The de Haas—van Alphen effect and the Fermi surface of sodium

Abstract

De Haas-van Alphen oscillations of magnetization have been studied in single crystals of sodium by means of a sensitive recording system based on the modulation technique of Shoenberg & Stiles (1964). From the observed variation of the de Haas-van Alphen phase as the crystal is rotated in a constant magnetic field, the anisotropy of the cross sectional area of the Fermi surface is deduced. Reasons are discussed for relating the experimental results to the Fermi surface of the high temperature, body centred cubic phase of the metal. The coefficients of a pseudopotential interpolation scheme due to Ashcroft (1965) are adjusted to fit the experimental results, and the lowest Fourier components of the effective lattice potential in sodium are deduced. The best fit is obtained with the single parameter | V 110 | = (0·225 ± 0·010) eV, and it is estimated that V 200 does not depart from zero by more than 0·3 eV. The Fermi surface of sodium is shown to be pulled out in the <110> directions, towards the faces of the first Brillouin zone, as would be expected for nearly free electrons. The extreme radial distortion of the Fermi surface from a free electron sphere is found to be rather less than 1 part in 10 3 .