The magnetic susceptibility of single crystals of zinc and cadmium

Abstract

During the past five years great progress has been made in the theory of the diamagnetic and paramagnetic properties of matter. Langevin’s theory of paramagnetism, long recognised as insufficient, has been replaced by a more general treatment due to B. Cabrera. The magnetism of metals for which no theory existed at all has been explained by W. Pauli as due to the spin of the free electrons contained in the volume V occupied by the metal. Owing to their enormous concentration in addition to their small mass, the electrons within the metal do not follow the ordinary laws for the gaseous state; in particular, the energy distribution is not Maxwellian. For a Maxwellian distribution, that is, for strongly decreasing energy with decreasing temperature, the electrons could not remain in the free state at low temperature, but would combine with the metallic ions between which they move. The electrons are instead subject to quantisation and the energy is distributed according to the principle of Pauli-Fermi. If ε k be the energy in the quantum state k , of one of the electrons contained in the volume V, ε m its spin, then there can be at the most up to G = 2 electrons representing this state, and then they must spin in opposite directions. Moreover, if mξ, mη, mζ are the components of the angular momentum of the electron along the three axes of the system of co-ordinates so that E = 1/2 mv 2 = 1/2 m (ξ 2 + η 2 + ζ 2 ), then there exist, in the interval between ε and ε + dε, 4πGV ( m/h ) 3 v 2 dv = 2πVG h -3 (2 m ) 3/2 ε1/2 dε possible states. Evidently the total energy will be E = Σ n k (ε k + ε m ), the only values for n , being either 0 or 1, with the condition that the total number N of electrons is N = Σ k n k . Now ε m , the energy due to the electron spin, is small compared with ε k and can be neglected in most problems. We may say that the state of the gas is defined if we know the most probable values of n k for the ε k , that is, whether n k is equal to 0 or 1 for a certain ε k . Owing to the presence of the electronic spin ε s = ± eh /4π mc (Bohr magneton) the energy distribution will be slightly changed when an external field H is applied. We have for the number of atoms with an orientation parallel to the field