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 $x^2-y^2$ $\to$ $xy$. In addition, the transition $x^2-y^2$ $\to$ $3z^2-r^2$ has an energy higher than $x^2-y^2$ $\to$ $yz/zx$, 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.

• Received 13 September 2013

DOI:https://doi.org/10.1103/PhysRevB.88.205129