Magnon relaxation in spin nematic

Magnon relaxation processes in the nematic phase of a magnet with spin S=1 are investigated for a general form of the isotropic exchange interaction, including bilinear and biquadratic interactions in respect to the site spin operators. The temperature dependence and momentum dependence of the magnetic decrement are found in the long-wavelength approximation. It is shown that the elementary excitations in a spin nematic (magnons) have all the properties of Goldstone excitations; in the limit of small wave vectors they have a linear dispersion law, while the damping is quadratic in the wave vector. The similarity of magnon behavior in a spin nematic to that in an antiferromagnet is noted