Orbitally driven spin-singlet dimerization in $S$=1 La${}_4$Ru${}_2$O${}_{10}$

Using x-ray absorption spectroscopy at the Ru-$L_{2,3}$ edge we reveal that the Ru${}^{4+}$ ions remain in the $S$=1 spin state across the rare 4d-orbital ordering transition and spin-gap formation. We find using local spin density approximation + Hubbard U (LSDA+U) band structure calculations that the crystal fields in the low temperature phase are not strong enough to stabilize the $S$=0 state. Instead, we identify a distinct orbital ordering with a significant anisotropy of the antiferromagnetic exchange couplings. We conclude that La${}_4$Ru${}_2$O${}_{10}$ appears to be a novel material in which the orbital physics drives the formation of spin-singlet dimers in a quasi 2-dimensional $S$=1 system.