Perpendicularly magnetized antidot lattice as a two-dimensional magnonic metamaterial

In this paper the effective properties of a perpendicularly magnetized magnonic crystal are theoretically studied. The magnonic crystal is a two-dimensional antidot lattice composed by circular holes embedded into a ferromagnetic film. Both the periodicity of the magnonic crystal and the diameter of the holes are in the nanometric range and the external magnetic field is applied perpendicularly to the plane. It is shown, according to a micromagnetic approach and analytical calculations, that the effective rules linking the effective wavelength and effective wave vector of collective modes to the corresponding Bloch quantities characterizing the dynamics of in-plane magnetized periodic systems remain valid also in this geometry. It is thus possible to classify two-dimensional antidot lattices with perpendicular magnetization as magnonic metamaterials. Other metamaterial properties arising from the band structure calculation such as the band gap amplitudes at the Brillouin zone boundaries are also discussed.