Magnetoresistance of Tin Over a Large Range of Magnetic Fields

Abstract

We have measured the magnetoresistance of a number of specimens of high-purity tin at liquid-helium temperatures and in fields up to 50 kG; two specimens were examined in fields up to 150 kG (at the National Magnet Laboratory, MIT). Although our results confirm previous work, we find a number of peculiar features not reported before. Our results are shown to be in agreement with the model of the Fermi surface of tin given by Weisz. The peculiar features of the magnetoresistance are due to two properties of this model: (i) the presence of two open surfaces (in zones 4 and 5) of opposite sign, and (ii) the coupling by magnetic breakdown of orbits on the third-zone surface to orbits on the fourth-zone surface. In particular, we find that the anisotropy of the magnetoresistance for field directions closer than 40°-45° to the $c$ axis shows strong development with magnetic field, and we discuss this effect in detail to show that it is due to the closing, by magnetic breakdown, of aperiodic open orbits on the fourth-zone surface of the model. Some magnetic breakdown occurs in fields of less than 5 kG, but, because of the range of energy gaps over the zone face between zones 3 and 4, it is still not complete at 140 kG.