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.

Figure 1

Examples of orbital and spin-coupling patterns on the honeycomb lattice of Ru ions. (a) Decoupled AF chain and ring with corresponding orbital pattern. (b) An example of the spin-singlet dimer covering minimizing the energy at zero Hund’s coupling. Thick (thin) lines denote AF (FM) intra- (inter-)dimer bonds, respectively. Dashed lines stand for the noninteracting bonds.

Figure 2

Lifting dimer degeneracy by magnetoelastic coupling. The small light (large dark) circles denote Ru (Li) ions. The arrows show the displacements of corresponding ions. (a) The sketch of Li displacements induced by dimerized Ru-Ru bond. (b),(c) Two examples of destructive interference of Li displacements induced by neighboring dimers. (d) The ground-state dimer pattern selected by magnetoelastic coupling. This pattern exactly corresponds to the one found in ${\mathrm{Li}}_2{\mathrm{RuO}}_3$ in Ref. 2.