Magnetic ground state of the dimer-based hexagonal perovskite Ba${}_3$ZnRu${}_2$O${}_9$

We investigate the magnetic ground state of single crystals of the ruthenium-dimer-based hexagonal perovskite Ba${}_3$ZnRu${}_2$O${}_9$ using magnetic susceptibility and resonant inelastic x-ray scattering (RIXS) measurements. While a previous study on powder samples exhibited intriguing magnetic behavior, questions about whether the spin state within a Ru${}_2$O${}_9$ dimer is a conventional $S=3\mathrm{/}2$ dimer or an orbital-selective $S=1$ dimer were raised. The RIXS spectra reveal magnetic excitations from Hund’s intraionic multiplet and intradimer spin-triplet transitions. The observed transition energies of the Hund’s intraionic multiplets align with the $S=3\mathrm{/}2$ ground state, contrasting with the theoretically proposed orbital-selective $S=1$ dimer state. High-temperature magnetic susceptibility analysis confirms the realization of the spin $S=3\mathrm{/}2$ dimer state, and the extracted intradimer coupling is consistent with the spin-triplet transition energy observed in the RIXS spectra. These results highlights the ability of “spectroscopic fingerprinting” by RIXS to determine the magnetic ground states of complex materials.