Highly Tunable Ru-dimer Molecular Orbital State in 6H-perovskite Ba$_3$MRu$_2$O$_9$

Molecular orbital (MO) systems with clusters of heavy transition metal (TM) ions are one of the most important classes of model materials for studying the interplay between local physics and effects of itinerancy. Despite a large number of candidates identified in the family of 4d TM materials, an understanding of their physics from competing \textit{microscopic} energy scales is still missing. We bridge this gap by reporting the first resonant inelastic X-ray scattering (RIXS) measurement on a well-known series of Ru dimer systems with a 6H-perovskite structure, Ba$_3$MRu$_2$O$_9$ (M$^{3+}$=In$^{3+}$, Y$^{3+}$, La$^{3+}$). Our RIXS measurements reveal an extremely fragile MO state in these Ru dimer compounds, evidenced by an abrupt change in the RIXS spectrum accompanying a tiny change in the local structure tuned by the M-site ion. By modelling the RIXS spectra, we attribute the enhanced electronic instability in Ba$_3$MRu$_2$O$_9$ to the combined effect of a large hopping and a small spin-orbit coupling in the Ru dimers. The unique combination of energy scales uncovered in the present study make Ru MO systems ideal model systems for studying quantum phase transitions with molecular orbitals.