Multimagnon and multispinon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:math> -edge RIXS spectra of an effective <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"

We investigate the multimagnon and the multispinon ${L}_{3}$-edge resonant inelastic x-ray scattering (RIXS) spectra of a spin-1/2 effective ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}}_{1}\ensuremath{-}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}}_{2}\ensuremath{-}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}}_{3}$ square lattice Heisenberg model in its N\'eel 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 N\'eel 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.