Three-dimensional linear spin-wave eigenmodes of a Permalloy disk having finite thickness are studied by micromagnetic simulations based on the Landau-Lifshitz-Gilbert equation. The eigenmodes found in the simulations are interpreted as linear superpositions (hybridizations) of 'approximate' three-dimensional eigenmodes, which are the fundamental gyromode G0, the spin-wave modes and the higher-order gyromodes GN (flexure modes), the thickness dependence of which is represented by perpendicular standing spin waves. This hybridization leads to new and surprising dependencies of the mode frequencies on the disk thickness. The three-dimensional character of the eigenmodes is essential to explain the recent experimental results on vortex-core reversal observed in relatively thick Permalloy disks.
@article{arxiv.1505.01148,
title = {Three-dimensional Character of the Magnetization Dynamics in Magnetic Vortex Structures - Hybridization of Flexure Gyromodes with Spin Waves},
author = {Matthias Noske and Hermann Stoll and Manfred Fähnle and Ajay Gangwar and Georg Woltersdorf and Andrei Slavin and Markus Weigand and Georg Dieterle and Johannes Förster and Christian H. Back and Gisela Schütz},
journal= {arXiv preprint arXiv:1505.01148},
year = {2016}
}