Van Alphen Measurements Research Articles

Conduction-electron Zeeman splitting in the noble metals.

Extremal cross-section areas, cyclotron effective masses, and cyclotron-orbit g factors (${g}_{c}$) have been calculated for three noble metals (copper, silver, and gold) using the relativistic linear muffin-tin orbital (LMTO) method with a Hamiltonian which includes an applied magnetic field. The calculations are compared with experimental results from de Haas--van Alphen measurements performed by other authors. The overall resemblance between theory and experiment shows that the major source of the deviation from the free-electron g value in the noble metals can be explained by spin-orbit interaction. The large difference between calculated and experimentally determined ${g}_{c}$ factors found for the neck orbit in gold is discussed.

Calculation of Compton profiles in ferromagnetic iron using LMTO wavefunctions

The authors report the calculations of magnetic Compton profiles in ferromagnetic iron. Self-consistent and parametrised band-structure calculations were performed using the linear muffin-tin orbital method. These calculations are consistent with other calculations and show a good agreement with the experimental data. Moreover the parametrised curves describe the measured magnetic Compton profiles in the low-momentum region more precisely than the self-consistent calculations. These results confirm the analysis of positron annihilation data made by Genoud and co-workers (1988), which require the use of a parametrised band-structure calculation. The main differences between both band structures concern the point N of the Brillouin zone: the large N-centred hole pocket of the minority third band given by the self-consistent calculation almost vanishes in the parametrised calculation. This trend is also supported by de Haas van Alphen measurements.

Observation of the magnetic field dependence of the cyclotron mass in the Kondo lattice CeB6.

Low-temperature, high-field deHaas--van Alphen measurements are presented which show that the conduction-electron mass in the Kondo lattice ${\mathrm{CeB}}_{6}$ decreases strongly with field. This field dependence is consistent with recent specific-heat results. The geometry of the Fermi surface does not depend on field. Thus we observe a reduction in the many-body enhancement of the electronic density of states at the Fermi energy which is described by a change of the itinerant-electron mass alone; the number of particles and the occupation of states in k space remain unchanged. We argue that ${\mathrm{CeB}}_{6}$ represents a different limit of heavy-fermion behavior as compared to ${\mathrm{UPt}}_{3}$.

Effect of spin-orbit coupling on the conduction-electron Zeeman splitting in platinum-group metals.

Local g factors, cyclotron effective masses, and cyclotron-orbit g factors (${g}_{c}$) for rhodium, palladium, iridium, and platinum have been calculated using a relativistic linear muffin-tin orbital method, including perturbation of a magnetic field. These calculations are compared with experimental results from de Haas--van Alphen measurements. Both measurements and calculations give an anisotropic ${g}_{c}$ factor for the \ensuremath{\Gamma}-centered electron sheet and the X pocket while they give a rather isotropic one for the \ensuremath{\alpha} orbit existing on the open-hole sheet. This indicates that the spin-orbit coupling is a major source of the anisotropic behavior of the ${g}_{c}$ factor in these metals.

Electronic structure and scattering in PdBx from de Haas-van Alphen measurements.

The relaxation times for electron scattering (Dingle temperatures) and the concentration dependence of extremal cross-sectional areas A of the Fermi surface of dilute palladium-boron alloys (PdB/sub x/ with 0< or =x<0.002) have been determined from de Haas--van Alphen measurements in fields up to 15 T and temperatures down to 0.4 K. The Fermi surface change d lnA/dx induced by boron in Pd is 1.3 for the (001) extremal cross-sectional area of the GAMMA-centered electron sheet and -16.5 and -14.6 for the smallest and largest cross-sectional area of the X-centered hole pocket. For the GAMMA-centered electron sheet d lnA/dx is approximately five times larger than in PdH/sub x/ and PdD/sub x/, and for the X pocket eight or four times larger than in PdH/sub x/ and PdD/sub x/, respectively. These experimental results are discussed in terms of a Thomas-Fermi--type potential and compared to band-structure calculations of Pd, PdH, and PdB and to average--t-matrix calculations for substoichiometric alloys. The Dingle temperatures are compared to electrical resistivity data and analyzed in terms of the Gupta-Benedek formula.

De Haas—van Alphen effect and Fermi surface of lutetium

We report de Haas---van Alphen measurements of the Fermi surface of lutetium at temperatures down to 0.3 K and in fields up to 150 kG in the ($10\overline{1}0$) and ($11\overline{2}0$) planes. Lutetium, having a filled $4f$ shell, serves as a nonmagnetic prototype of the structurally similar (hcp), trivalent, heavy rare-earth elements from Gd to Tm. The fact that no complete frequency branches were observed indicates that there are no closed pieces of the Fermi surface. We observed all but one orbit predicted by relativistic augmented-plane-wave calculations of Keeton and Loucks and by recent spin-orbit---linearized-augmented-plane-wave calculations of Tibbetts and Harmon. The data support a geometry similar to that of yttrium, and in good qualitative agreement with energy-band theory.

De Haas—van Alphen measurements in the ferromagnetic compoundsU3P4andU3As4

de Haas---van Alphen measurements are reported for the ferromagnetic actinide compounds ${\mathrm{U}}_{3}$${\mathrm{P}}_{4}$ and ${\mathrm{U}}_{3}$${\mathrm{As}}_{4}$. The large effective masses indicate $f$-electron interaction with conduction bands. The data are interpreted in terms of a semimetallic band structure producing a large electron sheet at point $\ensuremath{\Gamma}$ which is compensated by several smaller hole pockets along the $\ensuremath{\Gamma}\ensuremath{-}P$ line. The measured internal field is much smaller than expected on the basis of magnetization measurements. Several discrepancies with other measurements point to additional unobserved pieces of the Fermi surface.

De Haas-van Alphen effect in Sc metal

The first de Haas--van Alphen measurements on Sc are reported. A modified band structure is proposed to account for the very unexpected results.

Isotope effects in the electronic structure ofPdHxandPdDxfrom de Haas—van Alphen measurements

The concentration dependence of extremal cross-sectional areas of the Fermi surface of dilute $\mathrm{Pd}{\mathrm{H}}_{x}$ and $\mathrm{Pd}{\mathrm{D}}_{x}$ alloys ($0\ensuremath{\le}x\ensuremath{\le}0.005$) has been determined from de Haas---van Alphen measurements in fields up to 10.5 T. The data confirm the general features of the proton model: States at the Fermi level are lowered in energy and the electrons added to the metal by the dissolved hydrogen or deuterium are partially accommodated at the Fermi surface of the host. The de Haas---van Alphen measurements show for the first time that large isotope effects are present in the concentration dependence of some of the Fermi-surface sheets. The sheets that show the largest isotope effect are those that contain mostly states with a vanishing charge density at the hydrogen site. The experimental results are discussed in terms of a proton screening potential exhibiting a Thomas-Fermi behavior at short distance and Friedel-type oscillations at large distance.

Critical fieldsHcandHc2of superconducting niobium

New measurements of the thermodynamic critical field ${H}_{c}$ and the upper critical field ${H}_{c2}$ of a niobium crystal are interpreted by using realistic microscopic theory. The theory of ${H}_{c2}$ combined with band theory allows the ${H}_{c2}$ measurements to be compared with de Haas---van Alphen measurements. Eliashberg theory allows the ${H}_{c}$ measurements to be compared with other experiments that are sensitive to the electron-phonon interaction. Our measurements of ${H}_{c2}$ confirm the band theory of niobium as adjusted to match de Haas---van Alphen data. Our measurements of ${H}_{c}$ enable us to deduce the value of the electron-phonon-coupling parameter $\ensuremath{\lambda}$. Finally, we note a discrepancy between the value of the renormalization parameter $1+\ensuremath{\lambda}$ that is needed to match the ${H}_{c2}$ data with the band theory and the value of $1+\ensuremath{\lambda}$ that is required to give the observed ${H}_{c}$.

The hall coefficient for isotropic electron scattering

The Hall coefficient, R H, of the ternary alloys Cu>  AuGe and Cu  NiGe is found to be independent of temperature from room temperature down to (at least) 5 K. Above about 100 K the values of R H are in close agreement with those of pure copper. From these two observations we deduce that, in accordance with predictions from de Haas van Alphen measurements, the scattering for both electron-phonon and electron-impurity processes is isotropic.

Effect of pressure on the Fermi surface ofNb3Sb

The pressure dependences of three cross sections of the Fermi surface of Nb3Sb are determined from de Haas van Alphen measurements in solid He to several kbar. A large negative derivative is observed for the smallest cross section of the hole ellipsoid at M. © 1981 The American Physical Society.

The fermi surface of beryllium

AbstractThe Fermi surface (FS) of beryllium has been calculated using the augmented plane wave energy bands for the material. The extremum area and the FS caliper distances are in excellent agreement with the de Haas–van Alphen measurements, and are better than existing ab initio calculations.

De Haas–van Alphen measurements of mixed valent CeSn3 (invited)

We present the first Fermi surface measurements of a mixed valent metal, CeSn3. We find a complex Fermi surface with at least nine separate frequency branches. The measured effective masses are very large, ranging from 4.2 to 9.2. The results directly confirm the existence of coherent Bloch states in CeSn3 and strongly support an itinerant model of mixed valence based on hybridized energy bands. We compare the Fermi surface properties of CeSn3 to those of LaSn3, a non-mixed valent reference metal, and discuss how the comparison allows various proposed models of mixed valence to be tested. Preliminary band calculations using only exchange in the density functional are able to reproduce many of the qualitative features of the CeSn3 data.

Electron-phonon spectral function and mass enhancement of niobium

The electron-phonon spectral distribution function ${\ensuremath{\alpha}}^{2}(\ensuremath{\omega})F(\ensuremath{\omega})$ has been calculated for niobium. The electron energy bands and wave functions were obtained from a self-consistent augmented-plane-wave muffin-tin potential, and the electron-phonon matrix elements were evaluated using the so-called rigid-ion approximation. With this approximation, it is found that ${\ensuremath{\alpha}}^{2}(\ensuremath{\omega})$ is constant over the whole energy spectrum. The electron-phonon mass enhancement has also been calculated for local regions of the Fermi surface and found to be anisotropic. The calculated local values of the enhancement do not agree with experimental values available for different orbits from de Haas---van Alphen measurements. The discrepancy seems to arise because the bare-rigid-ion matrix elements are relatively small between states with nearly pure $l=2$ character.

Electronic structure of hcp transition metals

Using the linear muffin-tin-orbital method described in the previous paper, (Phys. Rev. B 12: 3060) the electronic structures of the hcp transition metals, Zr, Hf, Ru, and Os were calculated . It is shown how the band structures of these metals may be synthesized from the sp and d bands, and the effects of hybridization, relativistic band shifts and spin--orbit coupling are illustrated by the example of Os. By making use of parameters derived from the muffin-tin potential, trends in the positions and widths of the energy bands, especially the d bands, are discussed as a function of the location in the periodic table. The densities of states of the four metals are presented and the calculated heat capacities compared with experiment. The Fermi surfaces of both Ru and Os are found to be in excellent quantitative agreement with de Haas--van Alphen measurements, indicating that the calculated d-band position is misplaced by less than 10 mRy. Very small pieces of Fermi surface, which have not yet been observed experimentally, are predicted for Os. The limited amount of experimental information available for Zr can be fairly satisfactorily interpreted if the calculated d bands, are raised by about 10--20 mRy relative tomore » the sp bands. This gives rise to a Fermi surface which is topologically equivalent to that recently found in Ti, and which does not support open orbits when the magmetic field is sufficiently great that breakdown is complete. It is suggested that the Fermi surface of Hf is probably similar, although very little experimental evidence is available for this metal. Some comments are made about the calculational method, which has proved to be physically transparent, accurate and extremely fast, and the adequancy of the standard potential, which has now been successfully employed in calculations on the great majority of the transition metals. (auth)« less

Momentum distribution of photoelectrons emitted from Cu and Ag single crystals, and its polarization dependence

The angular-resolved energy-distribution functions for photoelectrons emitted from (111) Cu and Ag are presented at photon energies below 6.2 eV. They show a characteristic dependence on the polarization of the radiation in spite of the fact that the experiments are done at normal incidence. No such polarization dependence is observed for (110) and (001) Cu surfaces. The polarization dependence is traced to the angular dependence of the dipole matrix element characteristic for direct transitions; it allows one to separate the elastically emitted electrons from those emitted after being scattered. An interpolation scheme is used to calculate $E(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$ consistent with the experiments of this paper and with independent optical and de Haas---van Alphen measurements. The nearly-free-electron case is used as a guide in the interpretation, it reveals only qualitative similarities with the actual experiments.

High Field Magnetoresistance and Quantum Oscillations in Iron Whiskers

[100] and [111] iron whiskers were measured to determine the origin of open orbits responsible for anisotropy of the high field magnetoresistance. The marked strain dependence of the minima resulting from [Formula: see text] open orbits permits their unambiguous identification as resulting from magnetic breakdown at a symmetry degeneracy, de Haas–Shubnikov oscillations were observed, and complementary de Haas–van Alphen measurements showed the lower frequencies (in the range 1.2–1.5 MG) to correspond to a hole pocket of the minority spin Fermi surface.

Band Structure and Properties of Cesium Metal

Energy bands and wave functions for cesium metal have been obtained by an orthogonalized-plane-wave procedure using a conduction-electron potential constructed from first principles. The effects of correlation in the ground state have been included through a local model potential and are found to have a rather small influence on band properties. The Fermi surface is observed to be less distorted along the [110] direction than in earlier calculations, and is in better agreement with experiment. The ratios $\frac{{k}_{F}}{{{k}_{F}}^{0}}$ along three principal directions [110], [111], and [100] were found to be 1.032, 0.992, and 0.970, as compared to 1.033, 0.991, and 0.986 obtained from de Haas---van Alphen measurements. The calculated density of states is utilized to evaluate the specific heat, which, after suitable correction for electron-phonon interaction, is found to be about 1.03 times the experimental value. The spin susceptibility, after incorporating exchange enhancement effects, is predicted to be 0.7696\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ ${\mathrm{cm}}^{3}$ volume units, in good agreement with a recent experimental value of 0.80\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ inferred from the nuclear-magnetic-resonance measurements in liquid alkali-metal alloys. The Knight shift and the nuclear relaxation time ${T}_{1}$, which depend explicitly on the wave functions, are both found to be within 60% of experiment. Possible mechanisms which could improve the agreement of these two properties with experiment are discussed.

Plasma Edge in Bi2Te3

The reflectance minima associated with the free carrier plasma edges in p- and n-type Bi2Te3 have been observed at 78° and 300°K. The data together with the measured Hall and Seebeck coefficients have yielded combined band structure-relaxation time parameters when proper account is taken of the anisotropy. These are compared with the results of other experiments from which similar information has been obtained. For n-type Bi2Te3 fair agreement is found with galvanomagnetic and optical band structure determinations. For p-type material the agreement with the results of similar experiments is considerably poorer but recent de Haas—van Alphen and galvanomagnetic measurements have established the value of the parameter measured in this experiment to within approximately the experimental error.