  We synthesize and study single crystals of the layered honeycomb lattice Mott
insulators Na2RuO3 and Li2RuO3 with magnetic Ru4+(4d4) ions. The newly found
Na2RuO3 features a nearly ideal honeycomb lattice and orders
antiferromagnetically at 30 K. Single-crystals of Li2RuO3 adopt a honeycomb
lattice with either C2/m or more distorted P21/m below 300 K, depending on
detailed synthesis conditions. We find that Li2RuO3 in both structures hosts a
well-defined magnetic state, in contrast to the singlet ground state found in
polycrystalline Li2RuO3. A phase diagram generated based on our results
uncovers a new, direct correlation between the magnetic ground state and
basal-plane distortions in the honeycomb ruthenates.
