Magnon-phonon coupling effects on the indirect K -edge resonant inelastic x-ray scattering spectrum of a two-dimensional Heisenberg antiferromagnet

We compute the effects of magnon-phonon coupling on the indirect K-edge bimagnon resonant inelastic x-ray scattering (RIXS) intensity spectrum of a square lattice Heisenberg antiferromagnet. We analyze the effects of competing nearest and next-nearest magnetic and magnon-phonon coupling interaction in the RIXS spectrum, for both the antiferromagnetic (AF) and the collinear antiferromagnetic (CAF) phases of the model. Utilizing the Dyson-Maleev representation of spin operators, the Bethe-Salpeter ladder approximation scheme for the bimagnon interacting channel, and considering the lowest-order magnon-phonon-magnon scattering interaction, we highlight distinct features in the x-ray spectrum. Considering damping effects, arising due to the presence of phonons, we find that in the AF phase the RIXS intensity spectrum attains a maximum value primarily localized around the K±π2,±π2 point. For the CAF phase, the intensity is broadly distributed with a significant scattering intensity located around the Y±π2,0 point. Furthermore, in the CAF phase for suitable anisotropy, nearest-, and next-nearest-neighbor interaction parameters, the phonon effects can manifest as a distinct peak both below and above the bimagnon peak. Such a feature is in contrast to the antiferromagnetic spectrum where the effect due to the phonon peak was located consistently beyond the bimagnon peak in the high-energy end of the spectrum. Additionally, in the CAF phase we find the RIXS bimagnon-phonon spectrum to be more sensitive to anisotropy compared to its antiferromagnetic counterpart. We conclude that the ultimate effect of magnon-phonon effects in the indirect K-edge RIXS spectrum, in both the antiferromagnetic and the collinear antiferromagnetic phases, is an observable effect.