Between Mott and cluster Mott: spin-orbit entangled dimer singlets in Ba$_3$CeRu$_2$O$_9$

Abstract

The hexagonal 4d ruthenates Ba3MRu2O9 host structural dimers and exhibit a delicate balance of competing interactions. Hund's coupling, trigonal crystal-field splitting, and hopping for $a_{1g}$ and $e_g^\pi$ orbitals all fall within a narrow energy window. This yields a series of possible ground states, ranging from the localized Mott limit with (anti-) ferromagnetic exchange coupling via orbital-selective behavior to the cluster Mott limit with quasimolecular orbitals that are delocalized over the two dimer sites. Using resonant inelastic x-ray scattering, we show that Ba3CeRu2O9 with four holes per dimer resides in the intricate crossover regime between the localized Mott case and the quasimolecular limit. The spin-orbit entangled singlet ground state predominantly shows a Mott-like charge distribution with two holes per Ru site. At the same time, spin and orbital occupation contradict an exchange-based Mott scenario but agree with a cluster Mott approach. A quasimolecular trial wave function describes more than 70% of the ground state. In this crossover regime, small changes of, e.g., the crystal field may strongly affect the character of electronic states.