Electron-phonon interaction and itinerant-electron ferromagnetism

Starting from a consideration of how the phonon frequency would change with the spin splitting of the conduction-electron energy bands in an itinerant-electron ferromagnet, we find that in the paramagnetic region the effect of the electron-phonon interaction makes the temperature dependence of the spin susceptibility Curie-Weiss-type, with the Curie temperature $T_C$ much lower than in the Stoner theory. Further, for $T<\mathrm{}{T}_C$ we find that the phonon effect on magnetization can be large enough to account for the anomalous temperature dependence of spontaneous magnetization often observed in itinerant-electron ferromagnets, especially in Invar alloys. To confirm such a conclusion, with the same model and approximation we discuss also the very closely related problem of the magnetic field effect on the sound velocity in an itinerant-electron ferromagnet, and our theory is found to explain satisfactorily the varied observed results for both $T>\mathrm{}{T}_C$ and $T<\mathrm{}{T}_C$.