Two-dimensional dispersion of magnetostatic volume spin waves

Abstract. Owing to the dipolar (magnetostatic) interaction, long-wavelength spin waves in in-plane magnetized films show an unusual dispersion behavior, which can be mathematically described by the model of Damon and Eshbach and refinements thereof. However, solving the two-dimensional dispersion ω(k) requires the evaluation of a set of coupled trancedental equations and one has to rely on numerics. In this work, we present a systematic perturbative analysis of the spin wave model. An expansion in the in-plane wavevector k allows us to obtain explicit closed-form expressions for the dispersion relation and mode profiles in various asymptotic regimes. Moreover, we derive a very accurate semianalytical expression for the dispersion relation of the lowest-frequency mode that is staightforward to evaluate.