Spin-Wave Interaction in the Itinerant-Electron Model of Ferromagnetism

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Abstract
Using a simple itinerant-electron model of ferromagnetism with exchange interaction and Coulomb repulsion between band electrons, spin waves, and their interactions are discussed. In the random-phase approximation, we obtained the diagonal elements of spin-wave interactions which reduce to Dyson's result in the limit of localized electrons for our model. A diagrammatical interpretation of the result is also given. When the band with down spin is partially filled and that with up spin empty, the spin-wave interaction consists of the part arising from the modified exchange interaction, the part due to the electron kinetic energy and the Coulomb repulsion, and the part which involves both of these effects. Among these, the second seems to be rather small. For small values of the wave vectors of the spin waves involved, the spin-wave interaction depends on the wave vectors in the same way as in Dyson's result. The modification on the exchange interaction is such that the short-range part of the original exchange interaction is suppressed, whereas the long-range part remains unaffected. This arises from electron (hole) exchanges, and cancels in the limit of localized electrons.

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