Low-field Hall Coefficient Research Articles

Numerical approaches for calculating the low-field dc Hall coefficient of the doped Hubbard model

Using determinant Quantum Monte Carlo, we compare three methods of evaluating the dc Hall coefficient $R_H$ of the Hubbard model: the direct measurement of the off-diagonal current-current correlator $\chi_{xy}$ in a system coupled to a finite magnetic field (FF), $\chi_{xy}^{\text{FF}}$; the three-current linear response to an infinitesimal field as measured in the zero-field (ZF) Hubbard Hamiltonian, $\chi_{xy}^{\text{ZF}}$; and the leading order of the recurrent expansion $R_H^{(0)}$ in terms of thermodynamic susceptibilities. The two quantities $\chi_{xy}^{\text{FF}}$ and $\chi_{xy}^{\text{ZF}}$ can be compared directly in imaginary time. Proxies for $R_H$ constructed from the three-current correlator $\chi_{xy}^{\text{ZF}}$ can be determined under different simplifying assumptions and compared with $R_H^{(0)}$. We find these different quantities to be consistent with one another, validating previous conclusions about the close correspondence between Fermi surface topology and the sign of $R_H$, even for strongly correlated systems. These various quantities also provide a useful set of numerical tools for testing theoretical predictions about the full behavior of the Hall conductivity for strong correlations.

Electrostatic tuning of magnetism at the conducting (111) (La0.3Sr0.7)(Al0.65Ta0.35)/SrTiO3 interface

We present measurements of the low temperature electrical transport properties of the two dimensional carrier gas that forms at the interface of (111) (La0.3Sr0.7)(Al0.65Ta0.35)/SrTiO3 as a function of applied back gate voltage, Vg. As is found in (111) LaAlO3/SrTiO3 interfaces, the low-field Hall coefficient is electron-like but shows a sharp reduction in magnitude below V g ∼ 20 V, indicating the presence of hole-like carriers in the system. This same value of Vg correlates approximately with the gate voltage below which the magnetoresistance evolves from nonhysteretic to hysteretic behavior at millikelvin temperatures, signaling the onset of magnetic order in the system. We believe our results can provide insight into the mechanism of magnetism in SrTiO3 based systems.

On the low-field Hall coefficient of graphite

We have measured the temperature and magnetic field dependence of the Hall coefficient (RH) in three, several micrometer long multigraphene samples of thickness between ∼9 to ∼30 nm in the temperature range 0.1 to 200 K and up to 0.2 T field. The temperature dependence of the longitudinal resistance of two of the samples indicates the contribution from embedded interfaces running parallel to the graphene layers. At low enough temperatures and fields RH is positive in all samples, showing a crossover to negative values at high enough fields and/or temperatures in samples with interfaces contribution. The overall results are compatible with the reported superconducting behavior of embedded interfaces in the graphite structure and indicate that the negative low magnetic field Hall coefficient is not intrinsic of the ideal graphite structure.

Temperature-dependent transport in a sixfold degenerate two-dimensional electron system on a H-Si(111) surface

Low-field magnetotransport measurements on a high-mobility $(\ensuremath{\mu}=110,000\text{ }{\text{cm}}^{2}/\text{Vs})$ two-dimensional electron system on a H-terminated Si(111) surface reveal a sixfold valley degeneracy with a valley splitting $\ensuremath{\le}0.1\text{ }\text{K}$. The zero-field resistivity ${\ensuremath{\rho}}_{xx}$ displays strong temperature dependence for $0.07\ensuremath{\le}T\ensuremath{\le}25\text{ }\text{K}$ as predicted for a system with high degeneracy and large mass. We present a method for using the low-field Hall coefficient to probe intervalley momentum transfer (valley drag). The relaxation rate is consistent with Fermi-liquid theory but a small residual drag as $T\ensuremath{\rightarrow}0$ remains unexplained.

Spectral and Fermi surface properties from Wannier interpolation

We present an efficient first-principles approach for calculating Fermi surface averages and spectral properties of solids, and use it to compute the low-field Hall coefficient of several cubic metals and the magnetic circular dichroism of iron. The first step is to perform a conventional first-principles calculation and store the low-lying Bloch functions evaluated on a uniform grid of k-points in the Brillouin zone. We then map those states onto a set of maximally-localized Wannier functions, and evaluate the matrix elements of the Hamiltonian and the other needed operators between the Wannier orbitals, thus setting up an ``exact tight-binding model.'' In this compact representation the k-space quantities are evaluated inexpensively using a generalized Slater-Koster interpolation. Because of the strong localization of the Wannier orbitals in real space, the smoothness and accuracy of the k-space interpolation increases rapidly with the number of grid points originally used to construct the Wannier functions. This allows k-space integrals to be performed with ab-initio accuracy at low cost. In the Wannier representation, band gradients, effective masses, and other k-derivatives needed for transport and optical coefficients can be evaluated analytically, producing numerically stable results even at band crossings and near weak avoided crossings.

The Deviation from Matthiessen's Rule at 4.2 K in Dilute Copper-Gold-Germanium Alloys

The deviation from Matthiessen's rule (DMR) of dilute copper-gold-germanium alloys was measured at 4.2, 77 and 273 K. The low-field Hall coefficient of binary Cu-Au and Cu-Ge alloys was also measured at 4.2 K to determine anisotropy parameters for the explanation of the DMR in the ternary alloys. In order to control the shape factor of the ternary samples the germanium content was brought into binary Cu-Au samples by vapour deposition and diffusion annealing. The limitation of the usual two-group model for the investigated alloys is shown and a more accurate three-group model is presented. Especially the DMR at 4.2 K of the ternary samples in the range 20-30 nΩ cm (as well as the DMR at 273 K) can be substantiated by the low-field Hall coefficient and by the anisotropy of scattering rates obtained from the de Haas-van Alphen effect for the binary alloys.

The Deviation from Matthiessen's Rule and Electrical Dislocation Density Measurement in Dilute Cu-Au Alloys

The method of electrical dislocation density measurement, which was successful in plastically deformed pure noble metals, is applied for the first time to dilute alloys, and the parameters for the electrical dislocation density measurement, i.e. the temperature dependence of the deviation from Matthiessen's rule and of the low-field Hall coefficient were investigated in Cu–Au alloys with 0.075 and 0.3 at% gold. The results for the dislocation density, which rely on the modelling of the true dislocation resistivity by means of the two-group model are especially satisfactory for the 0.075 at% alloy. Additionally the dislocation density was checked by X-ray Bragg profile analysis. The comparison of the latter method with the electrical method shows that small dislocation loops originating from the agglomeration of deformation induced vacancies are part of the total dislocation density.

Resistivity and Hall effect at high temperatures in La0.67Ca0.33MnO3

The resistivity tensors of La0.67Ca0.33MnO3 films were investigated at temperatures from the Curie temperature up to 600 K in magnetic fields up to 20 T. The diagonal transport is described by hopping of a small spin polaron cluster of 4 ions to nearest-neighbor spins. A spin-dependent activation energy and a mean field approximation for the magnetization of clustered polaron spins and unclustered Mn ion spins allowed the description of ρ(B,T) with a minimum of free parameters. The electron-like low field Hall coefficient showed a thermally activated behavior with an activation energy higher than that extracted from diagonal data.

Low-field Hall coefficient of Al-4d dilute alloys: The role of the anisotropic impurity scattering

Abstract The role of the anisotropic impurity scattering in the determination of the low-field Hall coefficient of Al-4d dilute alloys is investigated by means of systematic theoretical calculations, as well as experimental measurements for AlZr and AlMo. The theoretical results, obtained without using any adjustable parameter, are in excellent agreement with the experimental data and a consistent interpretation of the systematic variation of the low-field Hall coefficient for aluminium-based dilute alloys with transition-metal impurities is given.

Two-channel DC-SQUID picovoltmeter for the measurement of low-field Hall coefficient and electrical resistance from 4.2 to 100 K

A two-channel DC-SQUID voltmeter developed for the measurement of low-field Hall coefficient and electrical resistance of high-purity copper single crystals between 4.2 and 100 K is described. The noise is 1.8 pVHz −1/2 at 4.2 K and increases to 12 pVHz −1/2 at 100 K. A sample current up to 2.5 Å and a magnetic induction up to 60 mT can be applied.

Magnetic domain size effect on resistivity and Hall effect of amorphous Fe83−xZr7B10Mx (M=Ni, Nb) alloys

Studies of effective permeability, core loss and saturation magnetostriction of Fe83−xZr7B10Mx (M=Ni, Nb) alloys revealed that the domain width is smallest around x=0.10. We measured the resistivity and low field Hall coefficients of these alloys and found that the maxima of resistivity and Hall coefficients occurred roughly at the same concentrations. Larger surface area of smaller domains is considered the reason.

Electronic properties of TiSi2 single crystals at low temperatures.

We report measurements of Hall effect, transverse magnetoresistance, and specific heat on high-quality ${\mathrm{TiSi}}_{2}$ (C54 phase) single crystals at low temperatures. We used crystals with low residual resistivity (typically ${\mathrm{\ensuremath{\rho}}}_{4.2\phantom{\rule{0ex}{0ex}}\mathrm{K}}$=0.15 \ensuremath{\mu}\ensuremath{\Omega} cm) and magnetic fields (B) up to 20 T. These facts allowed us to study the electronic properties from the low (${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$\ensuremath{\tau}\ensuremath{\ll}1) to the high field regime (${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$\ensuremath{\tau}\ensuremath{\gtrsim}1, ${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$=eB/m* being the cyclotron frequency and \ensuremath{\tau} the electron relaxation time) as a function of magnetic-field strength and temperature. The low field Hall coefficient ${\mathit{R}}_{\mathit{H}}$ is negative, almost constant ${\mathit{R}}_{\mathit{H}}$=-(0.5\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ ${\mathrm{m}}^{3}$/C between 100 and 300 K and it changes sign at \ensuremath{\sim}30 K. The angular dependence of magnetoresistance shows either minima or maxima when the magnetic field is parallel to the principal crystallographic axes. These structures are, however, less pronounced than in other silicides, such as ${\mathrm{PdSi}}_{2}$ and ${\mathrm{NbSi}}_{2}$, and this suggests only a weak anisotropy of the ${\mathrm{TiSi}}_{2}$ Fermi surface. The galvanomagnetic properties behave consistently with band-structure calculations of Mattheiss and Hensel [Phys. Rev. B 39, 7754 (1989)] who found that ${\mathrm{TiSi}}_{2}$ is a compensated metal with only closed orbits for the Fermi electrons. Using a simple two-band model we estimated, from the low field magnetoresistance, carrier density ${\mathit{n}}_{\mathit{e}}$=${\mathit{n}}_{\mathit{h}}$=(0.45--0.52)\ifmmode\times\else\texttimes\fi{}${10}^{22}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ assuming equal concentration of electrons and holes. Low temperatures (1.6T22 K) specific-heat (${\mathit{C}}_{\mathit{p}}$) measurements fit a linear ${\mathit{C}}_{\mathit{p}}$/T=\ensuremath{\gamma}+\ensuremath{\beta}${\mathit{T}}^{2}$ dependence, with \ensuremath{\gamma}=3.35\ifmmode\pm\else\textpm\fi{}0.05 mJ/${\mathrm{K}}^{2}$ mol and \ensuremath{\beta}=0.0201\ifmmode\pm\else\textpm\fi{}0.0005 mJ/${\mathrm{K}}^{4}$ mol. From these parameters we estimated the Debye temperature ${\mathrm{\ensuremath{\Theta}}}_{\mathit{D}}$=662\ifmmode\pm\else\textpm\fi{}4 K and the renormalized electronic density of states at the Fermi surface N(${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{F}}$)(1+\ensuremath{\lambda})=2.85 states/eV cell. \textcopyright{} 1996 The American Physical Society.

Low field Hall coefficient measurements of graphite ferric chloride intercalation compounds

Extensive investigatiofis have been carried out on various graphite intercalation compounds (GICs), but the nature of the microscopic mechanisms have not been fully understood. The transport properties of these compounds show drastic changes from the parent graphite [1] and require more theoretical investigations. As an extension of our studies on graphite ferric chloride intercalation compounds (GFeC13) of both pure and mixed stages, we report our measurements of the Hall coefficient at low magnetic fields. The graphite ferric chloride intercalation compounds of pure and mixed stages were prepared by the conventional two-zone vapour transport technique with the graphite zone at higher temperature than the intercalant zone. The temperature conditions used for the synthesis are given in Table I. This particular system was found to be environmentally stable. The samples were characterized initially by the increase in weight percentage over that of initial graphite. X-ray characterization was carried out using CoK« radiation of wavelength 0.17902 nm. The stages were identified from the (0 0 1) reflections of the X-ray diffractogram. According to the classical model of staging [2], the c axis repeat distance Ic is related to the stage number n by the simple relation:

Application of high performance DC SQUIDs in precision measurement technique

In this review the performance of a DC SQUID system with Nb-NbO/sub x/-Pb/In/Au window-type Josephson junctions is described. The SQUIDs and the SQUID control units were developed for universal applications in precision measurement technique. Under optimum conditions a flux noise level of 2/spl times/10/sup -6/ /spl Phi//sub 0///spl radic/Hz was achieved corresponding to an energy resolution of 3/spl times/10/sup -31/ J/Hz. The contribution gives the design of the DC SQUID device and summarizes recent results of its application in precision measurement technique. The applications include a cryogenic current comparator for non-destructive measurement of the beam intensity produced in a particle accelerator, a high-sensitive SQUID voltmeter for investigations of the low-field Hall coefficient of high purity metals, the upgrade of a multichannel RF SQUID neuromagnetometer for biomagnetic research, and a planned high-precision experiment in fundamental physics.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Low-field Hall coefficient of alpha -phase CuAl and dilute magnetic CuAl(Fe) alloys.

The low-field Hall coefficient of a number of dilute \ensuremath{\alpha}-phase CuAl alloys and CuAl containing 110-ppm Fe has been measured at 4.2 K as a function of the magnetic field. The difference in the values of the Hall coefficient between the two systems has been interpreted as arising from different anisotropies of the relaxation times of the host conduction electrons. By use of a two-group model for the conduction electrons of copper, it has been found that the relaxation time ratios ${\mathrm{\ensuremath{\tau}}}_{\mathit{B}}$/${\mathrm{\ensuremath{\tau}}}_{\mathit{N}}$ for the CuAl and CuAl 110-ppm Fe systems amount to 0.63 and 0.82, respectively. The difference in ${\mathrm{\ensuremath{\tau}}}_{\mathit{B}}$/${\mathrm{\ensuremath{\tau}}}_{\mathit{N}}$ between these two alloys has been attributed to the scattering of the conduction electrons by the localized magnetic moments of the Fe atoms.

The influence of δ' precipitates on the electrical resistivity and low-field Hall coefficient of AI-Li alloys

Abstract Measurements of the electrical resistivity in the temperature range 4.2–300 K and of the Hall coefficient at 4.2 K have been performed on an Al-Li alloy of 8 at.% Li concentration. Information on the microstructure of aged alloy were obtained from transmission electron microscopy. As the mean size of the δ' precipitates increases, the electrical resistivity at 4.2 K decreases, while the low-field Hall coefficient increases with a tendency to saturate. This behaviour can be explained qualitatively considering the anisotropic scattering of the electrons both on the δ' precipitates and the randomly distributed Li atoms in the matrix. The temperature dependence of the phonon resistivity of the aged alloy varies as T n, where 0.5< n < 3.5.

Calculation of the residual resistivity and the low-field Hall coefficient of 3d and 4sp impurities in aluminum.

We report systematic calculations of the residual resistivity and the low-field Hall coefficient of Al-based dilute alloys with 3d and 4sp impurities, by self-consistently solving the linearized Boltzmann equation. We employ the on-Fermi-sphere approximation, which allows us to combine the full anisotropy of the aluminum Fermi surface, obtained by the four-orthogonal-plane-wave method, with the phase shifts associated with isotropic impurity scattering, evaluated by self-consistent local-density-functional impurity-in-jellium calculations. Our results show that the anisotropic scattering increases the residual resistivity, thus obtaining better agreement with the experiment. Moreover, a consistent interpretation of the observed trends of the low-field Hall coefficient is presented.

Properties of BaPb1-xBixO3 as Observed in Single-Crystal Thin Films

The resistivity, low-field Hall coefficient, optical transmission, reflectivity, and upper critical field have been measured for BaPb1-xBixO3 single-crystal thin films as a function of Bi content x. It is found that the semiconductive temperature dependence of resistivity, which evolves as x increases from 0.25, is intrinsic to the BaPb1-xBixO3 system. When x exceeds 0.3, the resistivity abruptly increases and the superconductivity disappears. These changes are accompanied by a change in the sign of the Hall coefficient. Based on these experimental results, a systematic change of the electronic structure of the BaPb1-xBixO3 system is discussed. Furthermore, various physical properties of the BaPb1-xBixO3 system are also derived based on a simple assumption.

Strong anisotropic electron-impurity scattering in dilute AlLi alloys.

The Hall coefficient and the transverse magnetoresistance of dilute AlLi alloys at 4.2 K is reported. A large positive low-field Hall coefficient ${\mathit{R}}_{\mathit{H}}^{0}$ is found, in comparison to the free-electron Hall coefficient-value ${\mathit{R}}_{\mathrm{FE}}$ of aluminum. The cause of the large ${\mathit{R}}_{\mathit{H}}^{0}$ can be attributed to the strong anisotropic scattering of the electrons in the third zone of Fermi surface on the substitutional Li impurities.

Hall coefficient of cubic metals.

A systematic study of the low-field Hall coefficient ${\mathit{R}}_{\mathit{H}}$ of 23 cubic metals is done using tabulated Slater-Koster parameters for the band structure and a tetrahedron method to calculate the Fermi-surface integrals. In the approximation of an isotropic relaxation time, the Hall coefficient depends only on the Fermi-surface topology. The effect of the band structure is reflected in deviations of ${\mathit{R}}_{\mathit{H}}$ from the free-electron values -1/ne. In favorable cases, our calculations agree to \ensuremath{\approxeq}\ifmmode\pm\else\textpm\fi{}10% with experimental data. Some of the deviations can be traced back to inaccurate band structures, e.g., in Cs or to rapidly changing ${\mathit{R}}_{\mathit{H}}$ with ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{F}}$ leading to problems with convergence, e.g., in Pt. Discrepancies with experiment show the need for an anisotropic relaxation time, especially in Pd where small regions of high curvature dominate the Hall coefficient and in Al where two bands cross the Fermi surface. The similarity in the band structures of Rh, Pd, and Ag encourages the use of a rigid-band model, which agrees qualitatively with the experimental Hall coefficients for the alloys Rh-Pd and Pd-Ag.