Hallmarks of Hund's coupling in the Mott insulator Ca${}_2$RuO${}_4$

Abstract

A paradigmatic case of multi-band Mott physics including spin-orbit and Hund's coupling is realised in Ca${}_2$RuO${}_4$. Progress in understanding the nature of this Mott insulating phase has been impeded by the lack of knowledge about the low-energy electronic structure. Here we provide -- using angle-resolved photoemission electron spectroscopy -- the band structure of the paramagnetic insulating phase of Ca${}_2$RuO${}_4$ and show how it features several distinct energy scales. Comparison to a simple analysis of atomic multiplets provides a quantitative estimate of the Hund's coupling $J=0.4$ eV. Furthermore, the experimental spectra are in good agreement with electronic structure calculations performed with Dynamical Mean-Field Theory. The crystal field stabilisation of the d${}_{xy}$ orbital due to $c$-axis contraction is shown to be important in explaining the nature of the insulating state. It is thus a combination of multiband physics, Coulomb interaction and Hund's coupling that generates the Mott insulating state of Ca${}_2$RuO${}_4$. These results underscore the importance of Hund's coupling in the ruthenates and related multiband materials.