  In their ideal structure, double perovskites like Sr_2FeMoO_6 have
alternating Fe and Mo along each cubic axes, and a homogeneous ferromagnetic
metallic ground state. Imperfect annealing leads to the formation of structural
domains. The moments on mislocated Fe atoms that adjoin each other across the
domain boundary have an antiferromagnetic coupling between them. This leads to
a peculiar magnetic state, with ferromagnetic domains coupled
antiferromagnetically. At short distance the system exhibits ferromagnetic
correlation while at large lengthscales the net moment is strongly suppressed
due to inter-domain cancellation. We provide a detailed description of the spin
wave excitations of this complex magnetic state, obtained within a 1/S
expansion, for progressively higher degree of mislocation, i.e., antisite
disorder. At a given wavevector the magnons propagate at multiple energies,
related, crudely, to `domain confined' modes with which they have large
overlap. We provide a qualitative understanding of the trend observed with
growing antisite disorder, and contrast these results to the much broader
spectrum that one obtains for uncorrelated antisites.
