First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe

We perform a first principles calculation of the anomalous Hall effect in ferromagnetic bcc Fe. Our theory identifies an intrinsic contribution to the anomalous Hall conductivity and relates it to the $k$-space Berry phase of occupied Bloch states. This dc conductivity has the same origin as the well-known magneto-optical effect, and our result accounts for experimental measurement on Fe crystals with no adjustable parameters.