The Fermi surfaces of the noble metals

Abstract

Precision measurements of the angular dependence of the de Haas-van Alphen frequencies F (proportional to extremal areas of the Fermi surface) of the noble metals have been made, using the technique of following the oscillations in magnetic properties as the crystal is slowly rotated in a fixed magnetic field.The most thorough measurements were on copper and these and a few measurements on silver agree very well with the results of Joseph, Thorsen, Gertner & Valby (1966) and Joseph & Thorsen (1965); a few measurements were also made on gold to clear up some slight discrepancies between the data of Joseph, Thorsen & Blum (1965) and of Shoenberg (1962). The major part of the paper is concerned with the use of the most reliable data from all available sources to compute analytical representations of the Fermi surfaces in the form of Fourier expansions. The method of analysis is essentially the same as that used by Roaf (1962) to fit the data of Shoenberg (1962), but because of the greater accuracy and comprehensiveness of the data now available, an appreciably greater accuracy could be achieved in the formulae for the Fermi surfaces. Following Roaf, the volumes of the computed Fermi surfaces were chosen to be exactly those of the free-electron sphere and the excellent agreement between the computed and observed absolute values of F , demonstrates the validity of this assumption. The computed orientation dependence of F agreed with experiment not only in regions between fitting points but also as regards features not used in the fitting. In particular, the analytical formulae predicted non-central minima of area whose angular dependence agreed almost exactly with the behaviour of the subsidiary belly oscillations observed by Joseph & Thorsen. Moreover, the existence of a new non-central minimum area (the ' lemon ’) predicted by the formulae for copper and gold was confirmed experimentally in copper with F in close agreement with the computed prediction. The computed radius vectors of 5 and 7 coefficient formulae for the same metal (with unrelated coefficients) agree to within about 0.2% and this suggests that the formulae are reliable to this sort of accuracy in the radius vector; this compares with the accuracy of order 1% achieved by Roaf. Once the extremal areas of cross-section of the Fermi surface are known, those of a surface of constant energy slightly differing from the Fermi energy Ev can be immediately deduced if the cyclotron masses are known.