  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.
