Multiorbital spin susceptibility in a magnetically ordered state: Orbital versus excitonic spin density wave scenario

We present a general theory of multiorbital spin waves in magnetically ordered metallic systems. Motivated by the itinerant magnetism of iron-based superconductors, we compare the magnetic excitations for two different scenarios: when the magnetic order either sets in on the on-site orbital level; or when it appears as an electron-hole pairing between different bands of electron and hole characters. As an example, we treat the two-orbital model for iron-based superconductors. For small magnetic moments the spin excitations look similar in both scenarios. Going to larger interactions and larger magnetic moments, the difference between both scenarios becomes striking. While in the excitonic scenario the spin waves form a closed structure over the entire Brillouin zone and the particle-hole continuum is gapped, the spin excitations in the orbital scenario can be treated as spin waves only in a close vicinity to the ordering momenta. The origin of this is a gapless electronic structure with Dirac cones which is a source of large damping. We analyze our results in connection with recent neutron scattering measurements and show that certain features of the orbital scenario with multiple order parameters can be observed experimentally.