Ferromagnetic Relaxation by the Exchange Interaction between Ferromagnetic Electrons and Conduction Electrons

The Hamiltonian for the exchange interaction between the ferromagnetic $d$ electrons and the conduction $s$ electrons is derived. The ferromagnetic relaxation time caused by the $s-d$ exchange interaction is calculated in a spin wave approximation. When one uses a screened value of the exchange integral ($\frac{J_{\mathrm{atomic}}}{30}$), the calculated relaxation time for nickel at room temperature is 5×${10}^{-9\mathrm{}}$ sec as compared to the time 2.5×${10}^{-10\mathrm{}}$ sec needed to account for the experimental line width. The exchange relaxation may be dominant in materials such as alloys which have narrower lines than nickel.