An experimental determination of the fermi surface in lead

Abstract

The oscillatory variation of magnetic moment with magnetic field (de Haas-van Alphen effect) has been studied in lead single crystals in the range 1-2 to 4-2° K and at fields up to 80 kG using an impulsive-field technique. The oscillations consist of several terms with periods ranging from 0-53 x 10<super>-8</super>G<super>-1</super> to 5-4 x 10<super>-8</super>G<super>-1</super>. Particular attention has been paid to the variation of the periods with orientation of the field relative to crystal axes and the shape of the Fermi surface has been inferred from these results. The Fermi surface is found to consist of several pieces and application of the simple free-electron model has enabled these pieces to be fitted into the Brillouin zone scheme in a consistent manner. The surfaces found are (i) a sphere containing holes in the second zone, (ii) a multiply connected surface containing electrons in the third zone, and (iii) six ‘cushionshaped’ surfaces containing electrons in the fourth zone. The volumes within the surfaces have been estimated, giving roughly 0-45 hole per atom in the second zone and 0-45 electron per atom in the third and fourth zones, and the interpretation is consistent with ascribing a total of four valence electrons per atom to lead. From the temperature dependence of the amplitudes of the oscillations, ‘effective mass’ values have been obtained; using these data and the dimensions of the various surfaces, an estimate has been made of the electronic specific heat constant y and the probable form of the curve of density of states against energy is indicated. The proposed Fermi surface is shown to be reasonably consistent with other experimental evidence. The field and orientation dependence of the de Haas van Alphen amplitudes are discussed and the experimental amplitudes are compared with the theoretical amplitudes given by Lifshitz & Kosevich (1055); while the amplitudes of some of the oscillations are found to be considerably greater than those given by theory, others become unobservably small over large angular ranges. The de Haasvan Alphen effect has also been studied in dilute lead — bismuth alloys but no simple interpretation has been found for the observed changes in period.