  We present a study of the magnetic ground state of a two-band model with
nested electron and hole Fermi surfaces and both interband and intraband
Coulomb interactions. Our aim is to understand how the excitonic
spin-density-wave (ESDW) state induced by the interband Coulomb repulsion is
affected by the intraband interactions. We first determine the magnetic
instabilities of our model in an unbiased way by employing the random-phase
approximation (RPA) to calculate the static spin susceptibility in the
paramagnetic state. From this, we construct the mean-field phase diagram,
demonstrating the robustness of the ESDW against the intraband interaction. We
then calculate the RPA transverse spin susceptibility in the ESDW state and
show that the intraband Coulomb repulsion significantly renormalizes the
paramagnon line shape and suppresses the spin-wave velocity. We conclude with a
discussion of the relevance of this suppression for the commensurate ESDW state
of Mn-doped Cr alloys.
