Critical dynamics and relaxation of elementary excitations of the nematic phase of a non-heisenberg magnet with spin $S=1$

The relaxation of elementary excitations (magnons) in the nematic phase of a magnet with spin $S=1$ at the critical point of the nematic-to-ferromagnetic phase transition has been studied. Magnons in a three-dimen-sional nematic at the critical point have all of the properties of Goldstone excitations; in particular, their damping decrement tends to zero faster than the excitation frequency as the wave vector tends to zero. In the two-dimensional case, the ratio of the damping decrement to the frequency is small in the long-wavelength limit. The similarity between the behaviors of magnons in the spin nematic and in the isotropic Heisenberg ferromagnet has been underlined.