Spin-waves in cylindrical magnetic dot arrays with in-plane magnetization

The discrete spectrum of dipole-exchange spin-wave modes of a tangentially magnetized cylindrical magnetic dot is calculated from the solution of the Landau–Lifshitz equation and the magnetostatic Maxwell equations in a cylindrical geometry. The general surface spin-pinning conditions at the radial dot boundary are considered. The main simplifying assumptions are: (i) the dot radius is much larger than the dot height; (ii) the distribution of the variable magnetization along the dot height is uniform. The approximate dispersion equation for spin-wave modes in a dot is obtained in a simple analytical form similar to the form of the dispersion equation in an infinite film. The quantization effect of the spin-wave frequencies appears due to the finite dot radius and is essential for submicron magnetic dots. The discrete spin-wave frequencies are calculated in a practically important case of the square array of permalloy cylindrical dots. The relative intensities of spin-wave modes, when observed by Brillouin light scattering, are considered. The role of interdot dipole–dipole coupling is discussed.