Torque equilibrium spin wave theory study of anisotropy and Dzyaloshinskii-Moriya interaction effects on the indirect K− edge RIXS spectrum of a triangular lattice antiferromagnet

We apply the recently formulated torque equilibrium spin wave theory (TESWT) to compute the 1/S-order interacting K -edge bimagnon resonant inelastic x-ray scattering (RIXS) spectra of an anisotropic triangular lattice antiferromagnet with Dzyaloshinskii-Moriya (DM) interaction [1]. We extend the interacting torque equilibrium formalism, incorporating the effects of DM interaction, to appropriately account for the zero-point quantum fluctuation that manifests as the emergence of spin Casimir effect in a noncollinear spin spiral state. Using inelastic neutron scattering data from Cs₂CuCl₄ we fit the 1/S corrected TESWT dispersion to extract exchange and DM interaction parameters. We compare, and contrast the effects of spatial anisotropy and DM interaction on the RIXS spectra at various points across the magnetic Brillouin zone. We highlight the key features of the bi- and trimagnon RIXS spectrum at the roton like points whose behavior is quite different from an isotropic triangular lattice system [2]. Our calculation offers a practical example of how to calculate interacting RIXS spectra in a non-collinear quantum magnet using TESWT. [1] Jin et. al. Phys. Rev. B 100, 054410 (2019); [2] Luo et. al. Phys. Rev. B 92, 035109 (2015).