Investigation of Dipole-Forbidden $d-d$ Excitations in Strongly Correlated Transition-Metal Oxides Using Higher-Order Multipole, Non-resonant Inelastic X-Ray Scattering*

We have shown that quadrupole and higher order multipole non-resonant inelastic x-ray scattering (NIXS) at large wavevectors, $q$, provides direct access to dipole-forbidden $d-d$ excitations (Larson et al. \textit{Phys. Rev. Lett.} \textbf{99}, 026401 (2007)). NIXS measurements using the XOR/UNI beamline at the APS have shown that the large-$q $intensity of on-site excitons in NiO and CoO is highly anisotropic in $q$ and dominates the energy loss spectrum. Energy-resolved Wannier function analyses have shown that the anisotropies, including a nodal direction for NiO, provide direct information on the point-group symmetry of the particle-hole wave functions for transition-metal oxides. The interpretation of these large-$q$ NIXS measurements will be discussed in connection with energy-resolved Wannier function analyses and LDA+$U$ dynamical response calculations. Implications for the extension of such investigations to manganite systems will be considered.