Spin susceptibilities and the theory of itinerant-electron antiferromagnetism

Abstract

This article investigates the equilibrium states of antiferromagnetic itinerant-electron systems in the Hartree-Fock approximation. As a result, the spin susceptibilities are determined in the random phase approximation. The lowlying collective excitations are then obtained by finding the poles of these susceptibilities. We start by giving a brief review of the Hartree-Fock procedure and by indicating how the susceptibilities are obtained. The density matrix approach, where the ground state is interpreted as that minimizing the energy, is used throughout. Using an effective Coulomb interaction of the Hubbard type we consider two distinct systems: a one-band system with an incommensurate spin density wave in its ground state, and a many-band simply commensurate model for f.c.c. manganese. The first of these is such that the band structure and resulting susceptibilities can be obtained explicitly. The spin-wave energies and wave-vectors are found by a careful, small energy and momentum transfer, expansion of these susceptibilities for the case of a parabolic band. The spin-wave damping, which is shown to arise from spin-wave decay into quasiparticle quasihole pairs, is also obtained for this band structure. For the case of f.c.c. manganese the antiferromagnetic bands are obtained from a realistic 9-band paramagnetic model by using a many-band generalization of the Hubbard interaction. The enhanced spin susceptibilities are calculated, using the tetrahedral Brillouin zone integration method, and are presented along with their associated collective excitations. The results obtained are discussed with particular reference to the many-band effects. These effects are shown to be very much dependent on the particular form of interaction used.