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

## TL;DR

This study examines how cubic and quartic magnon interactions influence longitudinal excitation spectra in triangular lattice antiferromagnets, revealing significant energy reductions in 2D models and minimal effects in quasi-1D systems, aligning with experimental data.

## Contribution

It introduces a detailed analysis of cubic and quartic magnon interactions in triangular antiferromagnets, extending understanding of their effects on excitation spectra across different dimensionalities.

## Key findings

- 40% reduction in energy spectra at zone boundaries for 2D models
- Minor correction from cubic terms in quasi-1D due to weak inter-plane couplings
- Quartic terms significantly impact energy gaps, matching experimental results

## Abstract

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).