The anomalous Hall effect due to the spin chirality order and fluctuation is studied theoretically in a Kondo lattice model without the relativistic spin-orbit interaction. Even without the correlations of the localized spins, σxy can emerge depending on the lattice structure and the spin anisotropy. We reveal the condition for this chirality-fluctuation driven mechanism for σxy. Our semiquantitative estimates for a pyrochlore oxide Nd₂Mo₂O₇ give a finite σxy~10 Ω^-1 cm^-1 together with a high resistivity ρₓₓ~10^-4--10^-3 Ω cm, in agreement with experiments.
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Onoda et al. (2003) studied this question.