Electron Spin Waves in Nonmagnetic Conductors: Self-Consistent-Field Theory

Abstract

A general derivation of the electrodynamic response of a quantum many-electron gas in a nonmagnetic conducting solid immersed in an applied magnetic field is given. Self-consistent-field (SCF) theory of the equation of motion of the one-electron density matrix is used in such a way as to include, from the outset, one-electron effects such as complex energy band structure, spin-orbit coupling, and spin paramagnetism. This treatment specifically omits exchange effects such as those encountered in an extended random-phase approximation or Landau-Fermi liquid theory. The aim is to study the properties of wave propagation in the gas, looking for spin waves and/or characteristic effects which uniquely involve the spin degree of freedom and the paramagnetism of the equilibrium state. The derived results contain terms which have been neglected previously and terms which do not evolve from a simple generalization of previous treatments of the quantum dielectric theory of a Fermi gas. There are interesting spin effects in the plasma wave properties both with and without spin-orbit mixing of the one-electron states. In an effective mass approximation for the one-electron states, it is shown that there are resonances and cutoffs associated with electron spin resonance in the transverse wave propagation (both perpendicular and parallel to the magnetic field). For spin-orbit mixed states, one finds zeros of the longitudinal dielectric constant (for long wavelength) near the electron spin-flip frequency. The mechanism for the spin wave associated with this zero is a correlation of the motion of electrons with "opposite spins" by the long-range Coulomb field through the spin-orbit coupling of the crystalline eigenstates.