The theory of the magneto-resistance effects in metals

Abstract

General formulae are obtained for the effect of a magnetic field on the electrical and thermal conductivities of a metal in which there are two overlapping bands of normal form. Simple formulae are set up which, though not strictly valid for all temperatures and fields, reduce to the correct expressions in the three limiting cases of high temperatures, low temperatures and very strong magnetic fields. The behaviour of the electrical resistance at low temperatures is discussed, and it is shown that in certain cases the resistance may pass through a minimum as the temperature is increased provided the magnetic field is large enough. It is also shown that in general the Lorenz number is increased by the presence of a magnetic field, but that the thermal conductivity of the lattice is unaffected by a magnetic field.