Spin-wave spectra of insulating films: Comparison of exact calculations and a single-wave-vector model

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Abstract
Spin-wave spectra are usually calculated within the circular-precession approximation which neglects ellipticity of the microwave magnetization. This approximation yields rigorously correct results only for perpendicular resonance and becomes worse for parallel resonance. Even if the ellipticity is accounted for, only single-wave-vector modes are commonly postulated for nonperpendicular resonance. Such modes cannot satisfy the boundary conditions except for zero surface anisotropy energy when the model is exact for any configuration of applied external field. Rigorous results correspond to normal modes made up of waves with two different wave vectors. Calculations with a set of parameters typical for a 1000-Å-thick Permalloy film indicate that the exact results may significantly differ from the single-wave-vector model both in the position of the normal modes and their intensities. The predicted critical angle is also different from the π/4 observed. It is concluded that the exact procedure is, in principle, required.