The effects of three magnons interactions in the magnon-density waves of triangular spin lattices

We investigate the magnon-density waves proposed as the longitudinal excitations in triangular lattice antiferromagnets by including the cubic and quartic corrections in the large-s expansion. The longitudinal excitation spectra for the two-dimensional (2D) triangular antiferromagnetic model and quasi-one dimensional (quasi-1D) antiferromagnetic materials have been obtained for a general quantum spin number $s$. For the 2D triangular lattice model, we find a significant reduction (about 40 %) in the energy spectra at the zone boundaries due to both the cubic and quartic corrections. For the quasi-1D antiferromagnets, since the cubic term comes from the very weak couplings on the hexagonal planes, they make very little correction to the energy spectra, whereas the major correction contribution comes from the quartic terms in the couplings along the chains with the numerical values for the energy gaps in good agreement with the experimental results as reported earlier (Ref.~41).