Chirality-driven anomalous hall effect in weak coupling regime

Anomalous Hall effect arising from non-trivial spin configuration (chirality) is studied treating perturbatively the exchange coupling to localized spins. Scattering by normal impurities is included. Chirality is shown to drive locally Hall current and leads to overall Hall effect if there is a finite uniform chirality. This contribution is independent of the conventional spin-orbit contribution and shows distinct low-temperature behavior. In mesoscopic spin glasses, the chirality-induced anomalous Hall effect is expected below the spin-glass transition temperature. Measurement of the Hall coefficient would be useful in experimentally confirming the chirality ordering.