Three-dimensional Character of the Magnetization Dynamics in Magnetic Vortex Structures: Hybridization of Flexure Gyromodes with Spin Waves.

Matthias Noske,Markus Weigand,Manfred Fähnle,Georg Dieterle,Christian H Back,Johannes Förster,Ajay Gangwar,Andrei Slavin,Georg Woltersdorf,Hermann Stoll,Gisela Schütz

doi:10.1103/physrevlett.117.037208

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.

Highlights

The study of spin-wave (SW) excitations in micro- and nanosized magnetic elements is one of the most important topics in modern magnetism
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

Summary

Introduction

The study of spin-wave (SW) excitations in micro- and nanosized magnetic elements is one of the most important topics in modern magnetism. The presence of approximate eigenmodes in the spin-wave spectrum of a relatively thick magnetic disk with both increasing and decreasing frequency fundamental gyromode G0 1st order gyromode G1 2nd order gyromode G2 vortex core position h z y x r dependences on the disk thickness may lead to a crossing of the corresponding dispersion curves, and related hybridization of those approximate eigenmodes having similar symmetry of their spatial profiles [25].

Results

Conclusion