Abstract
A derivation is given of the dispersion relation for excitations from the spin-density wave ground state. Working in the random phase approximation, and taking a single tight binding electronic band with a delta function interaction between electrons, the author finds three types of collective mode, of which one is longitudinal and two transverse. Calculation shows that the former has a linear dispersion relation for small wave vectors, and is probably a zero-sound excitation modified by the magnetic ordering. One of the transverse modes is also linear in behaviour, and is identified as a spin wave excitation. The other behaves as omega = omega 0+Aq2 for small q, where omega 0 lies in the energy gap; on examining the approach to the ferromagnetic limit, it is demonstrated that omega 0 approaches zero, and the mode goes over smoothly into a ferromagnetic spin wave.

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