Large positive zero field splitting in the cluster magnet Ba$_3$CeRu$_2$O$_9$

We present the synthesis and magnetic characterization of a polycrystalline sample of the 6H-perovskite Ba$_3$CeRu$_2$O$_9$, which consists of Ru dimers based on face-sharing RuO$_6$ octahedra. Our low-temperature magnetic susceptibility, magnetization and neutron powder diffraction results reveal a non-magnetic singlet ground state for the dimers. Inelastic neutron scattering, infrared spectroscopy, and the magnetic susceptibility over a wide temperature range are best explained by a molecular orbital model with a zero-field splitting parameter $D$~$=$~85~meV for the $S_{tot}$~$=$~1 electronic ground state multiplet. This large value is likely due to strong mixing between this ground state multiplet and low-lying excited multiplets, arising from a sizable spin molecular orbital coupling combined with an axial distortion of the Ru$_2$O$_9$ units. Although the positive sign for the splitting ensures that Ba$_3$CeRu$_2$O$_9$ is not a single molecule magnet, our work suggests that the search for these interesting materials should be extended beyond Ba$_3$CeRu$_2$O$_9$ to other molecular magnets based on metal-metal bonding.