Classical Dimers and Dimerized Superstructure in an Orbitally Degenerate Honeycomb Antiferromagnet

We discuss the ground state of the spin-orbital model for spin-one ions with partially filled $t_{2g}$ levels on a honeycomb lattice. We find that the orbital degrees of freedom induce a spontaneous dimerization of spins and drive them into nonmagnetic manifold spanned by hard-core dimer (spin-singlet) coverings of the lattice. The cooperative “dimer Jahn-Teller” effect is introduced through a magnetoelastic coupling and is shown to lift the orientational degeneracy of dimers leading to a peculiar valence bond crystal pattern. The present theory provides a theoretical explanation of nonmagnetic dimerized superstructure experimentally seen in ${\mathrm{Li}}_2{\mathrm{RuO}}_3$ compound at low temperatures.