Nonreciprocal properties of GHz frequency surface spin waves in nanopatterned ferromagnetic films

Nonreciprocal properties of the magnetostatic spin waves propagating in thin ferromagnetic films are potentially useful for design miniaturized microwave isolators and circulators, essential elements in microwave technology. Here, we study theoretically surface magnetostatic spin waves propagating perpendicularly to the external magnetic field in thin ferromagnetic films with periodic pattern, i.e., in one dimensional magnonic crystals. We identified influence of a periodic pattern on a surface localization of the spin wave amplitude. In particular we showed, that the surface character vanishes at wavenumbers related to the symmetry points of the reciprocal space, making distribution of the amplitude across the film thickness symmetric. Moreover, we show, that the asymmetric amplitude distribution can be enhanced by modification one of the surfaces or surroundings of the ferromagnetic film. This modification introduces also nonreciprocal dispersion relations for spin waves. Despite the nonreciprocity of the dispersion relation, the surface spin waves form magnonic band gaps in the magnonic spectra. However, the band gaps are shifted to higher frequencies and wave vectors far from the border of the Brillouin zone in the case of nonreciprocal dispersion. The potential applications of nonreciprocal properties of spin waves are discussed.