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

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 TC, is approximately DQ²-2D|→a|ₐᵥ², for Q>|→a|, where |→a|ₐᵥ²=1/4(∇^M)ₐᵥ². This is predicted to be the dispersion observed by neutron scattering, with an inhomogeneous broadening, also of order D|→a|ₐᵥ². 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.