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We study theoretically the anomalous Hall effect due to the vector spinchirality carried by the local spins in the $s$-$d$ model. We will show thatthe vector spin chirality indeed induces local Hall effect in the presence ofthe electron spin polarization, while the global Hall effect vanishes ifelectron transport is homogeneous. This anomalous Hall effect can beinterpreted in terms of the rotational component of the spin current associatedwith the vector chirality.

The anomalous Hall conductivity due to the vector spin chirality