per Fe assuming $g=2$ [@clester; @msliu12]. For spin waves in the insulating Rb$_{0.89}$Fe$_{1.58}$Se$_2$, the total moment sum rule appears to be satisfied [@mywang11]. The fluctuating moments for BaFe$_2$As$_2$ and BaFe$_{1.9}$Ni$_{0.1}$As$_{2}$ are $\left\langle
m^2\right\rangle=3.17\pm 0.16$ and $3.2\pm 0.16\ \mu_B^2$ per Fe(Ni), respectively [@msliu12]. While these values are considerably smaller than those of the fully localized case, they are much larger than expected from the fully itinerant SDW using the random phase approximation [@hpark12]. A calculation combining DFT and dynamical mean field theory (DMFT) suggests that both the band structure and the local moment aspects (e.g. Hunds coupling) of the iron electrons are needed for a good description of the magnetic responses [@msliu12]. Figure 2i shows the energy dependence of $\chi^{\prime\prime}(\omega)$ for BaFe$_2$As$_2$ and BaFe$_{1.9}$Ni$_{0.1}$As$_{2}$, and it is clear that the impact of electron doping and superconductivity are limited to spin excitation energies below 100 meV. These results suggest that high-energy spin excitations are likely to arise from the local moments instead of FS nesting effects.

Deviations from the simple SDW Fermi surface nesting picture
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After the early research efforts on Fe-based superconductors [@johnston; @stewart; @paglione10], recent experimental and theoretical investigations are providing a more refined perspective of these materials. Below, 