Longitudinal Hall Effect

The "Hall Field" is defined as the electric field which is an odd function of the magnetic field. Because of the Onsager relations it is perpendicular to the current. It is split into the conventional transverse Hall field (TH-field) in the direction of B×I and a longitudinal Hall field (LH-field) in the direction I×(B×I). Some properties of the LH-field contrast with those of the TH-field. In particular, it vanishes (a) at saturation, (b) for spherical energy surfaces, and (c) when the magnetic field is parallel to an axis of rotation of the crystal. Its dependence on carrier concentration is the same as that of the TH-field; its sign, however, is determined by band structure as well as carrier sign. For a system consisting of $n$-type germanium the properties of the LH-field are investigated theoretically and experimentally.