Spin excitation spectra of iron-based superconductors from the degenerate double-exchange model

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's coupling. We employ the fermionic spinon representation for the local moments and perform a generalized RPA calculation on both spinons and itinerant electrons. We find that in the ($\pi$,0) magnetically-ordered state, the spin-wave excitation at ($\pi$,$\pi$) is pushed to a higher energy due to the presence of itinerant electrons, which is consistent with the previous study using Holstein-Primakoff transformation. In the non-ordered state, the particle-hole continuum keeps the collective spin excitation near ($\pi$,$\pi$) at a higher energy even without any $C_4$ symmetry breaking. The implications for the recent neutron scattering measurement at high temperature will be discussed.