Orbital Ferromagnetism and Anomalous Hall Effect in Antiferromagnets on the Distorted fcc Lattice

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