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Neutron scattering measurements of $dd$ and spin-orbit excitations below the Mott-Hubbard gap in CoO

Neutron scattering is used to investigate the single-ion spin and orbital excitations below the Mott-Hubbard gap in CoO. Three excitations are reported at 0.870 $\pm$ 0.009 eV, 1.84 $\pm$ 0.03, and 2.30 $\pm$ 0.15 eV. These were parameterized within a weak crystal field scheme with an intra-orbital exchange of $J(dd)$=1.3 $\pm$ 0.2 eV and a crystal field splitting 10Dq=0.94 $\pm$ 0.10 eV. A reduced spin-orbit coupling of λ=-0.016 $\pm$ 0.003 eV is derived from dilute samples of Mg$_{0.97}$Co$_{0.03}$O, measured to remove complications due to spin exchange and structural distortion parameters which split the cubic phase degeneracy of the orbital excitations complicating the inelastic spectrum. The 1.84 eV, while reported using resonant x-ray and optical techniques, was absent or weak for non resonant x-ray experiments and overlaps with the expected position of a $^{4}A_{2}$ level. This transition is absent in the dipolar approximation but expected to have a finite quadrupolar matrix element that can be observed with neutron scattering techniques at larger momentum transfers. Our results agree with a crystal field analysis (in terms of Racah parameters and Tanabe-Sugano diagrams) and with previous calculations performed using local-density band theory for Mott insulating transition metal oxides. The results also demonstrate the use of neutron scattering for measuring dipole forbidden transitions in transition metal oxide systems.