We report on the study of the magnetic excitations of Mott insulator \(\hbox {La}_{2}\hbox {CuO}_4\) by using resonant inelastic x-ray scattering (RIXS) and cluster calculations within the framework of exact diagonalization. Our results demonstrate experimentally that the bimagnon excitation in Cu \(L_3\) -edge RIXS is enhanced if the incident x-ray energy is slightly above the absorption edge. Through incident-energy-dependent momentum-resolved RIXS, we investigated the excitation of the bimagnon with predominantly \(A_{1g}\) symmetry. The bimagnons of \(\hbox {La}_{2}\hbox {CuO}_4\) exhibit a nearly flat dispersion with momentum along the Cu-O bond direction. This observation agrees with the bimagnon dispersion from the calculations on a single-band Hubbard model rather than a Heisenberg model with only the nearest neighbor exchange interaction. This means that the effect of the higher-order spin couplings such as the cyclic or ring exchange interactions caused by the coherent motion of electrons beyond nearest-neighbor sites is important for understanding the bimagnon dynamics of cuprates.
