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Magnetic films with a periodic pattern were considered for controlling spin waves (SWs) from 1976. The concept of magnonic crystals (MCs) was proposed as an SW counterpart of photonic crystals. The MC can be formed from a magnetic material with periodic distribution of the constituent materials or periodic modulation of some magnetic parameters or other parameters relevant to the propagation of SWs, such as the external magnetic field, geometry, temperature, or a surrounding of the homogeneous ferromagnetic medium. The chapter provides an overview of the theoretical results on the magnonic band structure in three-dimensional (3D) MCs. The most challenging problem related to experimental studies on 3D MCs is the fabrication of a high-quality structure with periodicity along three directions in the nanoscale. The research on 3D MCs was concentrated on the calculation of the magnonic band structure and influence of the material and geometrical parameters on the magnonic bandgaps. The chapter concludes with prospects for further development toward 3D MCs.

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 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

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

10th International Conference on Nanostructured Materials (NANO), Rome, ITALY, SEP 13-17, 2010; International audience; 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.

We study two-dimensional circular nanorings composed of elementary magnetic moments arranged in sites of a square lattice. Using a microscopic approach that takes into account the dipolar and nearest-neighbor exchange interactions, we calculate the spin-wave frequencies and profiles to draw conclusions regarding the stability of the assumed magnetic configuration. We show that, in contrast to square rings, in circular rings the exchange-driven reorientation is sensitive to both the external and internal sizes of the ring. We associate this behavior with the delocalized character of the lowest spin-wave excitation, and show that, consequently, the in-plane vortex state can be stabilized even in the case of strong exchange interactions.

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 antisquared 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-wave 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\ifmmode^\circ\else\textdegree\fi{} 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 antisquared spin-ice structures.