Theory of the Hall Effect in Ferromagnetic Substances

The Hall effect in ferromagnetic substances is computed on the basis of a simple model, making use of the transport theory of Kohn and Luttinger. The calculation is rigorous, but assumes a slowly varying scattering potential, a simple band, and very few conduction electrons. None of these assumptions are very realistic for a true ferromagnet, but we are interested here in only giving a discussion of the types of contributions which can occur. Terms related to those previously found by Smit and by Karplus and Luttinger, and some new ones, are found. In addition, some comments of Smit on the general problem of the ferromagnetic Hall effect are discussed.