Thermomagnetic Coefficients Research Articles

Theory of the thermomagnetic effects in thin films in a magnetic field of arbitrary magnitude

AbstractThermomagnetic effects of a thin film in a magnetic field normal to the film surface are studied for an arbitrary value of specularity parameter p. Using the solution of the Boltzmann equation for an arbitrary film thickness and magnetic field strength the basic thermomagnetic coefficients are calculated, the Nernst‐Ettingshausen coefficient (N‐E) Q, the thermopower in a magnetic field α(H), and the thermal conductivity in a magnetic field χ. A detailed analysis is given of their dependences on the thickness, magnetic field strength, and the parameter p. It follows from the analysis that in a weak magnetic field the thermopower α and the N‐E coefficient Q are practically p‐independent. The computer calculations show that α and Q oscillate as functions of the magnetic field strength, the oscillations of Q being more pronounced than those of the electronic thermal conductivity. χ varies monotonically with the magnetic field.

Weak‐Field Thermomagnetic Coefficients of a Trigonal Bismuth Sample

AbstractThe weak‐field thermomagnetic coefficients of bismuth with heat current in the trigonal direction have been measured in the range of temperatures from 10 to 65 K. The data are analysed in terms of the symmetry restrictions imposed by the 3m point group. The temperature dependences of the coefficients point to a diffusion thermoelectric power down to temperatures which depend on the coefficient in question, the highest temperature being around 40 K.

High-field magnetoresistance and magnetothermal e.m.f. in many-valley semiconductors with ellipsoidal energy surface

Thermomagnetic coefficients appropriate to a many-valley model of a semiconductor of the n -Germanium type are evaluated in the framework of the density matrix formalism developed earlier. These coefficients are determined for arbitrary values of the magnetic field, within the effective mass approximation. The phonon-drag contribution is not included in this work. An application is made to the four-ellipsoidal model of n-Ge under the conditions where elastic-acoustic phonon scattering is the predominant mechanism of scattering and the high-temperature limit of the phonon distribution is valid. The thermoelectric power (magneto-Seebeck effect) is found to increase with increasing values of the magnetic field except for a small region of low magnetic field values where it decreases in the longitudinal configuration only.

High-field galvano- and thermomagnetic effects in cadmium

Detailed results are presented of investigations on the galvano- and thermomagnetic coefficients of pure Cd (ρ 11 , ρ 21 , γ 11 , and γ 21 ). The transverse resistivity ρ 11 is almost perfectly quadratic in magnetic field (B 1.99 ) at the lowest temperatures, thus throwing doubt on the applicability of intersheet scattering models, which suggest significant departures fromB 2 . The lattice conductivity λ g is extracted from the high-field thermal data and is found to exhibit no pronounced anomalies, in contrast to the previously obtained data on the zero-field electronic thermal conductivity (to which λ g should be related in the simplest theory). The Hall resistivity ρ 21 is qualitatively similar to that obtained by previous workers, but the detailed field dependence is different. After corrections are made for the effects of λ g , the Righi-Leduc thermal resistivity γ 21 is found to behave like ρ 21 , though it is more sensitive to temperature, as might be expected for a thermal coefficient.

The peculiar behaviour of transport coefficients in the presence of inelastic scattering by optical phonons

AbstractA method is developed of calculating galvanomagnetic and thermomagnetic coefficients taking into account successively the inelastic scattering on the polarisation potential of the optical phonons together with the elastic scattering mechanisms. In the approximation of weak magnetic fields, the solution of the Boltzmann transport equation is expanded into a power series of the magnetic field by means of perturbation theory. Numerical computations for n‐GaAs with impurity concentrations of 1012 to 1020 cm−3 in the temperature range of 4.2 to 600 °K are made. The results are given as nomograms which are convenient for experimental data processing. The peculiarities of the behaviour of transport coefficients depending on the impurity concentration are analysed.

Galvano- and thermo-magnetic coefficients for a multi-band conductor

Galvano- and thermo-magnetic coefficients for a multi-band conductor

Quantum theory of Ohmic galvano- and thermomagnetic effects in semiconductors

A density-matrix formalism developed earlier for the evaluation of Ohmic magnetoconductivity is further elaborated and applied to other magnetotransport effects in nonpolar semiconductors in the presence of a magnetic field of arbitrary strength. The difference from earlier transport theories lies in a natural extension of the scattering dynamics beyond the strict Born approximation. The well-known divergence difficulties of older theories, usually removed by any of a number of ad hoc cutoff procedures, do not appear here. The transverse-conductivity expression turns out to be equivalent to that of some earlier theories of cyclotron resonance extrapolated to zero frequency, but derived in a different way. When applied to elastic scattering of electrons in a simple model of a semiconductor, the theory gives galvanomagnetic and thermomagnetic coefficients within the range of values usually seen experimentally, showing the basic correctness of the theory. It is then applied to the magnetophonon effect, where the resonance peaks are shown to be finite. An interesting inversion of one of the peaks in the Ettingshausen-Nernst coefficient is found. Landau-level broadening and phonon drag are not included in the present paper, although they can be incorporated when deemed important.

Galvano- and thermo-magnetic coefficients for a multi-band conductor

The reasons for the discrepancies between the expressions for the Righi-Leduc effect derived by Putley (1960) and by Honig and Harman (1963) are discussed. To obtain a correct result, the lattice thermal conductivity must be properly included in the calculations. Differences, attributed to sign convections, between the two formulations are discussed. Expressions for the principal transverse galvano- and thermo-magnetic coefficients for an isotropic multi-band conductor are tabulated.

Thermodynamic restrictions on thermoelectric, thermomagnetic and galvanomagnetic coefficients

All the consequences of the Clausius-Duhem nequality on thermoelectric, thermomagnetic and galvanomagnetic ffects are examined within the framework of a fourth-order heory developed in a previous paper. Besides the classical results, ome new conditions are derived and discussed.

Thermomagnetic Coefficients in a Quantizing Magnetic Field. I. Electronic Component

Thermomagnetic coefficients in a strong magnetic field (ω c τ≫1, ω c the cyclotron frequency and τ an appropriate relaxation time of electrons) are calculated by the method of the thermal Green function. Taking into account the interaction energy carried by an electron, we can correct the expression for the symmetric part of the thermomagnetic coefficients obtained by Ansel'm and Askerov. As a result, the symmetric part does not disturb the third law of thermodynamics. The resulted expression is used to discuss the magneto-oscillation of the thermoelectric power of Bi. The magnetic field dependence of the amplitude of the oscillation is investigated and shown not so simple as was proposed by Steele and Babiskin who showed that the amplitude is proportional to H 5/2 ( H is the magnetic field strength) according to their experimental data.

Vortex motion in superconductors

We review the recent theory of vortex motion in type-II superconductors as developed by Caroli and Maki and some more recent advances on this subject. Limiting ourselves to magnetic fields H slightly smaller than H c2, we have shown that the order parameter moves with a uniform velocity u such that E + u × B = 0, where B is the induction and E is the electric field in the vortex state. The moving order parameter implies the motion of vortex lines with the same velocity. Making use of the moving order parameter thus obtained various transport currents are calculated. The electric conductivity and the thermomagnetic coefficients are compared with recent experimental data.

Field dependence of thermomagnetic effects in bismuth

The results of the measurement of three low-field thermomagnetic coefficients a 231, a 3311 and a 3322 are reported. At 77K, the increase in Seebeck coefficient varies as B 2 at low-fields and the equality a 3311 = a 3322 is verified. The Nernst coefficient is investigated from 77 to 300 K at low and high fields and a sign reversal is observed at all temperatures.

Thermoelectric and Thermomagnetic Properties of n‐Ge in the Region of Phonon Drag Effects

AbstractThe influence of phonon drag effects on thermoelectric and thermomagnetic properties of n‐Ge is investigated. The role of different scattering mechanisms is discussed. From a comparison of the experimental data [11, 13] with the theory follows that the theoretical values of the thermoelectric and thermomagnetic coefficients agree better with experimental ones assuming that the phonon relaxation times depend on the wave vector and temperature as it was predicted by Simons [2].

Calculation of some thermomagnetic coefficients in degenerate semiconductors for mixed scattering by acoustical phonons and ionized impurities

In this paper, the authors have calculated the variation of the transverse Nernst–Ettingshausen coefficient, the transverse Righi–Leduc coefficient, and the Ettingshausen coefficient with impurity parameter. The influence of adiabatic thermomagnetic effects on the Hall and Nernst–Ettingshausen coefficients has also been studied. It has been shown that a correction term due to adiabatic effects can reach considerable values especially for the Nernst–Ettingshausen coefficient.

Thermomagnetic effects in cadmium arsenide

Adiabatic and isothermal thermomagnetic coefficients have been obtained for cadmium arsenide in the temperature range 65-300°K. By assuming acoustic scattering and a single parabolic conduction band model, agreement between experiment and theory has been demonstrated over most of the temperature range, but results indicate the presence of mixed acoustic and impurity scattering at the lower temperatures. However, the measured values of thermal conductivity cannot be entirely explained as a function of temperature since there is an anomalous increase at higher temperatures.

On the Phonon Drag Effect Contribution to Thermomagnetic Phenomena

AbstractCalculations are made of the acoustic and optical phonon drag effect contributions to some of the isothermal thermomagnetic coefficients. The scattering is considered to be a mixture of acoustic, optical, and ionized impurity scattering. It is found that the optical phonon drag is of more importance for the thermomagnetic effects than for the thermoelectric effects.

The Thermoelectric, Galvanomagnetic and Thermomagnetic Effects of Monovalent Metals. III. The Galvanomagnetic and Thermomagnetic Effects for Anisotropic Media.

A variational principle for the electron transport in a magnetic field is described, and the principle is applied to the calculation of the transverse effects of cubic metals in the transverse magnetic field by using an approximate trial function. Our method gives exact solution for the spherical energy hand model. For the anisotropic energy band, our method gives an approximate solution which coincides with the exact solution if the energy dependent relaxation time exists. Relations between the transverse galvanomagnetic and thermomagnetic coefficients, which hold for arbitrary scattering mechanism, are derived.

The Two-Band Effect in Conduction

For an isotropic two-band conductor in a transverse magnetic field, the various galvanomagnetic, thermomagnetic and thermoelectric coefficients are derived by elementary arguments in terms of those of the individual bands. The expressions are applicable to quasi-free electrons of any degree of degeneracy: for fully degenerate electrons they reduce to those already given by Sondheimer and Wilson. When the square of the thermoelectric power is comparable with the Lorenz number, as may happen in semiconductors, the expressions for the adiabatic thermomagnetic and thermoelectric effects become extremely complicated, though those for the isothermal effects remain reasonably simple.