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

We apply torque equilibrium spin wave theory (TESWT) to investigate an anisotropic XXZ antiferromagnetic model with Dzyaloshinskii-Moriya (DM) interaction in a triangular lattice. Considering the quasiparticle vacuum as our reference, we provide an accurate analysis of the non-collinear ground state of a frustrated triangular lattice magnet using the TESWT formalism. We elucidate the effects of quantum fluctuations on the ordering wave vector based on model system parameters. We study the single magnon dispersion, the two-magnon continuum using the spectral function, and the Raman spectrum of bimagnon and trimagnon excitations. We present our results for the $HH, VV$, and the $HV$ polarization Raman geometry dependence of the bimagnon and the trimagnon 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 our system. We calculate the Raman spectra of Ba$_3$CoSb$_2$O$_9$ and Cs$_2$CuCl$_4$.