Structures of Late Transition Metal Monoxides from Jahn-Teller Instabilities in the Rock Salt Lattice

Most late transition metal (LTM) monoxides crystallize in other than a rock salt structure, which is so common in the earlier transition metal monoxides. Here we present theoretical evidence based on density functional theory that an electron-phonon coupling involving a single soft mode in the cubic cell is responsible for the onset of the experimentally observed structures of the late transition metal monoxides.

Figure 1

The $d$-block of the Periodic Table of Elements. Transition metal elements which form monoxides, MO, are highlighted orange and green [12, 14]. ^HP stands for ”high pressure” form and ^vac for 25% vacancies.

Figure 2

Schematic ordering of metal $d(z^2)$ orbitals within a layer of rock salt representations of (a) both forms of AgO ($P{2}_1/c$ and $I{4}_1/a$), (b) CuO, PdO, PtO, HgO $Pnma$ and HgO $P\overline{1}$, and (c) HgO $P{3}_{1}21$ (cinnabar). The bold and dotted lines in (a) represent $d(z^2)$ orbitals for contracted ${\text{Ag}}^{1+}$ and elongated ${\text{Ag}}^{3+}$, respectively. Oxygen atoms are omitted for clarity.

Figure 3

Phonon dispersion curves calculated at the DFT (PBEsol) level for the LTM oxides in $Fm\overline{3}m$ cells [15]. Negative energy values represent imaginary frequencies.

Figure 4

Partial electronic DOS (states ${\mathrm{eV}}^{-1}$ ${\mathrm{cell}}^{-1}$) calculated at the hybrid DFT level [16] for the LTM oxides, in hypothetical cubic $Fm\overline{3}m$ cell (left), in modified $Fm\overline{3}m$ cell distorted by the phonon $L_3$ with no optimization performed (middle) and in the optimized experimentally observed crystal structures (right, spin-polarized calculations were performed for CuO—see text for details). In the case of AgO and HgO, the experimentally observed ground state structures were chosen: AgO $P{2}_1/c$ and HgO $Pnma$. For $t_{2\mathrm{g}}$ and $e_{\mathrm{g}}$ splitting and comparison with $\mathrm{DFT}(+\mathrm{U})$ results, see Supplemental Material [13].