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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.

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.