Spin-Wave Dynamics in the Presence of Magnetic Vortices

TL;DR

This paper investigates spin-wave excitations in nanosized magnetic dots and rings with vortex states, analyzing how exchange and dipolar interactions influence the spectrum and vortex stability using numerical methods.

Contribution

It introduces a numerical diagonalization approach to study spin-wave spectra in vortex states, highlighting the relationship between spectrum features and vortex stability.

Findings

Lowest-frequency mode indicates dipolar-exchange ratio

Vortex stability correlates with soft mode profile

Negative dispersion relation observed

Abstract

This chapter describes spin-wave excitations in nanosized dots and rings in the presence of the vortex state. The special attention is paid to the manifestation of the competition between exchange and dipolar interactions in the spin-wave spectrum as well as the correlation between the spectrum and the stability of the vortex. The calculation method uses the dynamic matrix for an all-discrete system, the numerical diagonalization of which yields the spectrum of frequencies and spin-wave profiles of normal modes of the dot. We study in-plane vortices of two types: a circular magnetization in circular dots and rings and the Landau state in square rings. We examine the influence of the dipolar-exchange competition and the geometry of the dot on the stability of the vortex and on the spectrum of spin waves. We show that the lowest-frequency mode profile proves to be indicative of the dipolar-to-exchange interaction ratio and the vortex stability is closely related to the spin-wave profile of the soft mode. The negative dispersion relation is also shown. Our results obtained for in-plane vortices are in qualitative agreement with results for core-vortices obtained from experiments, micromagnetic simulations, and analytical calculations.