Van Alphen Frequencies Research Articles

An Approximate Sum Rule for de Haas–van Alphen Frequencies of Free Electron-like Conductors

The general relationship between sums and differences of de Haas–van Alphen frequencies and certain cross sectional areas of the Fermi surface in the extended zone scheme is derived. As shown in the case of AuPb2, this result may help to interpret de Haas–van Alphen data of free electron-like conductors.

De Haas-van Alphen Effect in Dilute Alloys of Bismuth in Lead

An in situ NMR technique has been used to make accurate (\ensuremath{\sim}2 parts in ${10}^{4}$) measurements of several de Haas\char22{}van Alphen frequencies in pure lead for two of the primary symmetry directions, [100] and [110]. By the same method the variation of the [100] $\ensuremath{\beta}$ frequency with the addition of up to 0.2% bismuth has been investigated. The alloy results identify the $\ensuremath{\beta}$ oscillations as being due to an electronlike piece of Fermi surface. At small impurity concentrations, the dependence of the frequency on concentration is in good agreement with the rigid-band model. However, at the higher concentrations there is a tendency for the frequency changes to be smaller than predicted by the rigid-band model and we interpret this trend to be due to an increase in the density of states, indicating that electrons are beginning to fill the fourth zone. It is not clear from our results whether the fourth zone begins above or below the pure-lead Fermi energy, but taken at face value, our measurements would suggest that it begins about 4 meV above the Fermi energy.

De Haas–Van Alphen frequency variations and curvature of the Fermi surface

The angular variation of the extremal cross-sectional area of a surface formed by revolving an arc of a circle about an axis has been calculated for various ratios of arc radius to radius of revolution. By comparing with these results experimental rotation diagrams for portions of Fermi surfaces of metals which are approximately surfaces of revolution, values of local radii of curvature averaged over an extremal orbit can be deduced.

Relativistic Electronic Structure in Crystals. II. Fermi Surface of Tungsten

The relativistic augmented-plane-wave method developed in the first paper of this series has been applied to tungsten. Relativistic effects on the energy bands and the Fermi surface are presented. The angular dependence of de Haas---van Alphen frequencies, as well as other experimental results, are determined from the theoretical Fermi surface. A comparison with experimental results supports the general conclusion that relativistic effects reduced the size of the Fermi surface of tungsten.

The Fermi surface of beryllium

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.