Abstract
Dispersion relations of spin waves in ferromagnetic metals with multiple bands are obtained by the method of normal mode within the random phase approximation and a certain approximation for the Coulomb interaction. It is found that spin wave spectra consist of one acoustical branch, some optical branches and other branches due to inter-band transitions. The inter-band transitions have an important effect on the dispersion relation of an acoustical spin wave at larger momentum. The coefficient of the square of momentum in the dispersion relation of the acoustical spin wave is found to be the sum of D B and D H which are derived from the intra-atomic Coulomb and inter-atomic exchange interactions, respectively. For nickel, the value of D B is estimated as about 0.1 eVA 2 by using the model of two overlapping bands, and it is concluded that \(D_{B}{\lesssim}D_{H}\).
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