Ab initio calculation of $d$-$d$ excitations in quasi-one-dimensional Cu $d^9$ correlated materials

With wave-function-based electronic-structure calculations we determine the Cu $d$-$d$ excitation energies in quasi-one-dimensional spin-chain and ladder copper oxides. A complete set of local excitations has been calculated for cuprates with corner-sharing (Sr${}_2$CuO${}_3$ and SrCuO${}_2$) and edge-sharing (LiVCuO${}_4$, CuGeO${}_3$, LiCu${}_2$O${}_2$, and Li${}_2$CuO${}_2$) CuO${}_4$ plaquettes, with corner-sharing CuF${}_6$ octahedra (KCuF${}_3$), for the ladder system CaCu${}_2$O${}_3$, and for multiferroic cupric oxide CuO. Our data compare well with available results of optical absorption measurements on KCuF${}_3$ and the excitation energies found by resonant inelastic x-ray scattering experiments for CuO. The ab initio results we report for the other materials should be helpful for the interpretation of future resonant inelastic x-ray scattering experiments on those highly anisotropic compounds.

Figure 1

Chain of corner-sharing CuO${}_4$ plaquettes in Sr${}_2$CuO${}_3$. The ground-state hole orbital is $d_{x^2-y^2}$.

Figure 2

Chain of edge-sharing CuO${}_4$ plaquettes in LiVCuO${}_4$. The ground-state hole orbital is $d_{xy}$ in the chosen reference system. The six NN VO${}_4$ octahedra around the reference Cu site are highlighted in the figure.

Figure 3

Crystal structure of CuO and sketch of the cluster used for the calculations. The reference Cu and the fourteen adjacent Cu sites are shown in dark and light blue, respectively. O ions of the central octahedron are depicted in orange. The thin dashed line parallel to the $y$ axis connects the central Cu site and two Cu NN's along the same chain of edge-sharing CuO${}_4$ plaquettes. For each apical O, there are two NN Cu ions on adjacent chains parallel to the $y$ axis.

Figure 4

MRCI Cu $d$-$d$ excitation energies in 1D Cu $d^9$ compounds. Depending on the reference coordinate system, see text, the symmetry of the lowest $t_{2g}$ hole state (in red) is denoted either as $d_{xy}$ (corner-sharing chains of plaquettes or octahedra) or $d_{x^2-y^2}$ (edge-sharing chains). For KCuF${}_3$, the $e_g$ excited state (in orange) has $y^2$ symmetry. For all other compounds, the $e_g$ excited state has $z^2$ symmetry.