Low-field Hall Coefficient Research Articles

Size effect on the low field hall coefficient of Cu and Al single crystals

The size effects of the Hall coefficient R H of very pure single crystals of Cu and Al are measured down to 3≈5 × 10 −4 T at 4.2K. The sign of R H of Cu samples (B // [110]) changes from negative to positive at 0.025T. R H of Al sample (B // [001]) becomes more negative than bulk sample in the low field region. It is suggested that such measurement can be used to obtain informations on some limited region of Fermi surface.

The true low field Hall coefficient of pure aluminium at low temperatures

A study has been made of the true low field Hall coefficient, RH, of four samples of pure aluminium between 4.2 and 77K. All samples exhibited a low-temperature maximum in the temperature range 7-10K and the three purest samples possessed a minimum between 25 and 30K. An analysis of the low-temperature results is given using a three group model. It is found that, despite the dominance of impurity scattering, the low-temperature maximum may be explained if the mean free paths due to phonon scattering of second-zone holes and third-zone electrons have different temperature dependences. The experimental results on the four samples are found to obey the theoretical prediction that a single function exists when ((RH-RH(T=0))/(RHmax-RH(T=0))) is plotted against (T/Tmax). The theory also enables the anisotropy of mean free paths for phonon scattering of the second-zone free electrons and the third-zone electrons to be deduced from the Hall results and is found to agree with that deduced from radio frequency size effect and surface Landau level experiments.

The electrical resistivity of dilute aluminium alloys

Electron-phonon mean free paths deduced from measurements of the low-field Hall coefficient of aluminium (see ibid., vol.10 p.2739, 1980) have been employed in a calculation of the temperature-dependent part of the electrical resistivity rho T of dilute Al alloys. The independent group model is capable of explaining the minimum observed in the rho T/T3 versus T variation of nominally pure Al.

The true low field Hall coefficient of copper and copper containing defects at low temperatures

The true low field Hall coefficients of various high purity copper samples and samples containing low density defects have been examined in a field of 0.0085 T over the temperature range 4.2-77K. The results on pure copper are compared with measurements made in a field of 0.5145 T. The Hall effect in copper and its dilute alloys can be analysed satisfactorily in terms of a two-group model and the band parameters obtained are able to account for the extremely large deviations from Matthiessen's rule observed in copper containing dislocations. The temperature dependence of the electron-phonon scattering anisotropy is deduced from the Hall results and found to be in good agreement with an earlier theoretical calculation.

Low-field Hall coefficientRH0of dilute Al-3dalloys at 4.2 K

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Low-field Hall coefficient in dilute copper-hydrogen alloys and in quenched copper

Low-field Hall coefficients have been measured in dilute ChH alloys and in copper containing vacancies in order to investigate the difference between the electron-scattering rates measured in electronic transport coefficients and by de Haas-van Alphen effect. For CuH the relaxation times have the same anisotropy but differ in magnitude by a factor 1.6. In quenched copper the lattice strain around a vacancy gives a substantial contribution to the scattering rates of the neck electrons. This conclusion is in agreement with de Haas-van Alphen data obtained on quenched gold.

Graphite intercalation compounds: A simple model of Fermi surface and transport properties

A parametrized model of the $\ensuremath{\pi}$ bands of $n$-layer films of graphite is developed for the purpose of studying the Fermi-level properties of graphite intercalation compounds. Specifically, the charge transfer, the density of states, and the conductivity tensor as a function of magnetic field are considered. The first two quantities are proportional to the de Haas-van Alphen frequency and cyclotron mass, respectively. A numerical study is carried out for a single layer of graphite as a function of excess charge. It is shown that the anisotropic dispersion of the energy bands causes unusual galvanomagnetic behavior at small magnetic fields, such as a nonzero magnetoresistance mobility for moderate intercalant concentrations and also a change in the sign of the low-field Hall coefficient at high intercalant concentrations.

The low-temperature Hall coefficient of potassium

Measurements have been made of the Hall coefficient of 'pure' potassium over the range of temperature 4.2-16k for fields between 0.01 and 0.5 T. The predicted peak in the magnitude of the low-field Hall coefficient near 6K is visible, but it is an order of magnitude smaller than expected. A new feature is that the low-field coefficient also exhibits a minimum in its magnitude near 12K, and this is replaced by a maximum at fields above 0.25 T. The experiments show that the currently available theories of the Hall coefficient are inadequate.

Electrical and thermal conductivities of metals in weak magnetic fields

An energy dependent electron relaxation time is shown to explain the observed temperature dependence of the low field Hall and Righi-Leduc coefficients for the alkali metals. Theoretical model calculations, which only depend on the residual resistivity ratio and the Debye temperature, are presented.

Anisotropic scattering of conduction electrons on dilute Cu impurities in aluminum

The transverse magnetoresistivity δϱ/ϱ0 and the low-field Hall coefficient R 0 were measured in aluminum containing dilutely concentrated Cu impurities. It is found that the low-field Hall coefficient R 0 is positive, in contrast to the isotropic value, which is negative. The large and positive values of R 0 are due to the conduction electrons of aluminum that suffer an anisotropic scattering on the copper impurities. The simultaneous low-field magnetoresistance and Hall coefficient measurements, combined with the simple equations derived by Kesternich, permitted us to determine the anisotropy of the electronic scattering in terms of the mean free path ratios 1 ++/1 − and 1 −−/1 −.

Hall Coefficient of Dilute Aluminium Alloys II. Application

AbstractThe Hall coefficient of Al‐Ag, Al–Ga, and Al–Ge dilute alloys is measured at 4.2, 77, and 293 K as function of the magnetic field strength and solute concentrations. The range of validity of the practical formula given in the preceding paper is investigated for the case of the low field Hall coefficient of dilute alloys at 77 and 293 K.

Effects of warped energy surfaces on the low field hall coefficient of graphite

Unusual field dependence of the low field galvanomagnetic properties of graphite has been attributed to small pockets of mobile minority carriers in the corners of the Brillouin Zone. However, this explanation does not account for the sample or temperature dependence of these phenomena. An alternative explanation, based on the trigonal warping of the constant energy surfaces, is presented.

The true low-field Hall coefficient of high-purity coefficient of high-purity silver and silver containing low-density defects at low temperatures

Previous low-temperature Hall measurements on nominally pure noble metals have involved transition into the high-field regime. Hall coefficient (RH) results are reported on several high-purity samples of Ag and Ag containing low concentrations of Au, Cd, and dislocations in fields down to 0.0085 T (85G) sufficient to ensure true low-field conditions, and examine the results in terms of a changing relaxation time anisotropy factor x= tau N/ tau B of a two-group model with neck (N) and belly (B) regions of the Fermi surface. A new auxiliary quantity is introduced viz. the characteristic peak Hall coefficient which is a single function of temperature, characteristic of a pure metal, and is the locus of the peaks observed in RH on dilute alloys irrespective of the nature or concentration of nonmagnetic impurities or defects present.

The low field Hall coefficient of polyvalent metals. II. Ca

The formula by Tsuji for the low field Hall coefficient has been evaluated for Ca in the nearly free electron approximation. The total value consists of the free electron valueR0=-1/ne, due to the spherical Fermi surface part (free electrons), and the contributions of the distorted areas in the vicinity of the Bragg planes (Bragg electrons and holes). At room temperature the weight of the (111)-Bragg particles is 15 per cent ofR0. The touching of the Fermi surface at the (200)-planes creates Bragg holes, yielding a positive contribution to the Hall coefficient of 0.45R0.

Resonant scattering induced transport anomalies in zero-gap semiconductors

Based on a model of resonant scattering of conduction band electrons by acceptor center, a calculation of the conductivity and galvanomagnetic coefficients in zero-gap semiconductors is presented. The calculated shape for the anomalous dip in the temperature dependence of the conductivity is consistent with experimental observations in HgTe and Hg 1-xCd x Te alloys. It is shown that the resonant scattering of mobile carriers also induces anomalous behaviour in the low field hall coefficient and transverse magnetoresistance.

Influence of Fermi surface and defect structure on the lowfield galvanomagnetic properties of Al

Low-field Hall coefficient R and transverse magnetoresistance Delta rho / rho 0 were measured in Al single crystals. A definite defect structure (statistically distributed Frenkel pairs) was created in the specimens by low-temperature electron irradiation. This defect structure could then be changed in a controlled way by annealing at different temperatures. Eliminating the influence of defect concentration with the aid of the Kohler representation thus allowed the dependence of R and Delta rho / rho 0 on the defect structure to be investigated. Various effects of the Fermi surface geometry and of the scattering mechanism on R and Delta rho / rho 0 are discussed on the basis of simple equations for the low-field Hall coefficient and magnetoresistance.

Low-field Hall coefficient of zinc and cadmium

The applicability of a simplified energy surface, similar to the one used to explain the Hall coefficient of beryllium in a previous paper (Shiozaki 1975), to the other hexagonal close packed metals, zinc and cadmium, has been examined. A simplified Fermi surface has been constructed of the doughnut-like ring and ellipsoid pieces, its overall dimensions being chosen to resemble those of the experimentally determined surface. Good agreement is obtained with the simple model for the anisotropy and the sign of the Hall coefficients. It is found that the contribution from the second zone hole 'monster' is very considerable and it appears that the results are further improved only if the author improves the approximation for the 'monster'. It is concluded that the anisotropy of the relaxation time plays no important role.

Low-field magnetoresistance in metals

Low-field magnetoresistance and Hall coefficient are calculated in the anisotropic-relaxation-time approximation. Simple results are obtained for Fermi-surface models which can be composed of spherical, cylindrical, and planar surfaces. Influences of the Fermi-surface geometry and the scattering anisotropy on the low-field magnetoresistance are discussed. With small modifications the method is applied to polyvalent metals with nearly-free-electron Fermi-surfaces. Simultaneous magnetoresistance and Hall-coefficient measurements combined with a three-group model calculation for the electronic mean free path are suggested as a means to determine the anisotropy of the electronic scattering in nearly-free-electron-like polyvalent metals. In an Appendix the results are extended to the longitudinal magnetoresistance.

High magnetic field dependence of the Hall coefficient in n-type germanium and in other semiconductors with ellipsoidal surfaces of constant energy

The linear dependence of the Hall coefficient on one over the magnetic field squared at high-field strength has been derived using Boltzmann transport theory results for high-symmetry-orientation semiconductor samples with ellipsoidal surfaces of constant energy such as n-type germanium and silicon. This treatment justifies the practice of linearly extrapolating such Hall coefficient data to infinite fields to obtain the net carrier concentration. Comparison to experimental data taken on n-type germanium at 77 °K shows that the theory accurately perdicts the slope of this straight-line variation. A criterion is developed in terms of the conductivity mobility and the anisotropy of effective mass and scattering which specifies how large the magnetic fields must be to allow this extrapolation to be performed accurately. It is shown that up to 90% errors are obtained when a single scattering mechanism correction factor is applied to low-field Hall coefficient data to estimate carrier concentration in the n-type germanium samples studied.

Hall effect measurements of frenkel defect clustering in aluminium during high-dose reactor irradiation at 4.6 K

Abstract The low-field Hall coefficient R0 of irradiated aluminium at 4.6 K is independent of the Frenkel defect (FD) concentration, however sensitively dependent of their configuration. Since measurement of R0 is not too difficult, rather extensive investigations of FD clustering during irradiation can be performed, but only qualitative interpretations are possible. We have irradiated several pure Al samples with reactor neutrons at 4.6 K up to very high doses φt resp. resistivity increments Δρ0 (maximum 91% of extrapolated saturation value Δρ0 sat ≈ 980 nΩcm). Our main results are: 1. FD clustering within a single displacement cascade is not a very strong effect in Al, since the R 0 values are essentially the same after reactor and after electron irradiation. Rough cascade averages are: volume Vc ≈ 2.1 · 105 at. vol. and FD concentration cc ≈ 1100 ppm. 2. There is practically no dose-dependent FD clustering up to Δρ0 ≈ 350 nΩcm, since R 0 remains essentially constant there. It follows that dose-dependent FD clustering can only occur for high-order overlap of cascade volumes. The differential dose curve dΔρ0/dφt is perfectly linear in Δρ0 as long as R0 = const. 3. For Δρ0 > 350 nΩcm FD clustering becomes increasingly important and R 0 changes strongly. Surprisingly dR 0/dφt ≈ const whence there is a constant rate of cluster size increase in spite of the vanishing rate of FD production, evidence of the continuous regrouping of the lattice and its defects.