Theory of Spin Waves in a Thin Ferromagnetic Film with a Periodic System of Circular Antidots. Solutions that Correspond to the Crystal Band Theory

Abstract— The paper continues study of dipole-exchange spin waves in a two-dimensional magnonic crystal (a thin ferromagnetic film with a periodic system of circular antidots) started by the author in the previous paper. The proposed model considers the magnetic dipole-dipole interaction, the exchange interaction and the anisotropy effects. An improved method of obtaining the dispersion relation as well as the values’ spectra of the frequencies and wavenumbers for the investigated spin waves – the method based on using the Bloch-type solutions of the Landau-Lifshitz equation for the spin waves together with the Born–von Karman boundary conditions – is proposed. Exploitation of the above-mentioned method essentially extends the area of application of the obtained results compared to the previous paper. Newly obtained spectral characteristics are shown to exhibit crystal-type band structure with band gaps. The wave vector component that correspond to the wave propagating orthogonally to the film plane is shown to have narrow allowed bands, so its values' spectrum is near discrete