De Haas-van Alphen effect in rhodium

The de Haas-van Alphen effect has been used to study the extremal areas and effective cyclotron masses on all five sheets of the Fermi surface of rhodium for the magnetic field in a (110)-plane. The measured extremal areas are in good agreement with relativistic-augmented-plane-wave calculations. The resulting deviations correspond to energy shifts of the calculated bands not exceeding 4 mRy. Several extremal orbits on the fifth band Γ-centered electron sheet have been observed. The mass enhancement determined from the ratio between the calculated and measured effective cyclotron masses is found to vary substantially over the different sheets of the Fermi surface. A rather isotropie factor of 1.40 is obtained for the sixth band Γ-centered electron sheet. For the third and fourth band hole pockets we obtained enhancement factors in the region 0.9–1.4.     

De Haas-van Alphen effect in unconventional superconductors

A theory of the de Haas-van Alphen effect in type-II p-wave and D-wave superconductors (the latter corresponds to the B _1g one-dimensional representation of group D _4h ) has been developed. Solutions for the order parameter and density of quasiparticle states near the upper critical field have been calculated. If the curve enclosing the extremal cross section of the Fermi surface in the plane perpendicular to the external magnetic field coincides with the line of nodes of the superconducting order parameter, the effect of the transition to the superconducting state on the amplitude of magnetization oscillations is negligible. If the line of nodes is oriented differently with respect to the applied magnetic field, the de Haas-van Alphen oscillations are suppressed in a manner qualitatively similar to the case of conventional superconductors. Zh. éksp. Teor. Fiz. 113, 2174–2192 (June 1998)     

De Haas-van Alphen effect studies in quenched gold

Dingle temperatures for the scattering of conduction electrons at vacancies were measured for 10 extremal orbits in quenched Au single crystals.     

De Haas-van Alphen effect in In2Bi

We report de Haas-van Alphen measurements in the intermetallic compound In₂Bi in magnetic fields up to 15T. At least three dHvA frequency branches could be followed continuously at all field directions indicating three ellipsoid-type pieces of the Fermi surface. The largest two ellipsoids are likely located along the Brillouin zone edge HK.     

De Haas-van Alphen effect studies in dilute alloys of silver and gold

De Haas-van Alphen experiments have been used to determine the scattering temperatures which characterize the [111] neck and belly extremal orbits in some dilute alloys of silver and gold. The relaxation time is anisotropic withτ _N/τ _B≃2 in both Ag(Au) and Au(Ag) when the scattering is dominated by the solute. This anisotropy is in the opposite sense to that observed in another homovalent alloy Ag(Cu) and to that observed in the presence of charged impurities.     

de Haas-van Alphen effect in superconductors

A theory of the de Haas-van Alphen effect in type-II superconductors is proposed. The effect of the electron scattering by nonmagnetic impurities in a magnetic field in the potential produced by a nonuniform distribution of the order parameter in a mixed state is investigated. The magnitude of the order parameter and quasiparticle density of states are determined from the solution of the system of Gor’kov equations. It is shown that in the presence of even a small amount of impurities, the superconducting state near the upper critical field is gapless. In this region, the oscillatory (in the magnetic field) contribution to the density of states and the characteristic damping of the amplitude of the magnetization oscillations in the superconducting state are found. Zh. éksp. Teor. Fiz. 112, 1873–1892 (November 1997)     

De Haas-van Alphen studies of electron-scattering in dilute copper-based alloys

We have used the de Haas-van Alphen (dHvA) effect to study the relaxation times of “neck” and “belly” electrons in copper containing a range of dilute heterovalent and transition-metal solutes. The scattering (Dingle) temperaturex is derived from the variation of signal amplitude with magnetic field at a fixed temperature. Values ofx are believed accurate to within 0.1°K in a range ofx _N(neck) from ≃0.4°K to ≃6°K andx _B(belly) from ≃0.2°K to ≃3°K. Our results may be summarized as follows:Heterovalent solutes (Zn, Cd, Al; up to 0.1 at. %) .Transition-metal solutes (Ni, Co, Fe, Mn, Cr; up to 0.05 at.-%) . An anomalous dependence of dHvA amplitude on magnetic field has been observed for belly oscillations in several very dilute Cu Cr alloys. This anomaly is both concentration and temperature-sensitive, and is probably related to the Kondo effect.     

The de Haas-van Alphen effect in InBi

By using the field modulation technique, the frequency spectrum of the de Haas-van Alphen effect in the semimetallic compound InBi has been investigated for fixed directions of the magnetic field, lying in three symmetry planes of the tetragonal unit cell. The experiments were confined to frequencies above 10⁶ G. Specimens were spark cut from two, differently grown, single crystals. In both series of specimens, two continuous frequency branches were found, which almost agreed with one another and with previous work by Shapira et al. and others. They correspond to two slightly distorted ellipsoids of revolution, elongated along the c-direction, with a volume ratio of about two. Strong evidence is found, that low frequency branches, found in only one series of specimens and also found in previous work, are due to inclusions of In₅Bi₃ and/or In₂Bi crystals, having a strong crystal orientation relation to the InBi matrix.     

De Haas-van Alphen Effect of Free Electron Gas Revisited

The free electron gas in a uniform magnetic field at low temperature is restudied. The grand partition function previously obtained by Landau＇s quantitative calculation contains three parts, which are all approximate. An improved calculation is presented, in which two of the three parts are obtained in exact forms. A simple remedy for Landau and Lifshitz＇s qualitative calculation in the textbook is also given, which turns the qualitative result into the same one as obtained by the improved quantitative calculation. The chemical potential is solved approximately and the thermodynamic quantities are caiculated explicitly in both a weak field and a strong field. The thermodynamic quantities in a strong field obtained here contain both non-oscillating and oscillating corrections to the corresponding results derived from Landau＇s grand partition function. In particular, Landau＇s grand partition function is not sufficiently accurate to yield our nonzero results for the specific heat and the entropy. An error in the Laplace-transform method for the problem is corrected. The results previously obtained by this method are also improved.     

Hysteresis in the de Haas-van Alphen effect

A hysteresis loop is observed for the first time in the de Haas-van Alphen (dHvA) effect of beryllium at low temperatures and quantizing magnetic field applied parallel to the hexagonal axis of the single crystal. The irreversible behavior of the magnetization occurs at the paramagnetic part of the dHvA period in conditions of Condon domain formation arising by strong enough dHvA amplitude. The resulting extremely nonlinear response to a very small modulation field offers the possibility to find in a simple way the Condon domain phase diagram. From a harmonic analysis, the shape and size of the hysteresis loop is constructed.     

The de Haas-van Alphen effect in quasi-two-dimensional materials

We calculate the amplitude of magnetization oscillations for a quasi-two-dimensional electron system. In the two-dimensional case the behavior of this amplitude as a function of magnetic field and temperature differ completely from the conventional Lifshitz-Kosevich formula valid for three-dimensional metals. Previously only the ideal two-dimensional case has been considered, and the difference of the shape of the Fermi surface from cylindrical has not been taken into account. We obtain the general formula for the envelope of magnetization oscillations as a function of magnetic field, temperature, and the strength of the warping of the Fermi surface. This problem is important because of the great amount of interest in heterostructures and quasi-two-dimensional organic metals which has arisen in recent years. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 2, 139–144 (25 January 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

The de Haas-van Alphen effect in Kondo systems

In Kondo systems, de Haas-van Alphen experiments determine a spin-splitting term in the conduction-electron self-energy. It is shown that for all temperatures and magnetic fields, and in the presence of normal potential scattering, spin-splitting of Landau levels is given exactly with:

$\text{Re Σ↓(0) - Re Σ↑(0) = cJ〈S}{}_{\mathrm{z}}\text{〉}{}_{\mathrm{K}}$

Σ(0) is the conduction-electron self-energy at the Fermi level and 〈S_z〉_K is the expectation value for the impurity spin including Kondo effects.     

Evidence from the de Haas-van Alphen effect

The amplitude of the de Haas-van Alphen effect is reduced by collision broadening of the Landau levels approximately as if the temperature were raised by an amountx (the Dingle temperature) which is inversely related to an appropriate relaxation timeτ. Following a discussion of what is involved in obtaining significant estimates ofτ from experimental measurements ofx, the rather meagre available results are reviewed. For fairly pure samples, values ofx are often found which are as much as 50 times what would be expected from the resistive relaxation time; the evidence suggests that such high values ofx are due to small-angle scattering by imperfections, though they may also be due partly to phase smearing effects not connected with collision broadening. The most significant results come from studies of the increases ofx due to controlled additions of small amount of impurity. These increases are generally of much the same order of magnitude as would be expected from the increase or residual resistance, though detailed correlation with resistivity is hardly possible where thex measurements refer to a small part of a complicated Fermi surface. Recent results on impurities in the noble metals are beginning to give some indication of the anisotropy of scattering and because of the relative simplicity of the Fermi surface, a more detailed correlation with resistivity is possible. Particularly interesting anomalous behaviour is obtained for transition metal impurities which give rise to the Kondo effect. The possibility of studying phonon scattering through its effect onx is briefly discussed.     

De Haas-van Alphen effect in rare-earth hexaborides (RE=Pr,Nd, Gd)

The de Haas-van Alphen (dHvA) effect has been measured for antiferromagnetic PrB₆, NdB₆, and GdB₆. The dHvA data of PrB₆ and NdB₆ show paramagnetic Fermi surfaces which arise from magnetic breakdown through the small antiferromagnetic gaps in high fields very similar to those of LaB₆. In contrast, the antiferromagnetic Fermi surfaces which arise from new magnetic Brillouin zone boundaries introduced by the magnetic order seem to be very different in PrB₆ and NdB₆, respectively. In GdB₆ dHvA oscillations could be observed for the first time. In all three compounds magnetic phase transitions have been observed in the dHvA measurements in the field range of 10–12 T.Dedicated to Professor Hund on the occasion of his 95th birthday     

The de Haas-van Alphen effect and magnetic impurities

The de Haas-van Alphen (dHvA) effect in alloys containing magnetic impurities is a good tool to investigate the Kondo effect. We discuss first differences between the dHvA experiment for magnetic impurities and for nonmagnetic impurities. Then a review is made on the extent to which experimental data can be interpreted theoretically. The main part is devoted to theoretical analysis of Cu-based alloys, for which systematic data are available.     

Observation of the De Haas-van Alphen effect in an ln3 Yb powder

De Haas-van Alphen oscillations have been observed in the magnetization of a power sample of ln₃ Yb and are ascribed to a small spherical part of the Fermi surface.     

De Haas-van Alphen studies of conduction electron scattering in dilute alloys of copper

Measurements of the Haas-van Alphen Dingle temperatures per atomic percent solute have been obtained for seven different cyclotron orbits in dilute alloys of nickel, germanium and gold in copper. The measured values have been inverted using a Fourier series representation for τ _k ^?1 to determine the variation of the local scattering rate over the Fermi surface for each species of solute.     

Berry phase and de Haas-van Alphen effect in LaRhIn5

We explain the experimental data on the magnetization of LaRhIn5 recently published by Goodrich et al. [Phys. Rev. Lett. 89, 026401 (2002)]]. We show that the magnetization of a small electron group associated with a band-contact line was detected in that Letter. These data provide the first observation of the Berry phase of electrons in metals via the de Haas-van Alphen effect.     

Influence of impurities on the de Haas-van Alphen effect

A general theory is given for the effects of impurities or other localized defects in metals on the amplitudes (“Dingle factor”) and the periods of the de Haas-van Alphen oscillations. Starting from the Green's function for the crystal with defects, after configuration averaging a simple expression for the spectral density and the level broadening is obtained, expressed in terms of the transition matrix for a single defect. The density of states leading to the de Haas-van Alphen oscillations is gained by summing the spectral density over the electron states in the presence of the magnetic field. Using the transition matrices obtained earlier, the changes of the oscillations may be calculated for general localized defects and Fermi surfaces. A previous paper by Brailsford on the same topic is critically discussed.     

de Haas-van Alphen effect in single crystal MgB2

We report observations of quantum oscillations in single crystals of the high temperature superconductor MgB2. Three de Haas-van Alphen frequencies are clearly resolved. Comparison with band structure calculations strongly suggests that two of these come from a single warped Fermi surface tube along the c direction, and that the third arises from cylindrical sections of an in-plane honeycomb network. The measured values of the effective mass range from (0.44-0.68)m(e). By comparing these to calculated band masses, we find that the electron-phonon coupling strength lambda is a factor of approximately 3 larger for the c-axis tube orbits than for the in-plane network orbit, in accord with recent microscopic calculations.