A modal approach to modelling spin wave scattering

TL;DR

This paper introduces an efficient finite-element modal method for modeling spin wave scattering in magnonic devices, providing direct access to the scattering matrix and normalizing power transfer, validated against micromagnetic simulations.

Contribution

The paper presents a novel finite-element modal approach for spin wave scattering that reduces computational cost and offers direct insight into scattering processes, extending existing formulas to include exchange effects.

Findings

The method accurately predicts spin wave scattering in magnonic circuits.

It normalizes scattering coefficients to quantify power transfer.

Validation shows agreement with micromagnetic simulations.

Abstract

Efficient numerical methods are required for the design of optimised devices. In magnonics, the primary computational tool is micromagnetic simulations, which solve the Landau-Lifshitz equation discretised in time and space. However, their computational cost is high, and the complexity of their output hinders insight into the physics of the simulated system, especially in the case of multimode propagating wave-based devices. We propose a finite-element modal method allowing an efficient solution of the scattering problem for dipole-exchange spin waves propagating perpendicularly to the magnetisation direction. The method gives direct access to the scattering matrix of the whole system and its components. We extend the formula for the power carried by a magnetostatic mode in the Damon-Eshbach configuration to the case with exchange, allowing the scattering coefficients to be normalised to represent the fraction of the input power transferred to each output channel. We apply the method to the analysis of spin-wave scattering on a basic functional block of magnonic circuits, consisting of a resonator dynamically coupled to a thin film. The results and the method are validated by comparison with micromagnetic simulations.