Metamaterial properties of a 3D permalloy/cobalt magnonic crystal

In this paper a theoretical investigation, based on the micromagnetic dynamical matrix method, of the metamaterial properties of a three-dimensional binary magnonic crystal is performed. The system is formed by a periodic array of cobalt circular dots partially embedded into a permalloy film 16 nm thick. The periodicity of the system is a = 600 nm, the dot diameter is d = 310 nm and the dot thickness is L = 8 nm. The dispersion of the most representative magnonic mode confined in the permalloy film is calculated up to the fifth Brillouin zone for the external magnetic field H applied along the y axis and for the Bloch wave vector K along the x direction in the plane of the system. The collective mode dynamics is studied also within an effective medium approximation in the propagative regime.