Anisotropic dynamical coupling for propagating collective modes in a two-dimensional magnonic crystal consisting of interacting squared nanodots

Collective spin excitations in a planar array of interacting submicron magnetic squared dots have been studied by the Brillouin light-scattering technique. The dispersion curves of collective spin modes are characterized by periodical oscillations determined by the width of the artificial Brillouin zone. Because of the uniaxial symmetry introduced by the application of an external magnetic field H-0, the dynamical coupling and the frequency dispersion of collective modes are different when the wave vector is perpendicular or parallel to H-0. An analytical model has been exploited to calculate the dispersion of collective spin modes by numerically solving eigenvalue/eigenfunction problem for a band matrix which originates from linearized Landau-Lifshitz magnetic torque equation. A very good agreement between calculation and experiment was found. In addition, a micromagnetic approach has been exploited to achieve an independent evaluation of the collective modes frequency and a visualization of their spatial profile on a limited (3 x 3) array of dots.