The magnetoresistance of polycrystalline copper

Abstract

The effective medium theory has been applied to calculate the transverse magnetoresistance of random polycrystalline copper on the basis of the known Fermi surface, in order to explain the nearly linear variation of resistance with magnetic field up to very high values. Ziman’s (1958) conjecture that the conductivity tensor should be averaged over all orientations is shown to be a good first approximation, though it does suggest that the resistance should have been observed to approach saturation in some experiments, when the open orbits might play a dominant role at large values of w c T. The effective medium theory, by raising the saturation level considerably, eliminates this difficulty. The conductivity due to open and highly extended orbits, when calculated by geometrical analysis of the Fermi surface, is found to be quite sufficient to account for the observed behaviour. Certain residual discrepancies, especially a deficit in conductivity in very pure samples at large w c T, are explained as arising partly from size effects and small angle scattering, but mainly from the markedly non-random texture of drawn and annealed wires; it is concluded that there is no reason to doubt that standard theories of magnetoresistance are capable of interpreting the observations. Most of the calculations of conductivity due to open and extended orbits are straightforward in principle and remarkably insensitive to the least well known parameters involved, the relaxation time and the angular distribution of scattering, so that the theoretical predictions are reasonably secure. Only in dealing with the extended orbits in the vicinity of high symmetry directions are approximations of dubious validity invoked, and even they are provided with more or less plausible justification. For the most part, however, the work represents a drawing together of well established concepts, and their application to a real Fermi surface rather than to convenient but imprecise approximate models.