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We apply torque equilibrium spin wave theory (TESWT) to investigate ananisotropic XXZ antiferromagnetic model with Dzyaloshinskii-Moriya (DM)interaction in a triangular lattice. Considering the quasiparticle vacuum asour reference, we provide an accurate analysis of the non-collinear groundstate of a frustrated triangular lattice magnet using the TESWT formalism. Weelucidate the effects of quantum fluctuations on the ordering wave vector basedon model system parameters. We study the single magnon dispersion, thetwo-magnon continuum using the spectral function, and the Raman spectrum ofbimagnon and trimagnon excitations. We present our results for the $HH, VV$,and the $HV$ polarization Raman geometry dependence of the bimagnon and thetrimagnon excitation spectrum where $H (V)$ represents horizontal (vertical)polarization. Our calculations show that both the $HH$ and the $HV$polarization spectrum can be used to determine the degree of anisotropy of oursystem. We calculate the Raman spectra of Ba$_3$CoSb$_2$O$_9$ andCs$_2$CuCl$_4$.

Torque equilibrium spin wave theory of Raman scattering in an anisotropic triangular lattice antiferromagnet with Dzyaloshinskii-Moriya interaction