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.     

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.     

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.     

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)     

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.     

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.     

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.     

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.     

The influence of the chemical potential oscillations on the de Haas-van Alphen effect in quasi-two-dimensional compounds

The de Haas-van Alphen effect in quasi-two-dimensional metals is studied at arbitrary parameters. Oscillations of the chemical potential can substantially change the temperature dependence of harmonic amplitudes that is commonly used to determine the effective electron mass. The processing of the experimental data using the standard Lifshitz-Kosevich formula can therefore lead to substantial errors even in the strong harmonic damping limit. This can explain the difference between the effective electron masses determined from the de Haas-van Alphen effect and the cyclotron resonance measurements. The oscillations of the chemical potential and the deviations from the Lifshitz-Kosevich formula depend on the reservoir density of states that exists in organic metals due to open sheets of the Fermi surface. This dependence can be used to determine the density of electron states on open sheets of the Fermi surface. We present analytical results of the calculations of harmonic amplitudes in some limiting cases that show the importance of the chemical potential oscillations. We also describe a simple algorithm for a numerical calculation of the harmonic amplitudes for arbitrary reservoir density of states, arbitrary warping, spin-splitting, temperature, and Dingle temperature.     

The de Haas-van Alphen effect of graphite-arsenic pentafluoride interacalation compounds

The de Haas-van Alphen (dHvA) effect in four different samples of graphite-arsenic pentafluoride (AsF₅) intercalation compounds is studied. Each sample with different stage number exhibits different series of dHvA periods. The observed dHvA periods are compared with a model calculation based on the graphite rigid band and supplemented with band folding due to the c-axis superlattice structure of intercalation compounds. From the comparison, the charge transfer from the intercalant to graphite band is estimated to be between 0.2 and 0.3 holes per AsF₅ molecule. It is also found that the charge transfer rate is slightly dependent on the stage number and is smaller for lower stage compounds.     

Observation of the de Haas-van Alphen effect in WC

We report first observation of the de Haas-van Alphen (dHvA) effect in hexagonal WC. Observed dHvA frequencies range from the order of 10⁶ to 10⁷G. The carrier concentration estimated from the dHvA frequencies is the order of 0.1 per unit cell. The semimetallic nature of WC is discussed on the basis of the experimental data.     

Theory of the de Haas-van Alphen effect in doped semiconductors

The field dependence of the magnetization in doped semiconductors of the type InSb, InAs, GaAs, etc. is studied in high magnetic fields. The standard theory of the de Haas-van Alphen effect, mostly applicable to metals, is modified to include the long-range fluctuations of charge carriers. The experimental investigation of this effect can shed light on some open questions in semiconductor physics, e.g., the problem of tails in the electronic density of states. It is shown that in such systems the mean magnetization is sensitive to magnetic interactions. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 3, 181–186 (10 February 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

de Haas-van Alphen effect and the Fermi surface of PrNi5

The Fermi surface of PrNi₅ has been studied by the measurements of the de Haas-van Alphen (dHvA) effect at temperatures between 0.3 and in magnetic fields up to 12 T. Two dHvA frequencies have been obtained. The electronic structure of PrNi₅ was calculated using the full potential linearized augmented plane wave method. Five sheets of the Fermi surface and the multiple extremal cross sections were determined. First and second sheet have a hole-like structure. The agreement between theory and experiment is obtained by a small downward shift ( 0.1 eV) of the Fermi energy which is probably due to an underestimation of the role of 4 f electrons. Received 9 May 2000 and Received in final form 20 September 2000     

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.     

Dephasing calculations of de Haas-van Alphen scattering

A review and assessment of existing dephasing calculations is given.     

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.     

Magnetic domains in non-ferromagnetic metals: The non-linear de Haas-van Alphen effect

This review is devoted to an exposition of the principles of the physics of magnetic domains in non-ferromagnetic metals and diamagnetic phase transitions, which lead to the formation of the so-called Condon domains during magnetic oscillations in a three-dimensional electron gas. One of the goals of the review is to provide a deeper insight into the nature of this instability of the electron gas in normal metals and improve the understanding of this type of non-spin magnetism. We discuss theoretical aspects of the physics underlying magnetic ordering of conduction electrons in bulk metals and in thin films, and describe the behaviour of the susceptibility, thermal expansion, specific heat, compressibility, sound velocity, magnetic induction bifurcation, the order parameter, domain formation, wetting of domain walls, nucleation and kinetics of diamagnetic phase transitions. In the vicinity of diamagnetic phase transitions the results obtained coincide with those following from the Landau theory of phase transitions. The existence of the critical sample size for the diamagnetic phase transition in thin films is considered. We place special emphasis on the problem of the order of diamagnetic phase transitions. The survey is partly motivated as complementary to the recent review by G. Solt and V. Egorov describing the experimental situation in the field. Contents PAGE 1. Introduction 386 2. Diamagnetic phase transitions and Condon domains 390 2.1. Shoenberg's and Condon's consideration of the phenomena 390 2.2. Phase diagrams for one de Haas-van Alphen cycle 395 3. Critical phenomena at second-order diamagnetic phase transitions in three-dimensional metals 397 3.1. Introduction 397 3.2. Order parameter and susceptibility 397 3.3. Specific heat jump 403 3.4. Phase diagrams 407 3.5. Finite-size effects 410 3.6. Compressibility, thermal expansion and sound velocity 414 4. Condon domains and resonance methods of their investigation 417 4.1. Introduction 417 4.2. Nuclear magnetic resonance and Condon domains 418 4.3. Muon spin resonance spectroscopy and Condon domains 420 4.4. Critical exponents at diamagnetic phase transitions in silver and beryllium 426 4.5. Helicon resonance and Condon domains 428 4.6. Critical dynamics of the diamagnetic phase transition in aluminium 430 5. First-order diamagnetic phase transitions 431 5.1. Introduction 431 5.2. Domain formation 433 5.3. Kinetics 436 5.4. Wetting 441 5.5. Nucleation 442 5.6. Order of diamagnetic phase transitions 444 5.7. Hysteresis and Condon domains 445 6. Summary 446 7. Some open issues 448 Acknowledgements 450 References 451