Influence of Localized Umklapp Scattering on the Galvanomagnetic Properties of Metals

Abstract

The Boltzmann equation is used to investigate the influence of umklapp scattering on the galvano-magnetic properties of a nearly-free-electron bcc metal with a spherical Fermi surface. A phenomenological scattering function is used to describe the umklapp scattering. If the areas of the Fermi surface where umklapp scattering occurs are very small and the scattering very intense, the transverse magnetoresistance is found to increase linearly with the magnetic field to a saturation value. The linear variation can occur up to values of ${\omega }_c\tau$ as large as 150, i.e., well into the high-magnetic-field region. The Hall "constant" is also found to vary with the magnetic field strength. Application of the results to potassium, aluminum, and cadmium is briefly discussed.