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 that is translationally invariant along the waveguide. Our method is based on the propagating-wave dynamic-matrix approach by Henry et al. (Ref. 19) 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 Fredkin and Koehler which 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 and also serves as an efficient tool to investigate standard magnonic problems.
Highlights
Over the last few decades, a number of powerful analytical and numerical tools have been developed to describe the linear propagation characteristics of spin waves, the fundamental smallamplitude excitations in magnetically ordered substances
We have presented a finite-element propagatingwave dynamic-matrix approach to efficiently calculate the spin-wave dispersion in waveguides with arbitrary cross section and translationally invariant magnetic equilibrium along the propagation direction. This was achieved by numerically solving a plane-wave version of the linearized equation of motion of the magnetization
In contrast to dynamic micromagnetic simulations, spin-wave frequencies and mode profiles are obtained without any post-processing
Summary
Over the last few decades, a number of powerful analytical and numerical tools have been developed to describe the linear propagation characteristics of spin waves, the fundamental smallamplitude excitations in magnetically ordered substances. In an excellent work, Henry et al. succeeded to extend this dynamic-matrix approach for propagating spin waves in systems with a translational invariant magnetic equilibrium, using plane-wave demagnetization tensors They employed a finite-difference method to efficiently obtain the spin-wave dispersion by numerically solving the linearized equation of motion only in the cross section of the magnetic medium perpendicular to the propagation direction, modeling infinite magnetic slabs or thin flat waveguides using rectangular elements. This approach was already successfully applied, e.g., to study spin waves in multilayer systems and those propagating along Bloch domain walls.. We believe that this work is of particular interest for the emerging field of curvilinear magnonics and allows us to calculate spin-wave dispersions in various standard magnonic problems
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