Quantifying covalency and metallicity in pyrochlore ruthenates undergoing metal-insulator transitions

We use bulk-sensitive hard x-ray photoelectron spectroscopy to investigate the electronic structure of the cubic pyrochlore ruthenates Tl$_2$Ru$_2$O$_7$ and Hg$_2$Ru$_2$O$_7$, which show first-order temperature(T)-dependent metal-insulator transitions(MITs). Ru 3d core-level spectroscopy shows drastic changes as a function of T. The metallic-origin features in core-level spectra get quenched upon gap formation in valence band spectra. The results establish temperature-driven Mott-Hubbard MITs in three-dimensional ruthenates and reveals three energy scales : (a) $4d$-electronic changes occur on the largest ($\sim$eV) energy scale, (b) the band gap energies/charge gaps (E$_g$ $\sim$160-200 meV) are intermediate, and (c) the lowest energy scale corresponds to the transition temperature T$_{MIT}$($\sim$10 meV), which is also the spin gap energy of Tl$_2$Ru$_2$O$_7$ and the magnetic-ordering temperature of Hg$_2$Ru$_2$O$_7$. The results identify and quantify the role of covalency and metallicity in the pyrochlore ruthenates undergoing T-dependent metal-insulator transitions.