Theory of quantum antiferromagnetism of fermions in an optical lattice with a half-filled p band

We study Fermi gases in a three-dimensional cubic optical lattice with five fermions per site, i.e., the s band is completely filled and the p band with threefold degeneracy is half filled. We show that for repulsive interaction between fermions, the system will exhibit spin-3/2 antiferromagnetic order at low temperature. This conclusion is obtained both in strong interaction regime by strong coupling expansion and in weak interaction regime by the Hartree--Fock mean-field theory with analysis of the Fermi surface nesting. We also show that in the strongly correlated regime the N\'eel temperature for p band antiferromagnetism is 2 to 3 orders of magnitudes higher than that of s band, which is much more promising to be attained in cold atom experiments.