One-dimensional model for coupling between magnon and optical phonon

In this work, we propose and study a one-dimensional model of the effects of optical phonon/magnon coupling. The indirect interactions between magnetic ions are conducted by the sandwiched nonmagnetic ions. The vibrations of nonmagnetic ions invoke effective magnetic fields to spins and hence couple with the magnon. The quantum solutions of the model show energy gaps in the spin-wave dispersion induced by the magnon-phonon coupling. Classical simulations reveal the existence of hybrid magnon-phonon quasiparticles and the coherent phonon (magnon) induced by magnon (phonon).