Resonant X-Ray Raman Spectra of CuddExcitations inSr2CuO2Cl2

We present resonant x-ray Raman scattering results on ${\mathrm{Sr}}_2{\mathrm{CuO}}_2{\mathrm{Cl}}_2$, a model compound for high- $T_c$ superconductors. We demonstrate that the $\mathrm{dd}$ excitations can be observed and show that the polarization dependence can be used to identify the $\mathrm{dd}$ excitations. We find the transition from the $d_{x^2{-y}^2}$ ground state to the $d_{\mathrm{xy}}$ excited state at 1.35 eV and to the degenerate $d_{\mathrm{xz}}$ and $d_{\mathrm{yz}}$ excited states at 1.7 eV. From analysis of the polarization dependence we conclude that the $d_{{3z}^2{-r}^2}$ orbital energy is at 1.5 eV and not in the midinfrared (0.5 eV) as recently suggested. We use recent theoretical arguments to show that the $d_{{3z}^2{-r}^2}$ excitation is accompanied by a local spin flip resulting in a shift upwards of 0.2 eV due to the exchange interaction with the neighboring spins.