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Collective mode excitations and simulated $L$-edge resonant-inelastic x-ray scattering spectra in antiferromagnetic Ca$_2$RuO$_4$

Using the three-orbital Hubbard model, we investigate the low-energy excitation spectra in the antiferromagnetic phase of Ca$_2$RuO$_4$. We calculate the dynamical susceptibilities in the low-energy region by the random phase approximation and find that the anisotropic dispersion of the transverse mode is in good agreement with the spectra recently reported by inelastic neutron scattering experiments. By the fast-collision approximation, we simulate the resonant inelastic x-ray scattering (RIXS) spectra of the Ru $L_3$ edge from the dynamical susceptibilities. We show that the dispersion of the transverse mode is clearly observed in the calculated RIXS spectra and that the polarization dependence of the incident x rays enables one to distinguish between the excitations of the in-plane transverse mode and out-of-plane transverse mode.