Theory of Neutron Scattering in the Itinerant Model of Antiferromagnetic Metals. II

Calculations in a previous paper of neutron scattering from a Slater-model single-band itinerant antiferromagnet have been extended to the case of a spin-density-wave antiferromagnet in a multiband metal. The calculation in this paper uses a density matrix formulation of the time-dependent Hartree-Fock approximation or random-phase approximation. The results are qualitatively in agreement with the results of the Slater model. We get a spin-wave mode with a large neutron cross section on magnetic satellites, but a small cross section on chemical reciprocal-lattice vectors. We also find large single-particle-mode scattering on magnetic satellites due to an overdamped "longitudinal spin-wave" mode (a collective mode due to spin fluctuations along the magnetization direction), if the Fermi energy lies in the gap between the two magnetically split bands. If the Fermi energy lies in one of the bands, we get a "longitudinal spin-wave" collective mode outside of the single-particle continuum with a dispersion relation for small $q$ of the form $\omega =2g+D{q}^2$. This mode is due to the itinerant character of the electrons. By a coordinate transformation, these spin-wave excitations have been separated into excitations along and transverse to the direction of magnetization at each point in space. A method of using polarized neutrons to make this separation experimentally is also discussed.