Multiband Theory of Inelastic Neutron Scattering by Ferromagnetic Metals at Low Temperatures

Abstract

We have examined the behavior of the inelastic neutron scattering cross section of ferromagnetic metals at temperature $T=0$ as a function of scattering vector When spin-orbit coupling is negligible, because of invariance of the metals under rotation of the total spin of the system, there will be no inelastic neutron scattering at K=0. In those ferromagnetic metals for which hybridization with the conduction band is unimportant, this effect is shown to occur for K=a reciprocal-lattice vector ${\ensuremath{\tau}}_{n}$. It is argued that, for $\mathrm{K}\ensuremath{\ne}{\ensuremath{\tau}}_{n}$, there should still be no interband spin wave, optical spin wave, or Stoner-mode inelastic scattering, but only acoustic spin-wave scattering for ferromagnetic metals with magnetic bands sufficiently narrow to be nearly described by a Heisenberg model. It is shown by explicit calculation on a simplified multiband model that for wider-band ferromagnetic metals, if there exist optical and interband spin waves in addition to an acoustic spin-wave mode, it should still be difficult to observe Stoner modes. The effect of conduction-band-$d$-band hybridization on the inelastic neutron scattering from $3d$-series metals is examined: Its effect in nickel is shown to be small, but its effect is argued to be larger for iron. It is concluded that it should be easier to observe interband and optical spin waves and Stoner modes in iron than in nickel because this metal is further from being described by a Heisenberg model than nickel.