Effects of Vertex Corrections on the Chirality-Driven Anomalous Hall Effect

The anomalous Hall effect due to spin chirality, a non-coplanar spin configuration, studied previously for the case of weak exchange coupling [G. Tatara and H. Kawamura, J. Phys. Soc. Jpn. 71, 2613 (2002)] is reexamined here by taking account of vertex corrections due to normal impurities. This amounts to considering the diffusive nature of electron motion, as well as spin conservation at the scattering from normal impurities, and introduces the spin diffusion length. The preexisting circular persistent current, responsible for the anomalous Hall response, is identified by calculating the typical magnitude of the equilibrium current.