Energy minimum exciation in a ferromagnet

In a magnon-phonon interaction an energy minimum is obtained in the one-magnon ground-state dispersion. The magnon momentum at the minimum is half the product of the mass of the magnon and the sound velocity, $\text{h}\text{?}\text{k}{}_0\text{=}\text{1}\text{2}\text{h}\text{?}\text{ν × (cD)}{}^{-1}$.