Spin-orbit dimers in double perovskites

In Mott insulators, unquenched orbital degrees of freedom often frustrate the magnetic interactions and lead to a plethora of interesting phases with unusual spin patterns or non-magnetic states without long-range order. Here, we present a theoretical study of interplay of spin and orbital degrees in double-perovskite compounds with d$^1$ ions occupying the fcc sublattice. We show that the ground state of such a system is non-magnetic dimer pseudo-spin singlet with extensive orientational degeneracy of dimers. We discuss how the pseudo-spin state forming the singlet is altered upon increasing the strength of the relativistic spin-orbit coupling and show that the dimer 'gas' phase remains the ground state throughout. Our theoretical findings support and explain the experimentally observed non-magnetic amorphous valence bond state in Ba$_2$YMoO$_6$ and in related compounds.