  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.
