  The Berry phase due to the spin wavefunction gives rise to the orbital
ferromagnetism and anomalous Hall effect in the non-coplanar antiferromagnetic
ordered state on face centered cubic (fcc) lattice once the crystal is
distorted perpendicular to (1,1,1) or (1,1,0)- plane. The relevance to the real
systems $\gamma$-FeMn and NiS$_2$ is also discussed.
