Theoretical analysis of multimagnon excitations in resonant inelastic x-ray scattering spectra of two-dimensional antiferromagnets

Resonant inelastic x-ray spectroscopy (RIXS) has emerged as an important tool to explore magnetism in two-dimensional (2D) antiferromagnets realized in strongly correlated materials. Here, we consider the Heisenberg model with nearest- and next-nearest-neighbor hopping relevant to the study of magnetic excitations of the cuprate family. We compute the RIXS cross-section within the ultrashort core-hole lifetime expansion of the Kramers-Heisenberg scattering amplitude that allows a perturbative solution within linear spin wave theory (LSWT). We report detailed results for both spin-conserving and nonconserving channels. Apart from the widely discussed single-magnon and bimagnon contributions, we show that three-magnon contributions in the spin-nonconserving channel are useful to explain certain features of the RIXS data for 2D cuprates. We confirm the qualitative correctness of the LSWT conclusions for the three-magnon excitation with exact diagonalization. In this paper, we put constraints on the dispersion of the three-magnon in the Brillouin zone, opening avenues for realizing higher modes of quasiparticles using RIXS.