  We construct and analyze a microscopic model for insulating rock salt ordered
double perovskites, with the chemical formula A$_2$BB'O$_6$, where the B' atom
has a 4d$^1$ or 5d$^1$ electronic configuration and forms a face centered cubic
(fcc) lattice. The combination of the triply-degenerate $t_{2g}$ orbital and
strong spin-orbit coupling forms local quadruplets with an effective spin
moment $j=3/2$. Moreover, due to strongly orbital-dependent exchange, the
effective spins have substantial biquadratic and bicubic interactions (fourth
and sixth order in the spins, respectively). This leads, at the mean field
level, to three main phases: an unusual antiferromagnet with dominant octupolar
order, a ferromagnetic phase with magnetization along the $[110]$ direction,
and a non-magnetic but quadrupolar ordered phase, which is stabilized by
thermal fluctuations and intermediate temperatures. All these phases have a two
sublattice structure described by the ordering wavevector ${\boldsymbol Q}
=2\pi (001)$. We consider quantum fluctuations and argue that in the regime of
dominant antiferromagnetic exchange, a non-magnetic valence bond solid or
quantum spin liquid state may be favored instead. Candidate quantum spin liquid
states and their basic properties are described. We also address the effect of
single-site anisotropy driven by lattice distortions. Existing and possible
future experiments are discussed in light of these results.
