Singlet and triplet doped-hole configurations in ${\mathrm{La}}_2$${\mathrm{Cu}}_{0.5}$${\mathrm{Li}}_{0.5}$${\mathrm{O}}_4$

The ordered alloy ${\mathrm{La}}_2$${\mathrm{Li}}_{0.5}$${\mathrm{Cu}}_{0.5}$${\mathrm{O}}_4$ is found to be a band insulator in local density approximation (LDA) calculations with the unoccupied conduction band having predominantly ${\mathrm{d}}_{{\mathrm{x}}^2\mathrm{-}{\mathrm{y}}^2}$ symmetry and substantial weight in O 2p orbitals. This is equivalent to a predominant local singlet configuration ${\mathrm{d}}^9$L or a low-spin ${\mathrm{Cu}}^{3+}$ ion with both holes in orbits having ${\mathrm{d}}_{{\mathrm{x}}^2\mathrm{-}{\mathrm{y}}^2}$ symmetry, i.e., Zhang-Rice singlets. A fairly modest reduction of the apical Cu-O bond length is sufficient to stabilize a high spin triplet ${\mathrm{Cu}}^{3+}$ ionic configuration with holes in both ${\mathrm{d}}_{{\mathrm{x}}^2\mathrm{-}{\mathrm{y}}^2}$ and ${\mathrm{d}}_{3{\mathrm{z}}^2\mathrm{-}{\mathrm{r}}^2}$ orbits in LDA + U calculations. This leads us to identify the low energy triplet excitation found in nuclear quadrupole resonance studies by Yoshinari et al. as a local high-spin ${\mathrm{Cu}}^{3+}$ ionic configuration accompanied by a substantial reduction of the apical Cu-O separation, i.e., an anti-Jahn-Teller triplet polaron.