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Resonant inelastic x-ray scattering (RIXS) experiment was performed at the Mn L₃ edge. A 10 \% Mn-doped Sr₃Ru₂O₇ compound, where the Mn^3+ ions are in the 3d⁴ state, were probed for dd excitations. The dilute doping concentration allows one to treat the dopant Mn^3+ ions as effectively free in the host ruthenium compound. The local nature of dd RIXS spectroscopy permits one to use a single-site model to simulate the experimental spectra. The simulated spectra reproduces the in-plane 100 experimental RIXS spectrum. We also predict the intensity for the in-plane 110 direction and the out-of-plane spin orientation configuration 001. Based on our single-ion model we were able to fit the experimental data to obtain the crystal field parameters, the 10Dq value, and the intra-orbital spin-flip energy 2J (or 3J₇, where J₇ is the Hund's energy) of the Mn^3+ ion. Utilizing our computed RIXS quantum transition amplitudes between the various d orbitals of the Mn^3+ ion, the expression for the Kramers-Heisenberg cross section, and a self-consistent fitting procedure we also identify the energy boundaries of the non-spin-flip and spin-flip dd excitations present in the experimental data. From our fitting procedure we obtain 2J (3J₇) =2. 06 eV, a value which is in excellent agreement with that computed from the free ion Racah parameters. We also identified the charge transfer boundary. In addition to predicting the microscopic parameters, we find a quantum spin-flip transition in the non-cross (₈₍-₎ₔₓ, ₈₍-₎ₔₓ) x-ray polarization channels of the dd RIXS spectra. A similar transition, was previously predicted to occur in the - channel of the magnon spectrum in the non-collinear non-coplanar Kagome compound composed of Cu^2+ 3d^9 ion.
Chen et al. (Wed,) studied this question.