de Haas-van Alphen Effect and the Fermi Surface of Dilute Alloys of Zinc

Abstract

Torsion measurements have been made of the de Haas-van Alphen magnetic-susceptibility oscillations in dilute Zn-Cu (up to 0.2 at.%) and Zn-Al (0.1%) alloys in magnetic fields up to 33kG. Sizeable alloying effects occur in the two longest periods $P_1$ and $P_2$ (the two smallest orbits on the zinc Fermi surface). Both periods decrease by 30% with only 0.2% Cu. With 0.1% Al, $P_2$ increases substantially while $P_1$ is only slightly increased, by an amount comparable to the 4% uncertainty in period determination (the oscillation amplitude is very small in the alloys). Following an earlier suggestion of Harrison, these alloying changes have been interpreted using the nearly-free-electron construction. The model explains both the sign and the magnitude of the $P_1$ changes, in particular demonstrating that the dominant effect of the axial-ratio change can make a metal of lower electron concentration act to increase the size of an electron piece of the Fermi surface. The model accounts for the sign but not the magnitude of the $P_2$ changes, which are more than a factor of three larger than predicted by the model. No changes greater than 1% were observed in the third longest period $P_3$. An unexplained result is the observation of a period of order 400×${10}^{-7\mathrm{}}$ ${\mathrm{G}}^{-1\mathrm{}}$ for fields in the (0001) plane in crystals containing copper impurities, but not in pure zinc or Zn-Al.