A semi-analytical approach to calculating the dynamic modes of magnetic vortices with Dzyaloshinskii-Moriya interactions

TL;DR

This paper introduces a semi-analytical Landau-Lifshitz diagonalization method to analyze how interfacial Dzyaloshinskii-Moriya interactions affect the spin wave modes of magnetic vortices, with results validated against micromagnetic simulations.

Contribution

The paper presents a novel semi-analytical approach for calculating the effects of DMI on vortex spin wave modes, extending analysis capabilities beyond previous numerical methods.

Findings

DMI causes frequency shifts in vortex modes similar to extended films.

Only down-shifted modes are observed in disks, propagating radially inward or outward.

The semi-analytical method agrees well with micromagnetic simulations.

Abstract

Here we introduce a Landau-Lifshitz based diagonalization (LLD) method, and use this approach to calculate the effects of the interfacial Dzyaloshinskii Moriya interactions (DMI) on the radial-type spin wave modes of magnetic vortices in circular disks. The LLD method is a semi-analytical approach that involves the diagonalization of the magnetostatic kernel, exchange, and DMI contributions to extract the system eigenfrequencies and eigenmodes. The magnetic vortex state provides a convenient model system in which to investigate the effects of the DMI on the dynamics of a magnetic structures with confined geometries. Our calculations show that the DMI leads to shifts of the mode frequencies that are similar in magnitude to what is observed for spin waves of a comparable wavelength in extended films. However, unlike what is found in thin films, only the down-shifted modes are observed in the disks, and these corresponds to modes that propagate either radially outward or inward, depending on the vortex circulation. The semi-analytical calculations agree well with full micromagnetic simulations. This technique also applies to other systems with cylindrical symmetry, for example, magnetic skyrmions.