# Coupled mode theory for the acoustic wave and spin wave interaction in the magphonic crystals: Propagating magnetoelastic waves

## TL;DR

This paper develops a coupled mode theory to analyze and optimize the interaction between spin waves and acoustic waves in magphonic crystals, enabling efficient energy transfer and transducer design.

## Contribution

It introduces a coupled mode theory framework for magnetoelastic interactions in magphonic crystals, validated by simulations, to facilitate device optimization.

## Key findings

- Resonant coupling enables energy transfer between spin and acoustic waves.
- Forward and backward conversion are achievable depending on coupling direction.
- The model includes spin wave damping effects for realistic device efficiency.

## Abstract

We have investigated co-directional and contra-directional couplings between spin wave and acoustic wave in one-dimensional periodic structure (magphonic crystal). The system consists of two ferromagnetic layers alternating in space. We have taken into consideration materials commonly used in magnonics: yttrium iron garnet, CoFeB, permalloy, and cobalt. The coupled mode theory (CMT) formalism have been successfully implemented to describe magnetoelastic interaction as a periodic perturbation in the magphonic crystal. The results of CMT calculations have been verified by more rigorous simulations by frequency-domain plane wave method and time-domain finite element method. The presented resonant coupling in the magphonic crystal is an active in-space mechanism which spatially transfers energy between propagating spin and acoustic modes, thus creating propagating magnetoelastic wave. We have shown, that CMT analysis of the magnetoelastic coupling is an useful tool to optimize and design a spin wave - acoustic wave transducer based on a magphonic crystals. The effect of spin wave damping has been included to the model to discuss the efficiency of such a device. Our model shows that it is possible to obtain forward conversion of the acoustic wave to the spin wave in case of co-directional coupling and backward conversion in case of contra-directional coupling.