Resonant elastic x-ray scattering on the molecular orbital in Li₂RuO₃

In solid, the d-orbital electrons of transition metal (TM) elements are generally described in the atomic orbital limit because an overlap between adjacent orbitals is much smaller than other perturbations like d-p hybridization or Coulomb U. However, when ionic radii increase with the rise of periodicity or adjacent ions are getting closer like ones in edge-sharing or face-sharing octahedra, the enhanced overlap of orbitals can lead the molecular behavior of orbital clusters.
Li₂RuO₃ has a layered honeycomb structure composed of edge-sharing RuO₆ with strong dimerization. It enhances the orbital overlap so induces the spin-singlet, molecular orbital state. We measured the Bragg-forbidden (010) reflection in Li₂RuO₃ single crystal using resonant elastic x-ray scattering to identify the spatial distribution of the molecular orbitals. The peak was measured at the σ-π polarization change, but it is not a magnetic reflection as Li₂RuO₃ has no long-range magnetic order. We observed a distinct phase difference in the polarization dependence between Ru 2p-4d (t_2g) and 2p-4d (e_g) process. It also shows a fine structure from the crystal-field effect only at Ru L₃ edge but not at L₂ edge. This result elucidates the local shape of the molecular orbital of the Ru dimer.