Collective Excitations of Electrons in Degenerate Bands. I

Spin waves in the collective electron model of ferromagnetism are derived in a completely similar manner to that adopted in deriving exciton waves in insulators. The internal motion of an electron-hole pair forming the spin wave with a long wavelength is shown to be localized in the ordinary space. The frequency of the spin wave with long wavelength coincides with the result obtained by K. Y osida and T. Kasuya in the case where all electron spins are pointed toward the same direction in the ground state. It is concluded generally that spin waves break down unless there is a sufficiently large difference between the number of the electrons with up spin and the number of those with down spin.