We employ the determinant projector quantum Monte Carlo method to investigate the ground-state magnetic properties in the Mott insulating states of the half-filled
SU(4) and
SU(6) Fermi-Hubbard model in the two-dimensional square lattice, which is free of the sign problem. The long-range antiferromagnetic Neel order is found for the
SU(4) case with a small residual Neel moment. Quantum fluctuations are even stronger in the
SU(6) case. Numeric results are consistent with either a vanishing or even weaker Neel ordering than that of
SU(4).