Multimagnon and multispinon L₃-edge RIXS spectra of an effective ̃J ₁− ̃J₂− ̃J ₃ square-lattice Heisenberg model

We investigate the multimagnon and the multispinon L₃-edge resonant inelastic x-ray scattering (RIXS) spectra of a spin-1/2 effective J ₁−˜J₂−˜J ₃ square lattice Heisenberg model in its Néel ordered phase. Motivated by the observation of satellite intensity peaks above the single magnon dispersion in the L-edge RIXS spectrum, we propose a resonating valence bond (RVB) inspired RIXS mechanism that incorporates the local site ultrashort core-hole lifetime (UCL) expansion.We compute the multimagnon and the multispinon excitations using O(1/S) interacting spin-wave theory and Schwinger boson mean-field theory (SBMFT) formalism, respectively. We treat the x-ray scattering process up to second order in the UCL expansion. Our calculations of two-magnon, bimagnon, and three-magnon RIXS intensities reveal that interacting spin-wave theory fails to fully capture all the quantum correlations in the antiferromagnetic ordered phase. However utilizing the SBMFT framework, with a ground state that incorporates features of both the Néel order and fluctuating RVB components, we demonstrate that a RIXS bond-flipping mechanism provides an alternative deeper physical explanation of the satellite intensities. Specifically, we find that the spin-correlation spectra predicted by the fluctuating RVB mechanism aligns with higher-order UCL expansion results. We further show that the satellite intensity above the single-magnon mode can originate both from a one-to-three-magnon hybridization vertex process and from condensed spinons exhibiting Higgs mechanism. These features reflect the interplay of quantum fluctuation, entanglement, and gauge interaction effects of quantum magnetism probed by RIXS.