The Hall effect and related phenomena

Abstract A review is presented of the theory of the Hall effect and related phenomena in solids. Basic principles are illustrated by application of the Lorentz force to moving charges in a free-electron system. Application to a real solid is indicated through a consideration of the effects of band structure and charge-carrier scattering mechanisms. Association is also made with the off-diagonal elements of the conductivity tensor, and the influence of certain symmetries in the medium is discussed. Special mention is made of specific parameters useful in characterizing a material for Hall-effect applications, including the dependence of the parameters on temperature and impurity content. The question of the variation of Hall coefficient with magnetic field is examined in some detail, with particular attention to band structure and crystal anisotropy, scattering, inhomogeneities and multi-band effects. Differentiation is made between isothermal and adiabatic phenomena, and the importance of various thermomagnetic contributions is pointed out. Related galvanomagnetic phenomena which are discussed include magnetoresistance effect and also the magnetic-field dependence of the skin depth in the case of the transmission of a.c. fields through a disk.