title: Three-dimensional Character of the Magnetization Dynamics in Magnetic Vortex Structures: Hybridization of Flexure Gyromodes with Spin Waves.
abstract: Three-dimensional linear spin-wave eigenmodes of a vortex-state Permalloy disk are studied by micromagnetic simulations based on the Landau-Lifshitz-Gilbert equation. The simulations confirm that the increase of the disk thickness leads to the appearance of additional exchange-dominated so-called gyrotropic flexure modes having nodes along the disk thickness, and eigenfrequencies that decrease when the thickness is increased. We observe the formation of a gap in the mode spectrum caused by the hybridization of the first flexure mode with one of the azimuthal spin-wave modes of the disk. A qualitative change of the transverse profile of this azimuthal mode is found, demonstrating that in a thick vortex-state disk the influence of the "transverse" and the "azimuthal" coordinates cannot be separated. The three-dimensional character of the eigenmodes is essential to explain the recently observed asymmetries in an experimentally obtained phase diagram of vortex-core reversal in relatively thick Permalloy disks.
authors.affiliation: Max Planck Institute for Intelligent Systems, Heisenbergstraße 3, 70569 Stuttgart, Germany.
authors.forename: Matthias
authors.initials: M
authors.lastname: Noske
authors.affiliation: Max Planck Institute for Intelligent Systems, Heisenbergstraße 3, 70569 Stuttgart, Germany.
authors.forename: Hermann
authors.initials: H
authors.lastname: Stoll
authors.affiliation: Max Planck Institute for Intelligent Systems, Heisenbergstraße 3, 70569 Stuttgart, Germany.
authors.forename: Manfred
authors.initials: M
authors.lastname: Fähnle
authors.affiliation: Max Planck Institute for Intelligent Systems, Heisenbergstraße 3, 70569 Stuttgart, Germany.|University of Regensburg, Department of Physics, Universitätsstraße 31, 93053 Regensburg, Germany.
authors.forename: Ajay
authors.initials: A
authors.lastname: Gangwar
authors.affiliation: Martin Luther University Halle-Wittenberg, Department of Physics, Von-Danckelmann-Platz 3, 06120 Halle, Germany.
authors.forename: Georg
authors.initials: G
authors.lastname: Woltersdorf
authors.affiliation: Oakland University, Department of Physics, Rochester, Michigan 48309, USA.
authors.forename: Andrei
authors.initials: A
authors.lastname: Slavin
authors.affiliation: Max Planck Institute for Intelligent Systems, Heisenbergstraße 3, 70569 Stuttgart, Germany.
authors.forename: Markus
authors.initials: M
authors.lastname: Weigand
authors.affiliation: Max Planck Institute for Intelligent Systems, Heisenbergstraße 3, 70569 Stuttgart, Germany.
authors.forename: Georg
authors.initials: G
authors.lastname: Dieterle
authors.affiliation: Max Planck Institute for Intelligent Systems, Heisenbergstraße 3, 70569 Stuttgart, Germany.
authors.forename: Johannes
authors.initials: J
authors.lastname: Förster
authors.affiliation: University of Regensburg, Department of Physics, Universitätsstraße 31, 93053 Regensburg, Germany.
authors.forename: Christian H
authors.initials: CH
authors.lastname: Back
authors.affiliation: Max Planck Institute for Intelligent Systems, Heisenbergstraße 3, 70569 Stuttgart, Germany.
authors.forename: Gisela
authors.initials: G
authors.lastname: Schütz