Lifshitz-Kosevich Formula Research Articles

Anisotropic magnetotransport and extremely large magnetoresistance in NbAs2 single crystals

We report the extremely large magnetoresistance and anisotropic magnetoresistance in a non-magnetic semimetallic NbAs2 single crystal. Unsaturated transverse XMR with quadratic field dependence has been observed to be ~3 × 105 % at 2 K and 15 T. Up to 12.5 K, clear Shubnikov de Haas (SdH) quantum oscillations were observed from which two distinct Fermi pockets were identified. The corresponding quantum electronic parameters such as effective cyclotron mass and Dingle temperature were obtained using Lifshitz-Kosevich formula. From the field dependent Hall resistivity at 2 K, carrier concentrations ne(nh) = 6.7691 (6.4352) × 1025 m−3 and mobilities μe (μh) = 5.6676 (7.6947) m2 V−1 s−1 for electrons (e) and holes (h) were extracted using semiclassical two-band model fitting. We observed large anisotropic magnetoresistance about 84%, 75%, and 12% at 0.75 T and 6 K for three different orientations γ, θ and ϕ, respectively, similar to that in several topological semimetallic systems. Magnetic properties of NbAs2 are similar to the case of graphite, without any phase transition in the temperature range from 5 K to 300 K.

Modifications of the Lifshitz-Kosevich formula in two-dimensional Dirac systems

Starting from the Luttinger-Ward functional we derive an expression for the oscillatory part of the grand potential of a two dimensional Dirac system in a magnetic field. We perform the computation for the clean and the disordered system, and we study the effect of electron-electron interactions on the oscillations. Unlike in the two dimensional electron gas (2DEG), a finite temperature and impurity scattering also affects the oscillation frequency. Furthermore, we find that in graphene, compared to the 2DEG, additional interaction induced damping effects occur: to two-loop order electron-electron interactions do lead to an additional damping factor in the amplitude of the Lifshitz-Kosevich-formula.

Large magnetoresistance and Fermi surface study of Sb2Se2Te single crystal

We have studied the magnetotransport properties of a Sb2Se2Te single crystal. Magnetoresistance (MR) is maximum when the magnetic field is perpendicular to the sample surface and reaches a value of 1100% at B = 31 T with no sign of saturation. MR shows Shubnikov de Haas (SdH) oscillations above B = 15 T. The frequency spectrum of SdH oscillations consists of three distinct peaks at α = 32 T, β = 80 T, and γ = 117 T indicating the presence of three Fermi surface pockets. Among these frequencies, β is the prominent peak in the frequency spectrum of SdH oscillations measured at different tilt angles of the sample with respect to the magnetic field. From the angle dependence β and Berry phase calculations, we have confirmed the trivial topology of the β-pocket. The cyclotron masses of charge carriers, obtained by using the Lifshitz–Kosevich formula, are found to be mβ*=0.16mo and mγ*=0.63mo for the β and γ bands, respectively. The Large MR of Sb2Se2Te is suitable for utilization in electronic instruments such as computer hard discs, high field magnetic sensors, and memory devices.

Calculation of magnetic properties of metals by means of the magnetic-field-containing relativistic tight-binding approximation method

Magnetic properties of metals are investigated through electronic structure calculations based on the recently proposed magnetic-field-containing relativistic tight-binding approximation (MFRTB) method [Phys. Rev. B 91, 075122 (2015)]. It is found that electronic energy bands for a metal immersed in a uniform magnetic field have a cluster structure in which multiple energy bands lie within a small energy width. Each cluster corresponds to an energy level that is derived on the basis of the semiclassical approximation. While the cluster is responsible for the de Haas--van Alphen (dHvA) oscillations, constituent energy bands of the cluster cause additional oscillation peaks of the magnetization that are not explained by the conventional Lifshitz-Kosevich formula. Also, the energy width of the cluster leads to the reduction of the amplitude of the dHvA oscillations, which can be observed as the pseudo Dingle temperature and/or the overestimation of the curvature of the Fermi surface.

Quantum Hall conductance and de Haas–van Alphen oscillation in a tight-binding model with electron and hole pockets for(TMTSF)2NO3

Quantized Hall conductance and de Haas van Alphen (dHvA) oscillation are studied theoretically in the tight-binding model for (TMTSF)$_2$NO$_3$, in which there are small pockets of electron and hole due to the periodic potentials of anion ordering in the $a$-direction. The magnetic field is treated by hoppings as complex numbers due to the phase caused by the vector potential, i.e. Peierls substitution. In realistic values of parameters and the magnetic field, the energy as a function of a magnetic field (Hofstadter butterfly diagram) is obtained. It is shown that energy levels are broadened and the gaps are closed or almost closed periodically as a function of the inverse magnetic field, which are not seen in a semi-classical theory of the magnetic breakdown. Hall conductance is quantized with an integer obtained by Diophantine equation when the chemical potential lies in an energy gap. When electrons or holes are doped in this system, Hall conductance is quantized in some regions of a magnetic field but it is not quantized in other regions of a magnetic field due to the broadening of the Landau levels. The amplitude of the dHvA oscillation at zero temperature decreases as the magnetic field increases, while it is constant in the semi-classical Lifshitz Kosevich formula.

New insights on frequency combinations and ‘forbidden frequencies’ in the de Haas–van Alphen spectrum of κ-(ET)2Cu(SCN)2

de Haas–van Alphen oscillations of the organic metal κ-(ET)2Cu(SCN)2 have been measured up to 55 T at liquid helium temperatures. The Fermi surface of this charge transfer salt is a textbook example of a linear chain of orbits coupled by magnetic breakdown. Accordingly, the oscillation spectrum is composed of linear combinations of the frequencies linked to the α and magnetic breakdown-induced β orbits. The field and temperature dependence of all the observed Fourier components, in particular the ‘forbidden frequency’ which cannot correspond to a classical orbit, are quantitatively accounted for by analytical calculations based on a second order development of the free energy, i.e. beyond the first order Lifshitz–Kosevich formula.

π Berry phase and Zeeman splitting of Weyl semimetal TaP.

The recent breakthrough in the discovery of Weyl fermions in monopnictide semimetals provides opportunities to explore the exotic properties of relativistic fermions in condensed matter. The chiral anomaly-induced negative magnetoresistance and π Berry phase are two fundamental transport properties associated with the topological characteristics of Weyl semimetals. Since monopnictide semimetals are multiple-band systems, resolving clear Berry phase for each Fermi pocket remains a challenge. Here we report the determination of Berry phases of multiple Fermi pockets of Weyl semimetal TaP through high field quantum transport measurements. We show our TaP single crystal has the signatures of a Weyl state, including light effective quasiparticle masses, ultrahigh carrier mobility, as well as negative longitudinal magnetoresistance. Furthermore, we have generalized the Lifshitz-Kosevich formula for multiple-band Shubnikov-de Haas (SdH) oscillations and extracted the Berry phases of π for multiple Fermi pockets in TaP through the direct fits of the modified LK formula to the SdH oscillations. In high fields, we also probed signatures of Zeeman splitting, from which the Landé g-factor is extracted.

Non-Lifshitz–Kosevich field- and temperature-dependent amplitude of quantum oscillations in the quasi-two dimensional metal θ-(ET)4ZnBr4(C6H4Cl2)

According to band structure calculations, the Fermi surface of the quasi-two dimensional metal -(ET)4ZnBr4(C6H4Cl2) illustrates the linear chain of coupled orbits model. Accordingly, de Haas–van Alphen oscillations spectra recorded in pulsed magnetic field of up to 55 T evidence many Fourier components, the frequency of which are linear combinations of the frequencies relevant to the closed and the magnetic breakdown orbits. The field and temperature dependence of their amplitude are quantitatively accounted for by analytic calculations including, beyond the Lifshitz–Kosevich formula, second-order terms in damping factors due to the oscillation of the chemical potential as the magnetic field varies. Whereas these second-order terms are negligible for the orbits , and , they are solely responsible for the ‘forbidden orbit’ and its harmonic and have a significant influence on Fourier components such as and , yielding strongly non-Lifshitz–Kosevich behaviour in the latter case.

Calculation of magnetic oscillations via the magnetic-field-containing relativistic tight-binding approximation method: Revisiting the de Haas–van Alphen effect

The magnetic-field-containing relativistic tight-binding approximation (MFRTB) method [Phys. Rev. B 91, 075122 (2015)] is the first-principles calculation method for electronic structures of materials immersed in the magnetic field. In this paper, the MFRTB method is applied to the simple cubic lattice immersed in the magnetic field. The total energy and magnetization oscillate with the inverse of the magnitude of the magnetic field, which means that the de Haas--van Alphen oscillation is revisited directly through the MFRTB method. It is shown that the conventional Lifshitz-Kosevich (LK) formula is a good approximation to the results of the MFRTB method in the experimentally available magnetic field. Furthermore, the additional oscillation peaks of the magnetization are found especially in the high magnetic field, which cannot be explained by the LK formula.

How Are Heavy and Itinerant Electrons Born in a Dilute Kondo Alloy?

We report a continuous evolution of Fermi surface properties with temperature in a dilute Kondo alloy of Ce 0.02 La 0.98 Ru 2 Si 2 via measurements of the de Haas–van Alphen (dHvA) effect. The temperature variation of resistivity in this alloy exhibits a typical impurity Kondo behavior, i.e., the resistivity increases with decreasing temperature proportionally to -log T and becomes nearly constant below about 0.3 K. The Kondo temperature of this alloy is estimated to be about 1.3 K. The frequency of the dHvA oscillation from the main hole surface decreases with decreasing temperature implying that the hole surface shrinks with decreasing temperature. The temperature dependence of the frequency change is found to be similar to that of resistivity. The temperature dependence of this dHvA oscillation amplitude deviates largely from that expected from the Lifshitz–Kosevich formula conventionally employed to determine the effective mass from the temperature dependence. By assuming that the scattering of the co...

Spin splitting in graphene studied by means of tilted magnetic-field experiments

We have measured the spin splitting in single-layer and bilayer graphene by means of tilted magnetic field experiments. Applying the Lifshitz-Kosevich formula for the spin-induced decrease of the Shubnikov de Haas amplitudes with increasing tilt angle we directly determine the product between the carrier cyclotron mass m* and the effective g-factor g* as a function of the charge carrier concentration. Using the cyclotron mass for a single-layer and a bilayer graphene we find an enhanced g-factor g* = 2.7 \pm 0.2 for both systems.

Condon domain phase diagram for silver

We present the Condon domain phase diagram for a silver single crystal measured in magnetic fields up to 28T and temperatures down to 1.3K. A standard ac method with a pickup coil system is used at low frequency for measuring the de Haas-van Alphen effect (dHvA). The transition point from the state of homogeneous magnetization to the inhomogeneous Condon domain state (CDS) is defined as the point where a small irreversibility develops in the dHvA magnetization, as manifested by an extremely nonlinear response in the pickup voltage indicative of a threshold character. The third harmonic content in the ac response is used to determine with high precision the CDS phase boundary. The experimentally determined Condon domain phase diagram is in good agreement with the theoretical prediction calculated by the standard Lifshitz–Kosevich formula.

Generalized Lifshitz-Kosevich scaling at quantum criticality from the holographic correspondence

We characterize quantum oscillations in the magnetic susceptibility of a quantum critical non-Fermi liquid. The computation is performed in a strongly interacting regime using the nonperturbative holographic correspondence. The temperature dependence of the amplitude of the oscillations is shown to depend on a critical exponent nu. For general nu the temperature scaling is distinct from the textbook Lifshitz-Kosevich formula. At the `marginal' value nu = 1/2, the Lifshitz-Kosevich formula is recovered despite strong interactions. As a by-product of our analysis we present a formalism for computing the amplitude of quantum oscillations for general fermionic theories very efficiently.

Probing semiclassical magneto-oscillations in the low-field quantum Hall effect

The low-field quantum Hall effect is investigated on a two-dimensional electron system in an AlGaAs/GaAs heterostructure. Magneto-oscillations following the semiclassical Shubnikov-de Haas formula are observed even when the emergence of the mobility gap shows the importance of quantum localization effects. Moreover, the Lifshitz-Kosevich formula can survive as the oscillating amplitude becomes large enough for the deviation to the Dingle factor. The crossover from the semiclassical transport to the description of quantum diffusion is discussed. From our study, the difference between the mobility and cyclotron gaps indicates that some electron states away from the Landau-band tails can be responsible for the semiclassical behaviors under low-field Landau quantization.

De Haas–van Alphen Oscillations in the Underdoped High-Temperature SuperconductorYBa2Cu3O6.5

The de Haas-van Alphen effect was observed in the underdoped cuprate YBa2Cu3O6.5 via a torque technique in pulsed magnetic fields up to 59 T. Above a field of approximately 30 T the magnetization exhibits clear quantum oscillations with a single frequency of 540 T and a cyclotron mass of 1.76 times the free electron mass, in excellent agreement with previously observed Shubnikov-de Haas oscillations. The oscillations obey the standard Lifshitz-Kosevich formula of Fermi-liquid theory. This thermodynamic observation of quantum oscillations confirms the existence of a well-defined, closed, and coherent, Fermi surface in the pseudogap phase of cuprates.

High field measurements of the Condon domain phase diagram in silver

Condon domains form when the de Haas-van Alphen (dHvA) amplitude becomes large compared to the dHvA period, i.e. μ0∂M/∂B > 1, where M is the magnetization and B the induction. This equation defines the boundary between the homogeneous magnetization and the Condon domain state. The phase diagram in the (B, T) plane can be predicted using the Lifshitz-Kosevich formula. We present the Condon domain phase diagram for a silver single crystal measured in magnetic fields up to 28 T and temperatures Tdown to 1.3 K. A standard ac method with a pickup coil system is used at low frequency for the measurements of the de Haasvan Alphen (dHvA) e..ect. The transition point from the state of homogeneous magnetization to the inhomogeneous Condon domain state is found as the point where a small irreversibility in the dHvA magnetization arises, as manifested by an extremely nonlinear response in the pickup voltage showing threshold character. The experimental results are in good agreement with theoretical predictions based on the Lifshitz-Kosevich formula.

Study of rapid oscillations in (TMTSF) 2FSO 3 under pressure and under very high magnetic fields

(TMTSF) 2FSO 3 is very special in that its electric transport properties are described by electrons from two-dimensional Fermi surfaces (FS) whereas those in most other Bechgaard salts are intrinsically explained with electrons from weakly warped quasi-one- dimensional FS. Conventional Shubnikov-dc Haas oscillations, described with the Lifshitz-Kosevich formula, has been observed. In this study, we measured magnetoresistance along the least conducting direction ( c *) under pressures of up to 11 kbars and magnetic fields of up to 55 T, generated in a pulsed magnet, and found that the oscillations preserved two-dimensional nature to the highest measured field. There is no field-induced electronic transition. Pressure dependence and magnetic field dependence of parameters of oscillations are presented and discussed.

Estimation of the cyclotron mass from the de Haas–van Alphen oscillation in the two-dimensional and quasi-two-dimensional multiband systems

It is known that a cyclotron mass is obtained by fitting a temperature dependence of the Fourier harmonics of the de Haas--van Alphen oscillation to the temperature reduction factor in the Lifshitz-Kosevich (LK) formula in which the oscillation of the chemical potential is neglected. The LK formula, however, should be applied carefully in two-dimensional (2D) and quasi-two-dimensional (Q2D) systems at low temperatures, where the magnetic-field dependence of the chemical potential cannot be neglected. We compare the effective cyclotron mass, which is estimated by using the temperature reduction factor for the fixed chemical potential, with the cyclotron mass of the system. The cyclotron mass is fairly well obtained in 2D single-band systems when the density of states of the reservoir is negligible or much larger than the density of states of the 2D band. On the other hand, if the reservoir has the same order of the density of states as the 2D band, the effective cyclotron mass is shown to be estimated about 7% larger at low temperature and high field. In the 2D multiband systems the effective cyclotron mass for the heavier mass is underestimated about 9%, while the lighter effective cyclotron mass is obtained with very small errors.

Quasiparticle spectra of superconducting lattices

A quite general semiclassical theory of quasiparticles in the superconducting state will be developed using the language of modern semiclassics [M.C. Gutzwiller, Chaos in Classical and Quantum Mechanics, Springer-Verlag, 1990]. It will then be shown how this formulation of the problem can be used to derive a Lifshitz–Kosevich formula for the de Haas–van Alphen oscillations in the superconducting state. It will be argued that this formula implies oscillations with the same frequency as in the normal state but with reduced amplitudes. Experiments on the classic superconductor V 3Si will be discussed.

Quantum magneto-oscillations in a two-dimensional Fermi liquid

Quantum magneto-oscillations provide a powerful tool for quantifying Fermi-liquid parameters of metals. In particular, the quasiparticle effective mass and spin susceptibility are extracted from the experiment using the Lifshitz-Kosevich formula, derived under the assumption that the properties of the system in a nonzero magnetic field are determined uniquely by the zero-field Fermi-liquid state. This assumption is valid in three dimensions (3D) but, generally speaking, erroneous in 2D where the Lifshitz-Kosevich formula may be applied only if the oscillations are strongly damped by thermal smearing and disorder. In this work, the effects of interactions and disorder on the amplitude of magneto-oscillations in 2D are studied. It is found that the effective mass diverges logarithmically with decreasing temperature signaling a deviation from the Fermi-liquid behavior. It is also shown that the quasiparticle lifetime due to inelastic interactions does not enter the oscillation amplitude, although these interactions do renormalize the effective mass. This result provides a generalization of the Fowler-Prange theorem formulated originally for the electron-phonon interaction.