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 influence of many-body interactions on the de Haas-van Alphen effect

The de Haas-van Alphen (dHvA) effect, or Landau quantum oscillatory magnetization of metals, has been widely used to explore the single-particle aspects of electrons in metals with the aim of determining their Fermi surfaces. Its role in studying many-body effects in metals is less familiar, even though the influence of such interactions is well known. We present a general field-theoretic approach to this problem which shows that the paradigm for understanding the influence of many-body interactions in the dHvA effect should be shifted from the intuitively reasonable but potentially misleading arguments based on the electron self-energy on the real energy axis to an analysis of the self-energy along the imaginary energy axis. When viewed in this way, the dHvA effect assumes the role of a many-body self-energy filter in which the real part of the self-energy renormalizes the dHvA frequency while the imaginary part renormalizes independently the dHvA amplitude. We obtain a general theory for the dHvA effect in an interacting system which preserves the structure of the original non-interacting theory of Lifshitz and Kosevich. We then apply this extended Lifshitz-Kosevich theory to the analysis of several problems of interest, including electron-electron and electron-phonon interactions, heavy fermions and type II superconductors.     

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.     

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 oscillations with non-parabolic dispersions

de Haas-van Alphen oscillation spectrum of two-dimensional systems is studied for general power law energy dispersion, yielding a Fermi surface area of the form S(E) ∝ E ^α for a given energy E. The case α = 1 stands for the parabolic energy dispersion. It is demonstrated that the periodicity of the magnetic oscillations in inverse field can depend notably on the temperature. We evaluated analytically the Fourier spectrum of these oscillations to evidence the frequency shift and smearing of the main peak structure as the temperature increases.     

Anomalous de Haas-van Alphen oscillations in CeCoIn5

We present de Haas-van Alphen oscillation measurements showing a strong spin dependence of the quasiparticle mass enhancement in the heavy fermion superconductor CeCoIn5 at high magnetic fields. There is evidence that the Fermi-liquid temperature dependence of the oscillations, embodied in the Lifshitz-Kosevich equation, is breaking down on the most strongly renormalized Fermi surface sheets.     

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 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.     

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)     

Influence of magnetic impurities on the de Haas-van Alphen oscillations

Using a simple extension of Shiba's formula for the de Haas-van Alphen-oscillations, the influence of scattering by magnetic impurities is studied. Already for a classical spin model one obtains a minimum in the dHvA amplitudes as function of the magnetic-field, which is influenced by normal scattering. The change of this behavior for the Anderson model is studied within the Non-Crossing-Approximation, and raises questions for a comparison between experiment and theory.     

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.     

Magnetoquantum de Haas-van Alphen oscillations in spin-split two-dimensional Fermi liquid

Theory of magnetoquantum oscillations with spin-split structure in strongly anisotropic (two-dimensional (2D)) metal is developed in the formalism of level approach. Parametric method for exact calculation of oscillations wave forms and amplitudes, developed earlier for spin degenerate levels is generalized on a 2D electron system with spin-split levels. General results are proved: 1) proportionality relation between magnetization and chemical potential oscillations accounting for spin-split energy levels and magnetic field unperturbed levels (states of reservoir), 2) basic equation for chemical potential oscillations invariant to various models of 2D and 1D energy bands (intersecting or overlapping) and localized states. Equilibrium transfer of carriers between overlapping 2D and 1D bands, characterizing the band structure of organic quasi 2D metals, is considered. Transfer parameter, calculated in this model to be of the order of unity, confirms the fact that the wave form of oscillations in organic metals should be quasisymmetric up to ultralow temperature. Presented theory accounts for spin-split magnetization oscillations at magnetic field directions tilted relative to the anisotropic axis of a metal. Theoretical results are compared with available experimental data on organic quasi-2D metal α-(BEDT-TTF)₂KHg(SNC)₄ explaining the appearance of clear split structure under the kink magnetic field and absence above by the corresponding change in the electron g-factor rather than cyclotron mass. Received 20 December 2000 and Received in final form 13 July 2001     

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.     

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.     

Effect of the Fermi surface shape on the de Haas-van Alphen oscillations in layered conductors

In this paper, we theoretically analyze the effects of the Fermi surface (FS) shape on the magnetic oscillations in quantizing magnetic fields in quasi-two-dimensional layered conductors. The theory is developed based on a phenomenological model for the electron energy spectra introduced in the paper. The model enables various Fermi surface profiles to be taken into consideration; this gives it an advantage over the commonly used tight-binding approximation. It is shown that, when the FS curvature becomes zero at an effective cross-section with maximum/minimum cross-sectional area, this can significantly affect the amplitude, shape, and phase of the oscillations, as well as the field dependence of the amplitude. The text was submitted by the author in English.