Abstract
We derive spin-orbital Hamiltonians for cubic double perovskite ${A}_{2}M{M}^{\ensuremath{'}}{\mathrm{O}}_{6}$ Mott insulators with $5{d}^{1}$ or $5{d}^{2}$ magnetic ${M}^{\ensuremath{'}}$ ions and nonmagnetic $M$ ions. We find that with strong spin-orbit coupling, exchange and intersite Coulomb repulsion lead to orbital order at a temperature ${T}_{o}$ higher than the magnetic ${T}_{c}$. Orbital order produces a $T$-dependent moment below ${T}_{o}$ and stabilizes canted ferromagnetic (FM) and noncollinear antiferromagnetic (AFM) states below ${T}_{c}$. We explain many experimental puzzles including loss of entropy above ${T}_{c}$, deviations from a Curie-Weiss susceptibility, a negative Curie-Weiss intercept for FM systems, and why FM order is common in cubic $5{d}^{1}$ materials but all $5{d}^{2}$ systems are AFM.
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