Regulation of magnon-phonon coupling by phonon angular momentum in two-dimensional systems

The coupling between magnons and phonons modulates the transport properties of magnons, resulting in magnon polarons and magnon Seebeck effects, etc. Magnons possess well-defined angular momentum, while phonons are usually composed of linear atomic oscillations lacking angular momentum. However, in chiral systems, phonons become elliptical or circular; thus they will carry angular momentum. In this paper, we emphasize angular momentum and its role in the magnon-phonon coupling. Using a coupled-magnon-phonon model on the hexagonal lattice, we investigate the coupling of achiral and chiral phonons with three types of magnons, namely a magnon on one sublattice, ferromagnetic magnons, and antiferromagnetic magnons. We calculate the magnon-phonon dispersion relations and the strength of magnon-phonon coupling in the reciprocal space. We are particularly interested in the $K$ and ${K}^{\ensuremath{'}}$ points at the corner of the first Brillouin zone where the normal modes involve circular rotations of magnetization and displacement. We find a selective coupling wherein the coupling between magnons and phonons vanishes either when the magnitude of the magnon or phonon modes is zero or when the circular motion of magnetization is opposite to that of the displacements. These findings pave the way towards manipulating magnon polaron devices based on phonon angular momentum.