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A ferromagnet with spin anisotropies on the two-dimensional (2D) kagom\'e lattice is theoretically studied. This is a typical example of the flat-band ferromagnet. The Berry phase induced by the tilting of the spins opens the band gap and quantized Hall conductance ₗₘ=e^2/h is realized. This is the most realistic chiral spin state based on the ferromagnetism. We also discuss the implication of our results to the anomalous Hall effect observed in the metallic pyrochlore ferromagnets R₂Mo₂O₇ (R=Nd, Sm, Gd).
Ohgushi et al. (Fri,) studied this question.
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