Coupled-mode theory for the interaction between acoustic waves and spin waves in magnonic-phononic crystals: Propagating magnetoelastic waves

We have investigated codirectional and contradirectional couplings between spin wave and acoustic wave in a one-dimensional periodic structure (the so-called 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 has been successfully implemented to describe the magnetoelastic interaction as a periodic perturbation in the magphonic crystal. The results of CMT calculations have been verified by more rigorous simulations with the frequency-domain plane-wave method and the 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 a 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 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 codirectional coupling and backward conversion in case of contradirectional coupling. That energy transfer may be realized for broadband coupling and for generation of spin waves which are of different wavelength (in particular, shorter) than exciting acoustic waves.