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We study Fermi gases in a three-dimensional optical lattice with fivefermions per site, i.e. the s-band is completely filled and the p-band withthree-fold degeneracy is half filled. We show that, for repulsive interactionbetween fermions, the system will exhibit spin-3/2 antiferromagnetic order atlow temperature. This conclusion is obtained in strong interaction regime bystrong coupling expansion which yields an isotropic spin-3/2 Heisenberg model,and also in weak interaction regime by Hatree-Fock mean-field theory andanalysis of Fermi surface nesting. We show that the critical temperature forthis antiferromagnetism of a p-band Mott insulator is about two orders ofmagnitudes higher than that of an $s$-band Mott insulator, which is close tothe lowest temperature attainable nowadays.

Quantum Antiferromagnetism of Fermions in Optical Lattices with Half-filled p-band