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

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 , 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,R _so.R _so is calculated for liquid normal metals and transition metals to first order in S.O. coupling. In normal metals,R _so and 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 forR _so depending whether localized moments are present (magnetic model) or not (non-magnetic model). The sign ofR _so is determined by the value of thed-phase shift alone.R _so is proportional to the susceptibility ofd-electrons and can be large, leading to a positive Hall coefficient in the liquid transition metal.