Local-band theory of itinerant ferromagnetism. II. Spin waves

Abstract

The short-wavelength magnons which are observed by neutron scattering above as well as below the Curie temperature ${T}_{C}$ are studied by the methods of the local-band theory, described in the preceding paper. We find a temperature shift of the spin-wave constant $D$, of a type previously proposed, but which we estimate to be numerically small. A novel downward shift mechanism gives a lowering $\ensuremath{-}2D{|\stackrel{\ensuremath{\rightarrow}}{\mathrm{a}}|}_{\mathrm{av}}^{2}$, where ${|\stackrel{\ensuremath{\rightarrow}}{\mathrm{a}}|}_{\mathrm{av}}^{2}$ is proportional to the magnetic energy. ${|\stackrel{\ensuremath{\rightarrow}}{\mathrm{a}}|}_{\mathrm{av}}^{2}$ saturates shortly above ${T}_{C}$ at about 5 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}2}$ ${\mathrm{\AA{}}}^{\ensuremath{-}2}$ in both iron and nickel. The form of this term is strictly correct only for ${q}^{2}\ensuremath{\gg}{|\stackrel{\ensuremath{\rightarrow}}{\mathrm{a}}|}_{\mathrm{av}}^{2}$. However, it accounts for the greater part of the observed magnon energy shift, both in temperature dependence and shape of the dispersion curve. Finally, we find a new magnon-width mechanism ${\ensuremath{\Gamma}}_{q}$ proportional to ${|\stackrel{\ensuremath{\rightarrow}}{\mathrm{a}}|}_{\mathrm{av}}^{2}q$ which seems capable of accounting for the observed width.