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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.

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

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.

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

Ferromagnetic resonance (FMR) in exchange-coupled bilayer films has been the subject of intensive studies in recent years. From the experimental viewpoint, a characteristic feature of this FMR is that some specimens show single resonance, whereas others show double resonance. Moreover, double resonance can exhibit a regular pattern, in which the high-field (HF) line intensity surpasses that of the low-field (LF) line, or it can exhibit an inverted pattern with the HF line less intense than the LF line. There is a general belief that the inverted FMR pattern occurs when the HF line is an "optic mode", i.e. an out-of-phase composition of individual sublayer modes, and the LF line is an "acoustic mode", or an in-phase mode composition. The existing theoretical explanations of bilayer ferromagnetic resonance are, as a rule, based on phenomenological equation of motion of the magnetization vector. In this paper, we propose a theory of FMR in ultrathin bilayers based on an entirely microscopic approach, using the Heisenberg model of localized spins and assuming that the two ferromagnetic sublayers are exchange-coupled through their interface. This rigorous microscopic FMR theory does explain the inverted pattern of the bilayer FMR spectrum by assuming the HF line to correspond to an in-phase mode, but of interface-localized nature; this gives a possibility to explore the HF resonance line corresponding to the interface-localized mode as a potential source of information concerning the bilayer interface., Comment: 36 pages, 12 figures