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

We study Fermi gases in a three-dimensional optical lattice with five fermions per site, i.e. the s-band is completely filled and the $p$-band with three-fold 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 in strong interaction regime by strong coupling expansion which yields an isotropic spin-$3/2$ Heisenberg model, and also in weak interaction regime, by Hatree-Fock mean-field theory and analysis of Fermi surface nesting. We show that the critical temperature for this antiferromagnetism of a $p$-band Mott insulator is about two orders of magnitudes higher than that of an $s$-band Mott insulator, which is close to the lowest temperature attainable nowadays.