ABSTRACT
Magnetism is a subject of great scope, both in variety of phenomena and in theoretical challenges. In this chapter we limit ourselves to two of the latter: paramagnetism and diamagnetism in the electron gas. The electron gas is an oversimplified model of conduction electrons in a metal. Paramagnetism represents the tendency of electron spin magnetic moments to align with an applied magnetic induction field, making a characteristic contribution to the magnetic susceptibility of the system. Diamagnetism represents the fact that electrons in such a field have orbits whose perpendicular projections are circular, and the resultant current loops make a different contribution to the magnetic susceptibility. The treatment of electron paramagnetism is presented here in section 13.2 as a particularly instructive application of quantum statistical thermodynamics. In section 13.3, diamagnetism is discussed, where the quantization of electron orbits in a magnetic induction field, section 13.3.2, results in a spectacular change in the topology of the Fermi surface, sections 13.3.3 and 13.3.4, attended by periodic variation of the magnetic susceptibility as a function of magnetic induction field: the De Haas-van Alphen effect (section 13.3.5). A well-known but nonetheless surprisingly simple relationship between low-temperature paramagnetic and diamagnetic susceptibilities is arrived at in section 13.3.6. For paramagnetism, I have expanded somedetails ofHuang’s presentation (1967, especially sections 8.1, 8.3, 9.6, 11.1 and 11.5) in his excellent work on statistical mechanics, and for diamagnetism I have similarly adopted Pippard’s elegant discussion at the 1961 Les Houches Summer School [Pippard (1962, p. 11, section IIA)].
