Signatures of indirectK-edge resonant inelastic x-ray scattering on magnetic excitations in a triangular-lattice antiferromagnet

Abstract

We compute the $K$-edge indirect resonant inelastic x-ray scattering (RIXS) spectrum of a triangular-lattice antiferromagnet in its ordered coplanar three-sublattice ${120}^{\ensuremath{\circ}}$ magnetic state. By considering the self-energy corrections to the spin-wave spectrum, magnon decay rates, bimagnon interactions within the ladder approximation Bethe-Salpeter scheme, and the effect of three-magnon contributions up to $1/S$ order, we find that the RIXS spectra are nontrivially affected by magnon damping and anisotropy. For a purely isotropic model, the appearance of a multipeak RIXS structure is primarily dictated by the damping of magnon modes. A unique feature of the triangular-lattice indirect RIXS spectra is the nonvanishing intensity at both the zone center $\mathrm{\ensuremath{\Gamma}}$ point and the antiferromagnetic wave-vector $K$ point. Additionally, we find that a single-peak RIXS spectrum forms at the roton momentum which can be utilized as an experimental signature to detect the presence of rotonlike excitations. However, including $XXZ$ anisotropy leads to additional peak splitting, including at the roton wave vector. The observed splitting is consistent with our earlier theoretical prediction on the effects of spatial anisotropy on the RIXS spectra of a frustrated quantum magnet [C. Luo et al., Phys. Rev. B 89, 165103 (2014)].