Finite-element dynamic-matrix approach for spin-wave dispersions in magnonic waveguides with arbitrary cross section

TL;DR

This paper introduces a finite-element dynamic-matrix method for calculating spin-wave dispersions in arbitrarily shaped magnetic waveguides, significantly reducing computational effort while accurately handling complex geometries and non-collinear magnetizations.

Contribution

It extends the propagating-wave dynamic-matrix approach with finite-element techniques and a hybrid boundary-element method to efficiently analyze spin waves in complex, curved magnonic waveguides.

Findings

Validated method against existing techniques

Successfully modeled curvature effects in magnetic nanotubes

Demonstrated efficiency in computing spin-wave dispersions

Abstract

We present a numerical approach to efficiently calculate spin-wave dispersions and spatial mode profiles in magnetic waveguides of arbitrarily shaped cross section with any non-collinear equilibrium magnetization which is translationally invariant along the waveguide. Our method is based on the propagating-wave dynamic-matrix approach by Henry et al. and extends it to arbitrary cross sections using a finite-element method. We solve the linearized equation of motion of the magnetization only in a single waveguide cross section which drastically reduces computational effort compared to common three-dimensional micromagnetic simulations. In order to numerically obtain the dipolar potential of individual spin-wave modes, we present a plane-wave version of the hybrid finite-element/boundary-element method by Frekdin and Koehler which, for the first time, we extend to a modified version of the Poisson equation. Our method is applied to several important examples of magnonic waveguides including systems with surface curvature, such as magnetic nanotubes, where the curvature leads to an asymmetric spin-wave dispersion. In all cases, the validity of our approach is confirmed by other methods. Our method is of particular interest for the study of curvature-induced or magnetochiral effects on spin-wave transport but also serves as an efficient tool to investigate standard magnonic problems.