The Fermi surface of beryllium

Abstract

The Fermi surface of beryllium has been determined experimentally by studying the de Haas–van Alphen effect of single crystals in pulsed magnetic fields. The de Haas–van Alphen frequency (proportional to the extremal area of the Fermi surface normal to the field) was measured as a function of field direction. Consideration of the hexagonal symmetry of the Brillouin zone (discussed in the Appendix) shows that only six distinct classes of fre­quency variation with field direction are possible, and these considerations are used to deduce the locations and forms of the various sheets of the Fermi surface. The Fermi surface is found to consist of hole and electron surfaces of equal volume (each containing 0∙162 carrier per atom). The hole surface is somewhat like a coronet, i. e. a ring of six smoothed tetrahedra joined by small necks lying in the central (0001) plane of the first double Brillouin zone, and the electron surface is a set of six roughly ellipsoidal surfaces (cigars) lying on the vertical edges of the second double zone. Detailed shapes and sizes are deduced for the coronet and cigars such that the extremal areas of cross-section are consistent to within 1 % of those obtained from the observed de Haas–van Alphen frequencies. No oscillations of frequency corresponding to the outer (0001) orbit round the coronet were, however, observed; a study of the field dependence of amplitude of the oscillations from the coupled orbit round the cigar shows that this absence can be explained by magnetic breakdown of the {101̄0} band gap. The model described is in good agreement with the predictions of recent band structure calculations, and is consistent with other experimental evidence.