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Importance of tetrahedral coordination for high-valent transition metal oxides: YCrO$_4$ as a model system

We have investigated the electronic structure of the high oxidation state material YCrO$_4$ within the framework of the Zaanen-Sawatzky-Allen phase diagram. While Cr$^{4+}$-based compounds like SrCrO$_3$/CaCrO$_3$ and CrO$_2$ can be classified as small-gap or metallic negative-charge-transfer systems, we find using photoelectron spectroscopy that YCrO$_4$ is a robust insulator despite the fact that its Cr ions have an even higher formal valence state of 5+. We reveal using band structure calculations that the tetrahedral coordination of the Cr$^{5+}$ ions in YCrO$_4$ plays a decisive role, namely to diminish the bonding of the Cr $3d$ states with the top of the O $2p$ valence band. This finding not only explains why the charge-transfer energy remains effectively positive and the material stable, but also opens up a new route to create doped carriers with symmetries different from those of other transition-metal ions.