Figure 3

(a) Comparison of Gd₂O₃ (thick black line) and simulated Gd³⁺ (baseline; thin black line) RIXS spectra at 142.4 eV excitation photon energy. The simulation parameters for baseline spectrum are listed in Table 1. (b,c) Comparison of Gd₃N@C₈₀ (thick black line) and simulated RIXS spectra (thin yellow line) with optimized energy parameters (1% reduction in 4f–4f Coulomb interactions, 10% reduction in SOC, and J _ex  = 40 meV; parameters are listed in Table 1) at excitation photon energy of (b) 142.4 eV and (c) 143.1 eV. The experimental Gd₂O₃ RIXS spectra (thick black line) and baseline simulations plus J _ex  = 30 meV (thin red line) are also shown in the bottom part of the same figures. For comparison, spectra are scaled differently in different energy windows. For 142.4 (143.1) eV excitation energy, the simulation is scaled up by a factor of 6 (15) in [3.4 eV, 4.0 eV] window; in [4.0 eV, 4.4 eV] window, the simulation and experiment are scaled up by a factor of 150 (200) and 5 (5), respectively; in [4.4 eV, 5.4 eV] window, the simulation is scaled up by a factor of 20 (20). The scaling factors (red for simulations and black for experiments) are also listed in the figures.