Side-Jump Mechanism for Ferromagnetic Hall Effect

Abstract

We show the equivalence of the side-jump model of the ferromagnetic Hall effect recently proposed by Berger and the anomalous velocity contribution obtained by Luttinger and others. Specifically, starting from the cited anomalous velocity expression, we give a derivation (to the lowest Born order) of the (vector) side jump which an electron undergoes during a collision with an impurity for a system of ferromagnetically polarized free electrons, each interacting with the impurity centers, together with the concomitant spin-orbit interaction. The side jump obtained is independent of the strength and form of the impurity potential and agrees with the result of Berger.