Effective orbital symmetry of CuO: Examination by nonresonant inelastic x-ray scattering

We report on measurements of nonresonant inelastic x-ray scattering (NIXS) to unravel the effective symmetry of Cu 3d orbitals in the ground state of CuO. A clear feature of energy loss at about 2 eV exists in the NIXS spectrum, arising from dd excitations; the intensities of these excitations display a pronounced anisotropy. The comparison between the measured angular distributions of scattering and those from theoretical predictions by the tesseral harmonics indicates that, in terms of a hole picture, the lowest-energy dd excitation is the orbital transition x(2) - y(2) -> xy. In addition, the transition x(2) - y(2) -> 3z(2) - r(2) has an energy higher than x(2) - y(2) -> yz/zx, in contrast to a previous interpretation. Our results imply a large Jahn-Teller-like splitting between x(2) - y(2) and 3z(2) - r(2) orbitals. The theory assuming a C-4h symmetry explains the angular dependence of the NIXS spectra fairly well, implying that this symmetry is a reasonable approximation. This demonstrates that NIXS can provide important information for modeling of the electronic structure of d ions embedded in a complicated crystal field.