Excited-state exchange interaction in NiO determined by high-resolution resonant inelastic x-ray scattering at the Ni M2,3 edges

The electronic and magnetic excitations of bulk NiO have been determined using the ${}^{3}{A}_{2g}$ to ${}^{3}{T}_{2g}$ crystal-field transition at the Ni ${M}_{2,3}$ edges with resonant inelastic x-ray scattering at 66.3- and 67.9-eV photon energies and 33-meV spectral resolution. Unambiguous assignment of the high-energy side of this state to a spin-flip satellite is achieved. We extract an effective exchange field of $89\ifmmode\pm\else\textpm\fi{}4$ meV in the ${}^{3}{T}_{2g}$ excited final state from empirical two-peak spin-flip model. The experimental data is found consistent with crystal-field model calculations using exchange fields of 60--100 meV. Full agreement with crystal-field multiplet calculations is achieved for the incident photon energy dependence of line shapes. The lower exchange parameter in the excited state as compared to the ground-state value of 120 meV is discussed in terms of the modification of the orbital occupancy (electronic effects) and of the structural dynamics: (A) With pure electronic effects, the lower exchange energy is attributed to the reduction in effective hopping integral. (B) With no electronic effects, we use the $S=1$ Heisenberg model of antiferromagnetism to derive a second-nearest-neighbor exchange constant ${J}_{2}$ = $14.8\ifmmode\pm\else\textpm\fi{}0.6$ meV. Based on the linear correlation between ${J}_{2}$ and the lattice parameter from pressure-dependent experiments, an upper limit of 2% local Ni-O bond elongation during the femtosecond scattering duration is derived.