Osmates on the verge of a Hund's-Mott transition: The different fates of NaOsO$_3$ and LiOsO$_3$

We clarify the origin of the strikingly different spectroscopic properties of the chemically similar compounds NaOsO$_3$ and LiOsO$_3$. Our first-principle many-body analysis demonstrates that the highly sensitive physics of these two materials is controlled by their proximity to an adjacent Hund's-Mott insulating phase. In mildly correlated $5d$ oxides, this physics is triggered by the {\sl cooperative} action of intraorbital repulsion and Hund's exchange in half-filled $t_{2g}$ outer-shells. Small material-specific details hence result in an extremely sharp change of the electronic mobility, explaining the surprisingly different properties of the paramagnetic high-temperature phases of the two compounds.