Hall Effect in Ferromagnetics

TLDR

The extraordinary Hall effect in ferromagnets is large and temperature‑dependent because spin‑orbit interaction of polarized conduction electrons dominates. The analysis shows that interband matrix elements combined with spin‑orbit coupling generate a Hall current perpendicular to both field and magnetization, proportional to magnetization, with a Hall constant scaling as the square of ordinary resistivity and weakly dependent on temperature and impurities, in agreement with experiment.

Abstract

Both the unusually large magnitude and strong temperature dependence of the extraordinary Hall effect in ferromagnetic materials can be understood as effects of the spin-orbit interaction of polarized conduction electrons. It is shown that the interband matrix elements of the applied electric potential energy combine with the spin-orbit perturbation to give a current perpendicular to both the field and the magnetization. Since the net effect of the spin-orbit interaction is proportional to the extent to which the electron spins are aligned, this current is proportional to the magnetization. The magnitude of the Hall constant is equal to the square of the ordinary resistivity multiplied by functions that are not very sensitive to temperature and impurity content. The experimental results behave in such a way also.