Motivated by the observation of spatially anisotropic exchange constants in
the iron pnictide materials, we study the spin-wave spectra of the
J1aββJ1bββJ2β Heisenberg models on a square-lattice with nearest
neighbor exchange J1aβ along x and J1bβ along y axis and a second
neighbor exchange J2β. We focus on the regime, where the spins order at
(Ο,0), and compute the spectra by systematic expansions around the Ising
limit. We study both spin-half and spin-one Heisenberg models as well as a
range of parameters to cover various cases proposed for the iron pnictide
materials. The low-energy spectra have anisotropic spin-wave velocities and are
renormalized with respect to linear spin-wave theory by up to 20 percent,
depending on parameters. Extreme anisotropy, consisting of a ferromagnetic
J1bβ=ββ£JFββ£, is best distinguished from a weak anisotropy (J1aββJ1bβ=J1β, J2β>J1β/2) by the nature of the spin-waves near the wavevectors
(0,Ο) or (Ο,Ο). The reported spectra for the pnictide material
CaFe2βAs2β clearly imply such an extreme anisotropy.Comment: 6 pages, 10 figure