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An antiferro-magnetic (AF) low moment solution, 0.4 $\mu_\mathrm{B}$/Fe, isfound in the case of LaOFeAs for an intermediately strong Coulomb interaction$U$ of 2.5--3.0 eV. This solution is stabilized over a large moment solutiondue to the gain in exchange energy in the formation of large multipoles of thespin magnetization density. The multipoles are of rank four and can beunderstand as a kind of spin-orbital ordering. Parallels can be drawn to thestabilization of the AF order in e.g. CaCuO$_2$.

The low spin moment in LaOFeAs is due to a hidden multipole order caused by spin orbital ordering