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

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 $-2\mathrm{}D{\left|\overrightarrow{\mathrm{a}}\right|}_{\mathrm{av}}^2$, where ${\left|\overrightarrow{\mathrm{a}}\right|}_{\mathrm{av}}^2$ is proportional to the magnetic energy. ${\left|\overrightarrow{\mathrm{a}}\right|}_{\mathrm{av}}^2$ saturates shortly above $T_C$ at about 5 × ${10}^{-2\mathrm{}}$ ${\mathrm{\AA }}^{-2\mathrm{}}$ in both iron and nickel. The form of this term is strictly correct only for $q^2\gg {\left|\overrightarrow{\mathrm{a}}\right|}_{\mathrm{av}}^2$. 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 ${\Gamma }_q$ proportional to ${\left|\overrightarrow{\mathrm{a}}\right|}_{\mathrm{av}}^{2}q$ which seems capable of accounting for the observed width.