A new mechanism for the anomalous hall coefficient with application to liquid metals

Abstract

The effect of spin-orbit coupling of conduction electrons on the Hall coefficient of liquid metals is studied and a new mechanism for the anomalous Hall coefficient is suggested. S.O. coupling causes asymmetric scattering and a current, perpendicular to the magnetic field and to the electric field, is set up. This leads to an additional Hall coefficient\(\tilde R_{so} \), as was first calculated by Luttinger. But S.O. coupling also causes a dipole to appear near each ion, leading to an electrical polarization and an additional Hall coefficient,Rso.Rso is calculated for liquid normal metals and transition metals to first order in S.O. coupling. In normal metals,Rso and\(\tilde R_{so} \) are proportional to the Pauli susceptibility. Both are positive for electron-like charge carriers. S.O. coupling leads to a maximum deviation from nearly free electron value in the Hall coefficient of a heavy, four or five-valent liquid metal with short mean free path. In transition metals, different expressions are obtained forRso depending whether localized moments are present (magnetic model) or not (non-magnetic model). The sign ofRso is determined by the value of thed-phase shift alone.Rso is proportional to the susceptibility ofd-electrons and can be large, leading to a positive Hall coefficient in the liquid transition metal.