Local-band theory of itinerant ferromagnetism. III. Nonlinear Landau-Lifshitz equations

Abstract

To provide insight into the results of the two preceding papers (I and II), the Landau-Lifshitz equation has been analyzed. it is found, as in II, that the magnon energy, close to and above the Curie temperature $T_C$, is approximately ${\mathrm{DQ}}^2-2\mathrm{}D{\left|\overrightarrow{\mathrm{a}}\right|}_{\mathrm{av}}^2$, for $Q>\left|\overrightarrow{\mathrm{a}}\right|$, where ${\left|\overrightarrow{\mathrm{a}}\right|}_{\mathrm{av}}^2=\frac{1}{4}{\left(\nabla \hat{M}\right)}_{\mathrm{av}}^2$. This is predicted to be the dispersion observed by neutron scattering, with an inhomogeneous broadening, also of order $D{\left|\overrightarrow{\mathrm{a}}\right|}_{\mathrm{av}}^2$. At low temperature, the first nonlinear approximation is made to see how this result can be reconciled with the usual form given in the Landau theory.