Coupling of phonons and spin waves in triangular antiferromagnet

We investigate the influence of the spin-phonon coupling in the triangular antiferromagnet where the coupling is of the exchange-striction type. The magnon dispersion is shown to be modified significantly at wave vector (2pi,0) and its symmetry-related points, exhibiting a roton-like minimum and an eventual instability in the dispersion. Various correlation functions such as equal-time phonon correlation, spin-spin correlation, and local magnetization are calculated in the presence of the coupling.