Analysis of charge states in the mixed-valent ionic insulator AgO

The doubly ionized $d^9$ copper ion provides, originally in ${\mathrm{La}}_2{\mathrm{CuO}}_4$ and later in many more compounds, the platform for high temperature superconductivity when it is forced toward higher levels of oxidation. The nearest chemical equivalent is ${\mathrm{Ag}}^{2+}$, which is almost entirely avoided in nature. AgO is an illustrative example, being an unusual nonmagnetic insulating compound with an open $4d$ shell on one site. This compound has been interpreted in terms of one ${\mathrm{Ag}}^{3+}$ ion at the fourfold site and one ${\mathrm{Ag}}^{+}$ ion that is twofold coordinated. We analyze more aspects of this compound, finding that indeed the ${\mathrm{Ag}}^{3+}$ ion supports only four occupied $4d-\mathrm{based}$ Wannier functions per spin, while ${\mathrm{Ag}}^{+}$ supports five, yet their physical charges (as quantified by their spherical radial charge densities) are nearly equal. The oxygen $2p$ Wannier functions display two distinct types of behavior, one type of which includes conspicuous Ag $4d$ tails. Calculation of the Born effective charge tensor shows that the mean effective charges of the Ag ions differ by about a factor of 2, roughly consistent with the assigned formal charges. We analyze the $4d$ charge density and discuss it in terms of recent insights into charge states of insulating (and usually magnetic) transition-metal oxides. What might be expected in electron- and hole-doped AgO is discussed briefly.

Figure 1

Crystal structure of monoclinic AgO. ${\mathrm{Ag}}^{\mathrm{III}}$ sits at the center of a slightly distorted but planar oxygen square, while ${\mathrm{Ag}}^{\mathrm{I}}$ forms an O-Ag-O linear trimer with its nearest neighbors. Differences in coordination numbers and bond lengths suggest distinct charge states for ${\mathrm{Ag}}^{\mathrm{III}}$ and ${\mathrm{Ag}}^{\mathrm{I}}$. The figure was produced using vesta [24].

Figure 2

Atom-projected density of states of AgO. Above: $\mathrm{LDA}+U$ calculation with AMF double counting. Below: TB-mBJ potential calculation as described in the text. The bottom of the gap is taken as the zero of energy. In both cases the ${\mathrm{Ag}}^{\mathrm{III}}$ DOS extends to low energy ($-7$ eV) as well as dominating over ${\mathrm{Ag}}^{\mathrm{I}}$ in the unoccupied band around 1 eV. The differences are the size of the gap—larger for TB-mBJ—and the width of the highest occupied band, which is $20\%$ narrower for the TB-mBJ case.

Figure 3

Isosurface plots of the Ag $4d$ maximally localized Wannier functions of AgO; red and blue denote opposite signs. The top three are O-centered, $2p$-based; note that the latter two have substantial contributions from an Ag orbital only at one end. The next four are centered at the ${\mathrm{Ag}}^{\mathrm{III}} d^8$ site and are more confined but larger on the Ag site, while the bottom five are centered at the ${\mathrm{Ag}}^{\mathrm{I}} d^{10}$ site. Each of the four ${\mathrm{Ag}}^{\mathrm{III}}$ WFs contains more $4d$ charge than does an ${\mathrm{Ag}}^{\mathrm{I}}$ WF, but the latter WFs include more neighboring O $2p$ contribution. All isosurface values are the same. These WFs were obtained from a $10\times 16\times 11$ Brillouin zone mesh.

Figure 4

Black solid line: radial charge densities $4\pi r^2\rho \left(r\right)$ versus distance from the Ag nucleus, in a.u. Red solid line: sum from the five ${\mathrm{Ag}}^{\mathrm{I}}$ WFs. Black solid line: sum from four ${\mathrm{Ag}}^{\mathrm{III}}$ WFs. Dashed lines: corresponding contributions from the O $2p$ WFs within the Ag spheres. The O WFs make large contributions to the ${\mathrm{Ag}}^{\mathrm{III}}$ atomic density.