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

Abstract

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 $4d\ensuremath{-}\mathrm{based}$ 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.