de Haas-van Alphen measurements of the Fermi surfaces of rubidium and cesium

We present the results of a detailed investigation of the geometry of the Fermi surfaces of rubidium and cesium by means of the de Haas-van Alphen (dHvA) effect. By using samples of random orientation, mounted with the least constraints possible, we have obtained extensive coverage of the entire Fermi surface. An in situ NMR sample enabled the infinite-field phase of the signal, as well as absolute areas, to be determined. The spin-splitting factor cos (gm*/2m ₀ ), was found to be positive for both metals. The data, taken in magnetic fields up to 52 kG and at temperatures down to 1.1 K, was fitted by a 10- and 12-term cubic harmonic model expansion for rubidium and cesium, respectively. These models indicate that the Fermi surfaces are somewhat more distorted than those derived from previous investigations. A large change in the signal amplitude of cesium with crystal orientation suggests a variation in the productgms* over the Fermi surface. Effective mass measurements in cesium show a significant discrepancy between the measured dHvA and specific heat masses.National Research Council of Canada Postdoctoral Fellow.     

The low-temperature de Haas-van Alphen effect

An investigation has been carried out of the quantum oscillations of the magnetic susceptibility of an isotropic metal at constant pressure and at low temperatures in strong magnetic fields, when the amplitude of the density of electron states is of the order of the classical value. It is shown that quantum magnetostriction gives rise to a dependence of susceptibility on the ratio of the contributions to the moduli of elasticity due to electrons and to the lattice. The shape of susceptibility oscillations depends substantially on the Fermi-liquid interaction parameters. Conditions are discussed under which the thermo-dynamic stability at the oscillation peaks may be broken. The low-temperature oscillations of the derivative of volume with respect to the magnetic field are also considered. It is shown that at points of magnetic instability, jumps in volume are possible.     

The de Haas-van Alphen effect in calcium

The results of a detailed investigation of the de Haas-van Alphen effect in calcium are presented. The data, taken for the two major crystallographic planes in magnetic fields up to 36 kG and temperatures down to 0.1 K, indicate that the Fermi surface consists of a multiconnected monsterlike hole sheet in the first band and lens-shaped electron sheets in the second band. This indicates a Fermi surface geometry much more nearly free electron like than previously believed, and analysis in terms of a multi-OPW local pseudopotential model yields good agreement with the data.Work supported in part by the U.S. Army Research Office (Durham), the Advanced Research Projects Agency, and the National Science Foundation. Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the University of Chicago.     

The de Haas-van Alphen effect in MgHg

The de Haas-van Alphen effect has been observed in the quadrivalent -brass compound MgHg. Five frequency groups have been measured in the {110} and {100} planes along with some effective masses at high symmetry points. All five groups observed are well explained by Skriver's relativistic LMTO band calculation. A football-shaped piece predicted in the third band has the size and shape of an observed closed section which was inverted with tetragonal harmonics. The remaining orbits arise from the multipliconnected second band surface, a surface formed by connecting pockets at andR with arms along 111.NRCC Research Associate.     

Absolute amplitudes in the de Haas-van Alphen effect

Absolute amplitudes of the neck oscillations in the de Haas-van Alphen effect of silver, gold, and copper have been measured for various orientations around 111 infields up to 100 kG by means of a new kind of torque magnetometer. These amplitudes are found to agree with the predictions of the Lifshitz-Kosevich theory within an uncertainty of order 20% for silver, 5% for gold, and 10% for copper. This confirms theoretical expectation that many-body modifications to the Lifshitz-Kosevich theory should not be appreciable in our experimental conditions.     

The de Haas-van Alphen effect in PdTe2

The de Haas-van Alphen effect has been measured in the layer compound PdTe ₂ . Frequency branches from 0.1 kT to 4.5 kT were observed in the three principal planes. Effective masses were also measured. The number of branches suggests a complicated Fermi surface which is not well explained by existing band structures.     

Conduction electrong-factors in ruthenium and osmium from de Haas-van Alphen measurements

Conduction electrong-factors have been deduced from de Haas-van Alphen line shapes in the hexagonal group VIII 4d transition metal ruthenium and the electronically analogous 5d metal osmium. The values for orbits normal to [0001] are 1.8±0.1 and 1.3±0.1 for the ellipsoids centered on the lineLM in ruthenium and osmium, respectively, and 1.9±0.2 for the -centered ellipsoid in ruthenium. The more marked suppression of theg-factor in osmium, where spin-orbit coupling is stronger, is consistent with recent theoretical studies of transition metalg-factor trends.     

The de Haas-van Alphen effect in the intermetallic compound Cu2Sb

The de Haas-van Alphen effect has been studied in the intermetallic compound Cu₂Sb (tetragonal structure) by the modulation method in fields up to 100 kG. Numerous frequency branches have been obtained in the (100), (110), and (001) planes, and several cyclotron effective masses have been determined. The results show some compatibility with the nearly-free-electron model in the single- or double-zone scheme. The lattice parameters have been determined at room temperature and at liquid-helium temperatures.     

Magnetic interaction effect and Dingle temperature of de Haas-van Alphen oscillations in lead

The amplitude of the de Haas-van Alphen (dHvA) oscillation in lead in the symmetric direction (110) has been determined by analyzing the change in the amplitude of the fundamental frequency of the oscillation due to magnetic interacton (MI) with . The Dingle plot of the amplitude thus determined gives the Dingle temperature 0.08 K, as compared with 0.51 K determined by the conventional method in an identical sample. The large difference in the Dingle temperatures noted above is inconsistent with the old treatment of MI, but is consistent with the new treatment because in the latter treatment the amplitude of responsible for MI is the local amplitude before dephasing over the sample. Based on this fact, we suggest that MI can be used to determine the Dingle temperature of the dHvA oscillation without being affected by the inhomogeneity of the sample.     

Accurate measurement of changes in electron scattering in the de Haas-van Alphen effect

A new method for the accurate determination of smallchanges in the Dingle temperature measured in the de Haas-van Alphen effect is described. The method is illustrated with some measurements in copper and potassium, in which changes in the Dingle temperature of only a few millikelvin could be resolved.Supported by the Science Research Council.     

The de Haas-van Alphen effect in Sb(Sn) and Sb(Te) alloys

Measurements have been made of the de Haas-van Alphen effect in Sb(Sn) alloys containing up to 0.58 at % Sn and Sb(Te) alloys with up to 0.26 at % Te. The maximum electron period in the bisectrix-trigonal plane increased from 14.66 × 10^–7 G^–1 in pure Sb to 68.0 × 10^–7 G^–1 in the most concentrated Sn-doped sample, whereas the maximum hole period decreased from 16.33 × 10^–7 to 7.4 × 10^–7 G^–1 . The Te doping had the opposite effect—increasing the number of electrons and decreasing the number of holes. The results of measurements of effective mass and Fermi surface area are found to be consistent with a rigid-band model of these dilute alloys. Both electron and hole bands are strongly nonparabolic and a two-band model is used to estimate that the gap below the electron pocket at L is 110 ± 25 meV. The Fermi levels of electrons and holes in Sb are estimated to be 150 ± 10 and 180 ± 40 meV, respectively. It is predicted that the electron pockets will be completely emptied for an alloy with 0.78 ± 0.07 at % Sn. Pseudopotential calculations suggest that the rigid-band model is a reasonable approximation in these dilute alloys.     

The fermi surface of ruthenium as determined by the de Haas-van Alphen effect

The many de Haas-van Alphen frequencies observed in the hcp transition metal ruthenium have been investigated using the field modulation method in conjunction with a Fourier analysis technique. The observed frequency spectrum is explained in terms of the band structures calculated by Mattheiss for rhenium (also hcp) by invoking the rigid-band model. While the correct rhenium band structure is inadequate, that calculated without relativistic corrections can account quantitatively for all the observed frequencies. The details of the size and shape of the smaller pieces of Fermi surface provide a sensitive test for any band structure calculated for ruthenium. The model also explains qualitatively the amplitude behavior of the various frequencies except for some details when magnetic breakdown is operative.     

De Haas-van Alphen experiments in the superconducting state

Landau quantum oscillations of the magnetization, commonly referred to as the dHvA effect, appear to be a general property of superconductors in the mixed state. This is both intriguing from a fundamental point of view, and fortunate in that it provides a microscopic probe with which to explore the many-body environment of a superconductor. The results of experiments to date can be understood rather well in terms of a general theory of the dHvA effect for an interacting system. We indicate the nature of this and comment on the implications for molecular and oxide superconductors.     

A de Haas-van Alphen study of niobium: Fermi surface,cyclotron effective masses,and magnetic breakdown effects

The Fermi surface of niobium has been investigated using the de Haas-van Alphen effect. Data were taken at temperatures as low as 0.3 K and in fields as high as 130 kG. An on-line minicomputer was used to Fourier-transform the digitized signals. Many new extremal area data have been obtained, including oscillations associated with the previously unobserved -centered hole octahedron and and N-centered orbits on the so-called jungle gym. An additional set of signals has been observed near [100], which are thought to be a result of magnetic breakdown between the second zone octahedron and third zone jungle gym. A separate low-frequency signal was observed and is believed to be a result of magnetic-breakdown-induced quantum interference oscillations. Anisotropies of the cyclotron effective mass have been determined for many orbits on all three of the Fermi surface sheets. Finally, the area data have been used to parametrize the Fermi surface in terms of scattering phase shifts in a Korringa-Kohn-Rostoker band structure formalism.Work performed under the auspices of the U.S. Energy Research and Development Administration and the National Science Foundation under Grant DMR-74-12186.Supported in part by a stipend from the Argonne Center for Educational Affairs.     

The de Haas-van Alphen effect and Fermi surface of the ordered alloy β′-AgZn

The de Haas-van Alphen effect has been measured in the ordered alloy -AgZn by the modulation method, improving and extending the results of earlier observations. The results are in good agreement with recent theoretical calculations of the Fermi surface, although some of the predicted orbits have not been observed. The hole octahedron in the first band and the triangular hole in the second band have been identified unambiguously, and the shape of the octahedron has been determined by inversion.National Research Council of Canada postdoctorate fellow.     

The de Haas-van Alphen effect and the Fermi surface of the intermetallic compound AuPb2

The de Haas-van Alphen effect has been measured in the intermetallic compound AuPb₂ (body-centered tetragonal structure) by the modulation method in fields up to 100 kG. Thirty-two frequency branches have been observed in the (100), (110), and (001) planes, and several cyclotron effective masses have been determined. The nearly-free-electron model has been used to construct a Fermi surface, which explains the large frequency branches and is compatible with the high-field magnetoresistance results of Bass, Edwards, and Schroeder. It has been possible to determine the shape of some sheets by inversion of the de Haas-van Alphen data. The lattice parameters have been determined at room temperature and at liquid helium temperature.Canada Council Fellow.     

De Haas-van Alphen effect study of magnetic interaction in lead

Frequency and amplitude modulation (FM and AM) of a high-frequency (HF) de Haas-van Alphen oscillation due to magnetic interaction (MI) with a low-frequency (LF) oscillation in lead has been examined for field directions parallel to and close to 110, in the light of the old and of a new treatment of MI based on uniform and inhomogeneous inductions over the sample, respectively. The de Haas-van Alphen signals have been measured by the standard low-frequency field modulation method. The strength of AM and the sideband around HF have been examined as a function of the strength of FM and it is found that the experimental data deviate significantly from the prediction by the old treatment. Moreover, the deviation depends not only on the particular sample chosen to study, but also on the orientation, suggesting that the MI effect is influenced by the microscopic inhomogeneity of the sample. The absolute amplitude of LF also has been measured and is found again to deviate significantly from the prediction by the old treatment. However, the measured amplitude shows a satisfactory agreement with the prediction by the new treatment. In conclusion, the new treatment is a plausible theory which can describe all our experimental results, not only qualitatively but also quantitatively.     

de Haas-van Alphen measurements and phase shift analysis of electronic scattering anisotropy in solid solutions of Ga in Au

Measurements of the electronic scattering anisotropy due to dilute concentrations of gallium in gold have been carried out using the de Haas-van Alphen effect. These measurements have been analyzed using the partial wave approach, and the results have been compared with those for other noble metal-heterovalent impurity systems. Gallium, which has a valence difference of 2 with respect to gold, exhibits a much smaller change in lattice constant upon alloying than any of the other noble metal-heterovalent impurity systems studied to date. The results reported here indicate that the Friedel phase shifts for solid solutions of Ga in Au are considerably different from those for the other systems, in which impurity-induced strain is expected to play a larger role. The phase shifts for solid solutions of Ga in Au indicate that the Coulomb potential is effectively screened within a relatively short distance from the impurity site.Research supported by the Materials Research Center of Northwestern University, the National Science Foundation under grant No. GH-42593, and the U.S. Energy Research and Development Administration. During part of this work D. Dye was the recipient of an Argonne thesis parts research appointment.