Orbital and spin magnetism and dielectric response of electrons in metals

A survey is given of the theory of orbital and spin magnetism of electrons in metals, and of the relation of this to dielectric response theory. In particular, the orbital magnetic behaviour of Bloch electrons in a static but spatially varying magnetic field is discussed. It is shown that the treatment of Hebborn and Sondheimer can be generalized to include this spatial dependence of the applied magnetic field and that the result may be written compactly in terms of the zero field canonical density matrix, or Green function. It is further shown that the frequency dependence of both the orbital and spin susceptibility can be obtained, again from the density matrix, by calculating the current. The connection with neutron scattering is exhibited and for the case of nickel the way in which such experiments can lead to estimates of the role of the electron interactions is discussed. The effect of a magnetic field on phonon spectra in metals is considered briefly. Finally it is suggested that it may be of interest to study the effect of the magnetic field on the periodic potential usually employed to calculate energy levels of electrons in magnetic fields. Some modifications of pair forces between ions is to be expected in very high fields.