy matrix. We show that the introduction of a non-magnetic spacer significantly modifies the total internal magnetic field especially at the edges of the grooves and dots. This permits the manipulation of the magnonic band structure of spin waves localized either at the edges of the dots or in matrix material at the edges of grooves. According to the micromagnetic simulations two types of end modes were found. The corresponding frequencies are significantly influenced by the end modes localization region. We also show that, with the use of a single ferromagnetic material, it is possible to design a magnonic crystal preserving properties of bi-component magnonic crystals and magnonic antidot lattices. Finally, the influence of the non-magnetic spacers on the technologically relevant parameters like group velocity and magnonic band width are discussed., Comment: 18 pages, 5 figures

We have investigated theoretically (with micromagnetic simulations and plane wave method) and experimentally (with ferromagnetic resonance and Brillouin light scattering) three types of antidot lattices (ADLs) based on permalloy thin films with increased complexity of the unit cell: simple square, bi-component square and wave-like ADL. We have found that placing a small additional antidot in the center of the unit cell of the square ADL modify significantly the spin wave spectrum and its dependence on the orientation of the in-plane magnetic field. We also check the further changes of spin wave spectrum resulting from the introduction of air-gaps connecting small and large antidots. In particular, the presence of small antidots change the dependence of the frequency of the fundamental mode on the angle of the in-plane applied magnetic field. The air-gaps strongly discriminates the propagation of spin waves in two principal direction of ADL lattice, orthogonal to each other. In spite of these spectral changes, the spatial distribution of the spin wave amplitude generally preserves some similarities for all three structures. We also highlighted out the role of defects in the ADL in the observed spectra. The obtained results can be interesting for the magnonics applications of the magnonic crystals., Comment: 22 pages, 10 figures and submitted to Physical Review Letters B

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 ultra-narrow 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-Hanchen (GH) shift for beams reflected and refracted by an interface between two semi-infinite ferromagnetic media; the results for the refracted beam are the first to be reported to date. 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.

We present an approach enabling generation of narrow spin wave beams in thin homogeneous ferromagnetic films. The main idea is to match the wave vector of the spin wave with that corresponding to the spectral maximum of the exciting microwave magnetic field only locally, in the region of space from which the beam should be launched. We show that this can be achieved with the aid of a properly designed coplanar waveguide transducer generating a nonuniform microwave magnetic field. The resulting two-dimensional spin wave beams obtained in micromagnetic simulations propagate over distances of several micrometers. The proposed approach requires neither inhomogeneity of the ferromagnetic film nor nonuniformity of the biasing magnetic field, and it can be generalized to yield multiple spin wave beams of different width at the same frequency. Other possible excitation scenarios and applications of spin wave beam magnonics are also discussed.

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 influence of the surface magnetic anisotropy present at the film edge on the reflection, especially in the context of the Goos-Hanchen 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-Hanchen shift which is sensitive to the magnitude of the anisotropy and of the bending of spin wave beam. We have demonstrated that the demagnetizing field provide graded increase of the refractive index for spin waves, which is responsible for the bending.

We investigate theoretically skyrmion magnonic crystal, i.e., the dynamics of the magnetization in a chain of the ferromagnetic nanodots being in skyrmion magnetic configuration. We show that collective excitations are possible to be observed in the structure. We present the dispersion relation of the coupled skyrmions. It exhibit a periodical property in dependence on wave vector, characteristic feature of the band structure in magnonic crystals. Spatial analysis of the magnetization amplitude associated with the magnonic bands confirms type of the excited modes, as breathing and clockwise gyrotropic dynamical skyrmions. These high and low frequency excitations, propagate with negative and positive group velocity, respectively, and can be explored for study fundamental properties and technological applications in spintronics and magnonics., Comment: Pacs 75.70.Kw, 75.30.Ds, 75.40.Gb, 75.75.-c, 75.78.Fg

We studied finite Fibonacci sequence of Co and Py stripes aligned side-by-side and in direct contact with each other. Calculations based on continuous model including exchange and dipole interactions were performed for structures feasible for fabrication and characterization of main properties of magnonic quasicrystals. We have shown the fractal structure of the magnonic spectrum with a number of magnonics gaps of different width. Also localization of spin waves in quasicrystals and existence of surface spin waves in finite quaiscrystal structure is demonstrated., Comment: 7 pages, 5 figures

The magnonic band gaps of the two types of planar one-dimensional magnonic crystals comprised of the periodic array of the metallic stripes on yttrium iron garnet (YIG) film and YIG film with an array of grooves was analyzed experimentally and theoretically. In such periodic magnetic structures the propagating magnetostatic surface spin waves were excited and detected by microstripe transducers with vector network analyzer and by Brillouin light scattering spectroscopy. Properties of the magnonic band gaps were explained with the help of the finite element calculations. The important influence of the nonreciprocal properties of the spin wave dispersion induced by metallic stripes on the magnonic band gap width and its dependence on the external magnetic field has been shown. The usefulness of both types of the magnonic crystals for potential applications and possibility for miniaturization are discussed.

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., Comment: 9 pages, 6 figures

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 has been reproduced and verified by the well established plane wave method for an antidot lattice, when magnetization dynamics at antidot boundaries is pinned. The micromagnetic simulation based method can also be used to obtain iso--frequency countours of spin waves. Iso--frequency contours are analougous 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 has 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.

We theoretically study the spin-wave spectra in magnonic waveguides periodically patterned with square anti-dots in nanoscale with pinned magnetization at the edges. We show that the breaking of the mirror symmetry of the waveguide by the structural changes can result in a magnonic band gap closing. These intrinsic symmetry breaking can be compensated by properly chosen asymmetric external bias magnetic field, i.e. in an extrinsic way. As a result the magnonic gaps existing in the ideal symmetric structure can be recovered. The model used for the explanation also suggests that this idea could be generic both for exchange and dipolar interaction regimes of spin-waves and also for other types of waves, e.g., electrons in the graphene ribbons., Comment: 5 pages, 4 figures

We have computed the electronic and hole spectra of a 3D superlattice consisting of layers of GaAs rods of finite height arranged in a hexagonal lattice and embedded in an AlGaAs matrix, alternating with spacer layers of homogeneous AlAs. The spectra are calculated in the envelope function approximation, with both light-hole and heavy-hole subbands and hole spin degeneracy taken into account. The application of thick spacers allows to investigate the band structure of isolated layers of cylindrical rods. We estimate the ultimate efficiency of solar energy conversion in a solar cell based on an array of cylindrical quantum dots versus the dot height, and determine the optimal value of this parameter., Comment: 4 pages, 3 figures

We consider quantum wire arrays consisting of GaAs rods embedded in Al$_{x}$Ga$_{1-x}$As and disposed in sites of a square or triangular lattice. The electronic and hole spectra around the conduction band bottom and the valence band top are examined versus geometry of the lattice formed by the rods, concentration of Al in the matrix material, and structural parameters including the filling fraction and the lattice constant. Our calculations use the envelope function and are based on the effective-mass approximation. We show that the electronic and hole spectra resulting from the periodicity of the heterostructure, depend on the factors considered and that the effect of lattice geometry varies substantially with lattice constant. For low lattice constant values the minigaps are significantly wider in the case of triangular lattice, while for high lattice constant values wider minigaps occur in the square lattice-based arrays. We analyse the consequences of our findings for the efficiency of solar cells based on quantum wire arrays., Comment: 20 pages, 10 figures

Magnetostatic normal modes are investigated here in elongated rods. The dipolar field resulting from the dipole-dipole interactions is calculated numerically in points of the axis connecting opposite rod face centers (\emph{central axis}) by collecting individual contributions to this field coming from each of the atomic planes perpendicular to the central axis. The applied magnetic field is assumed to be oriented along the central axis, and the magnetization to be uniform throughout the sample. The \emph{frequency} spectrum of magnetostatic waves propagating in the direction of the applied field is found numerically by solving the Landau-Lifshith equation of motion with the spatially \emph{nonhomogeneous} dipolar field taken into account; the mode amplitude \emph{profiles} are depicted as well. While energetically highest modes have \emph{bulk-extended} character, the modes forming the lower part of the spectrum are localized in the subsurface region (\emph{bulk-dead modes}). Between these two mode types, magnetostatic modes of a new type (\emph{comb modes}) are found to occur, characterized by two clearly discernible regions: a zone of fast amplitude oscillations inside the rod, and narrow slow-oscillation regions at the borders. Absorbing virtually no energy from an applied alternating field, comb modes will have no significant contribution to the magnetic noise., Comment: 16 pages, 6 figures, conferences paper: Physics of Magnetism'05, Poznan, Poland

A theory of three-dimensional (3D) hypothetical magnonic crystal (conceived as the magnetic counterpart of the well-known photonic crystal) is developed and applied to explain the existence of a spin-wave frequency gap recently revealed in low-doped manganites $La_{1-x}Ca_{x}MnO_{3}$ by neutron scattering. A successful confrontation with the experimental results allows us to formulate a working hypothesis that certain manganites could be regarded as 3D magnonic crystals existing in nature., Comment: 5 pages, 3 figures, submitted to PRL

We investigate the dynamical properties of a system of interacting magnetic dipoles disposed in sites of an sc lattice and forming a cubic-shaped sample of size determined by the cube edge length (N-1)a (a being the lattice constant, N representing the number of dipolar planes). The dipolar field resulting from the dipole-dipole interactions is calculated numerically in points of the axis connecting opposite cube face centers (central axis) by collecting individual contributions to this field coming from each of the N atomic planes perpendicular to the central axis. The applied magnetic field is assumed to be oriented along the central axis, magnetizing uniformly the whole sample, all the dipoles being aligned parallelly in the direction of the applied field. The frequency spectrum of magnetostatic waves propagating in the direction of the applied field is found numerically by solving the Landau-Lifshitz equation of motion including the local (nonhomogeneous) dipolar field component; the mode amplitude spatial distributions (mode profiles) are depicted as well. It is found that only the two energetically highest modes have bulk-extended character. All the remaining modes are of localized nature; more precisely, the modes forming the lower part of the spectrum are localized in the subsurface region, while the upper-spectrum modes are localized around the sample center. We show that the mode localization regions narrow down as the cube size, N, increases (we investigated the range of N=21 to N=101), and in sufficiently large cubes one obtains practically only center-localized and surface-localized magnetostatic modes., Comment: 20 pages, 9 figures in postscript, useing Revtex4.cls