Theory of Inelastic Neutron Scattering in the Itinerant Model Antiferromagnetic Metals. I

Abstract

The susceptibility functions ${\chi }^{-+}(\mathrm{K}, \omega )$ and ${\chi }^{\mathrm{zz}}(\mathrm{K}, \omega )$ are calculated in the random-phase approximation at zero temperature for the Slater model of itinerant antiferromagnetism using the Hubbard Hamiltonian; from these susceptibility functions the neutron-scattering cross section is calculated. A pole is found in ${\chi }^{-+}(\mathrm{K}, \omega )$ corresponding to a spin-wave model As in the Heisenberg model of spin waves, the residue of this pole approaches zero as the scattering vector K approaches a chemical reciprocal lattice vector $\tau$, and becomes infinite as K approaches a magnetic reciprocal-lattice vector Q. The non-spin-flip single-particle-mode scattering is found to become infinite at an energy corresponding to the magnetic splitting of the bands at the boundary of the magnetic Brillouin zone if the Fermi level lies in this gap. If the Fermi level does not lie in the gap, then there is a pole in ${\chi }^{\mathrm{zz}}(\mathrm{K}, \omega )$ for K near a magnetic reciprocal-lattice vector, at an energy equal to the gap energy when K = Q, corresponding to a collective excitation. Acoustic plasmon poles in ${\chi }^{\mathrm{zz}}(\mathrm{q}, \omega )$ are also discussed.