The theory of the galvanomagnetic and thermomagnetic effects in metals

Abstract

The methods of a previous paper are used to discuss the effect of a magnetic field on the thermoelectric power of a metal containing two overlapping energy bands of normal form. Exact solutions of the transport equation are obtained for the three limiting cases of high temperatures, low temperatures and very strong magnetic fields, and it is shown that the formulae can be generalized to give approximate expressions for all temperatures and all fields. The magnetic change of the thermoelectric power is found to be small at very low and high temperatures, and to pass through a maximum at intermediate temperatures. The transverse galvano- and thermomagnetic effects are also considered, and the formulae which hold for free electrons are generalized so as to be approximately valid for all temperatures. For free electrons, the Hall coefficient remains constant as the temperature decreases, the Righi-Leduc coefficient increases, and the Ettingshausen and Ettingshausen-Nemst coefficients decrease and change sign at very low temperatures. The corresponding formulae for a metal containing two bands are also obtained, and are used to show that the theoretical predictions for free electrons cannot hold for real metals except in special cases. Finally, the two-band model is used to discuss the effect of the magnitude of the magnetic field on the coefficients of the transverse effects.