Fermi Surface Cross Research Articles

Energy Levels of Bloch Electrons in Magnetic Fields

From the calculation of the energy levels of conduction electrons in a simple model of a metal in a magnetic field three interesting results emerge. (a) Quantum corrections to Onsager's semiclassical quantization formula are found to be sufficiently small that the usual interpretation of the de Haas-van Alphen effect should provide an accurate measure of Fermi-surface cross sections in potassium. (b) The undetermined constant appearing in Onsager's formula is found to be $\frac{3}{4}$ for effects due to "lens" orbits in hexagonal metals when the magnetic field lies in the basal plane. (c) The quantization of energy levels in a variety of periodic open orbits is predicted to be observable in principle through cyclotron-resonance experiments in a suitable geometry in the intermediate magnetic-breakdown regime.

Effect of pressure on the fermi surface of Zr

Pressure derivatives of Fermi surface cross sections of Zr along major symmetry directions were obtained using the fluid He phase shift technique. The values range from -8 × 10 -4 to 3 × 10 -3 kbar -1 as compared to the free electron scaling prediction of ∼ 7 × 10 −4 kbar -1.

Ultrasonic Measurements of Nonextremal Fermi-Surface Parameters in Bi at 9.3 GHz

The origin of oscillations in the rotation pattern of 9.3-GHz ultrasound in Bi is discussed. The oscillations are shown to be associated with nonextremal Fermi-surface cross sections. In addition, anomalous quantum oscillations are reported. These may be $\ensuremath{\Delta}n\ensuremath{\ne}0$ transitions.

Effect of Hydrostatic Pressure on the Electron Fermi Surfaces in Pd and Pt

We present measurements of the pressure derivative $\frac{d(\mathrm{ln}S)}{\mathrm{dp}}$ of the Fermi surface cross section $S$ at [100] and [111] for the electrons in Pd and Pt in the range 0-25 atm. The results suggest that the electron pressure derivatives in these metals are nearly isotropic. Along [100] $\frac{d(\mathrm{ln}S)}{\mathrm{dp}}=(4.0\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4} \mathrm{and} (3.2\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{kbar}}^{\ensuremath{-}1}$ for Pd and Pt, respectively.

Oscillatory magnetostriction and deformation potentials in bismuth

The oscillatory transverse and logitudinal components of the magnetostriction in single crystal bismuth has been measured. The rates of change of the Fermi surface cross sections with stress are obtained which, when applied to the deformation potential model, give E 1=−1.6±1 eV and E 2=+2.8±1.5 eV.

A computer calculation of Fermi surface cross sections using the empty lattice model

A computer program has been written in Fortran IV to calculate the areas of Fermi surface cross sections using the empty lattice model often referred to as the one-OPW model. The program employs the Harrison (1960) construction and will work for any structure with any Fermi radius. For hexagonal structures both the single and double zone schemes may be employed. Any plane may be selected by the user. This plane may be rotated a specified number of times about two axes and also shifted along one of the axes in order to search for extremal orbits along this axis. In applying the program to complicated Fermi surfaces a qualitative sketch of the surface may be necessary for the correct interpretation of the computer output. A copy of the deck of cards comprising the program may be obtained from the Depository of Unpublished Data.

Electronic Structure of Rare-Earth Metals. I. Relativistic Augmented-Plane-Wave Calculations

Relativistic augmented-plane-wave calculations for Gd, Dy, Er, and Lu are reported. Energy bands, histograms of the density of states, and Fermi-surface cross sections are given. The Fermi surfaces of Dy, Er, and Lu are found to be quite similar to the one given earlier for yttrium. The Fermi surface of Gd is found to differ from the others by the absence of a feature. Nesting between the sheets of the webbing is correlated with the occurrence of periodic moment arrangements in Dy, Er, and alloys of Y and of Lu with certain magnetic rare earths.

De Haas-van Alphen Effect in p-Type PbTe and n-Type PbS

A study of the de Haas-van Alphen oscillations in the magnetic susceptibility has been carried out in p-type PbTe and n-type PbS. Measurements have been made on oriented single crystal samples with carrier concentrations of the order of 1018/cm3 in pulsed magnetic fields up to 125 kgauss. The results for p-type PbTe indicate that the valence bands have a maximum at k=0, and four equivalent maxima at the {111} Brillouin zone faces. The 〈111〉 ellipsoids have a longitudinal mass to transverse mass ratio of 6.4±0.3. From the temperature dependence of the amplitude of the oscillations we obtain a value of 0.043±0.006 m0 for the transverse effective mass. The data indicate that the (000) maximum and the (111) maxima lie within 0.002±0.002 ev of each other. The data also indicate an effective broadening temperature of about 8°K which is attributed to inhomogeneities in the carrier concentrations in the samples investigated. Preliminary results on n-type PbS show a single isotropic Fermi surface cross section with a cyclotron mass of 0.14±0.04m0. The direct and indirect optical interband transitions are discussed in the light of these results.