Spin waves in an itinerant electron model of an antiferromagnet

The spin wave velocity in a one band itinerant electron model of an antiferromagnet is calculated using the equations of motion for the generalized transverse susceptibility. The formula is written down approximately, in terms of the ground state antiferromagnetic energy bands and is then evaluated in limits corresponding to wide and narrow antiferromagnetic energy gaps. A special case of the former yields an expression corresponding to the energy of a spin wave in a Heisenberg antiferromagnet. In the latter case it is found that the spin wave velocity tends to zero as the energy gap tends to zero, which is a new result. The problem of whether the spin wave velocity is real when the Fermi level is not in the gap is discussed.