Spin-Orbit Dimers and Non-Collinear Phases in $d^1$ Cubic Double Perovskites

We formulate and study a spin-orbital model for a family of cubic double perovskites with $d^1$ ions occupying a frustrated fcc sublattice. A variational approach and a complimentary analytical analysis reveal a rich variety of phases emerging from the interplay of Hund's and spin-orbit couplings (SOC). The phase digram includes non-collinear ordered states, with or without net moment, and, remarkably, a large window of a non-magnetic disordered spin-orbit dimer phase. The present theory uncovers the physical origin of the unusual amorphous valence bond state experimentally suggested for Ba$_2B$MoO$_6$ ($B$=Y,Lu), and predicts possible ordered patterns in Ba$_2B$OsO$_6$ ($B$=Na,Li) compounds.