  Using a degenerate double-exchange model, we investigate the spin excitation
spectra of iron pnictides. The model consists of local spin moments on each Fe
site, as well as itinerant electrons from the degenerate $d_{xz}$ and $d_{yz}$
orbitals. The local moments interact with each other through antiferromagnetic
$J_{1}$-$J_{2}$ Heisenberg interactions, and they couple to the itinerant
electrons through a ferromagnetic Hund coupling. We employ the fermionic spinon
representation for the local moments and perform a generalized random-phase
approximation calculation on both spinons and itinerant electrons. We find that
in the $\left(\pi,0\right)$ magnetically-ordered state, the spin-wave
excitation at $\left(\pi,\pi\right)$ is pushed to a higher energy due to the
presence of itinerant electrons, which is consistent with a previous study
using the Holstein-Primakoff transformation. In the paramagnetic state, the
particle-hole continuum keeps the collective spin excitation near
$\left(\pi,\pi\right)$ at a higher energy even without any $C_{4}$ symmetry
breaking. The implications for recent high temperature neutron scattering
measurements will be discussed.
