Quadratic Dependence of Spin-Wave Resonance Fields on Mode Number for Permalloy Films

Abstract

Permalloy films (75% Ni‐25% Fe) which show some interesting new features have been made by evaporation in a vacuum initially at 5×10⁻⁸ Torr. Subsequent to evaporation, the films were annealed at 250°C for 12 h in the presence of a field of 25 Oe applied in the plane of the film. The following spin‐wave resonance results have been observed on 2100‐Å, 1320‐Å, and 800‐Å‐thick films using a microwave frequency of 9.4 GHz: (1) Except for the first mode in the perpendicular orientation, the resonance fields H_n fit a quadratic dependence on mode number n strikingly well if the first mode is labelled 0 rather than 1, both for the parallel (∥) and the perpendicular $\mathrm{(\perp )}$ orientations‐the fit to a quadratic dependence on n is not good if the first mode is labeled 1. (2) The slopes of the curves of H_n vs n² are equal for the ∥ and $\perp$ cases in the case of the thickest film. (3) The intensities decrease as 1/n² and 1/n⁴ for the 2100‐Å‐thick film and as 1/n⁴ for the 1320‐Å‐thick film. These results can be explained if the magnetization is assumed to be quite uniform throughout the film volume and very close to the film boundaries so that the surface spins act as if they are nearly free for all modes except the first one in the $\perp$ case and for all modes in the ∥ case.