excitations are longitudinally elongated ellipses that are rotated 90$^\circ$ from that of the electron-doped BaFe$_{2-x}T_x$As$_2$ (Fig. 2f) [@jtpark; @clester; @hfli; @hqluo12]. Furthermore, INS measurements on powder samples of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ reveal that spin excitations change from commensurate to incommensurate for $x\ge 0.4$, although their exact line shape and incommensurability in reciprocal space are unknown [@castellan]. Finally, INS experiments on hole-overdoped KFe$_2$As$_2$ found incommensurate spin fluctuations along the longitudinal direction (inset in Fig. 2a), again consistent with the FS nesting picture [@chlee11]. Figure 2a shows the electronic phase diagram of hole-doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$ based on the present understanding of these materials.

Although FS nesting is compatible with a number of experimental observations for the evolution of spin excitations in electron/hole-doped iron-based superconductors, there are several aspects of the problem where such a scenario cannot be reconciled with experiments. In a recent INS experiment on optimally electron-doped BaFe$_{1.9}$Ni$_{0.1}$As$_2$, magnetic excitations throughout the Brillouin zone have been measured in absolute units and compared with spin waves for AF BaFe$_2$As$_2$ [@msliu12]. In the fully localized (insulating) case, the formal Fe$^{2+}$ oxidation state in BaFe$_2$As$_2$ would give a $3d^6$ electronic configuration and Hund’s rules would yield $S=2$. The total fluctuating moments should be $\left\langle m^2\right\rangle=(g\mu_B)^2
S(S+1)=24\ \mu_B^2$ 