Metamaterial description of magnonic modes along ΓM direction in a 2D antidot lattice

In this paper the metamaterial properties of a two-dimensional magnonic crystal consisting of a periodic array of circular holes (antidots) embedded into a continuous film of permalloy are studied according to micromagnetic calculations based on the dynamical matrix method and to analytical calculations. The magnetic field is applied along the diagonal of the square primitive cell and perpendicularly to the in-plane Bloch wave vector. This geometry corresponds to the high-symmetry direction ΓM in the reciprocal space. Bragg´s law for magnonic modes at Brillouin zone boundaries is derived by using the notion of effective wavelength. It is also shown that, in the stationary regime, the geometric scattering of collective modes from holes can be regarded as a metamaterial effect having a different meaning with respect to the well-known Bragg diffraction.