Spin-Orbit Dimers and Noncollinear 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 complementary analytical analysis reveal a rich variety of phases emerging from the interplay of Hund's rule and spin-orbit coupling. The phase digram includes noncollinear ordered states, with or without a net moment, and, remarkably, a large window of a nonmagnetic disordered spin-orbit dimer phase. The present theory uncovers the physical origin of the unusual amorphous valence bond state experimentally suggested for Ba_{2}BMoO_{6} (B=Y, Lu) and predicts possible ordered patterns in Ba_{2}BOsO_{6} (B=Na, Li) compounds.