Crystal structure evolution induced by the Jahn-Teller effect in mixed-valence silver fluoride Ag$_3$F$_5$

Abstract

The silver fluoride Ag$_3$F$_5$ consists structurally of square-planar units formed by four fluoride ions coordinated to a central silver ion, which possesses a partially filled $d$-subshell and the formal valence of +5/3. In this study, we demonstrate that the previously published crystal structure of Ag$_3$F$_5$ is unstable due to the Jahn-Teller effect, arising from the presence of two energetically degenerate $d_{x^2-y^2}$ states sharing a single electron hole. Through a full structural relaxation within the DFT+U framework, we identified a new crystal structure for Ag$_3$F$_5$ with reduced symmetry and an energy gain of 151~meV per formula unit relative to the published structure. In this relaxed structure, magnetic chains are formed by silver ions with an electronic hole occupying the $d_{x^2-y^2}$ orbital. These results highlight the crucial role of electron correlation effects and related structural distortions in determining the properties of such materials.