experiments have mapped out spin waves on single crystals of CaFe$_2$As$_2$ [@diallo09; @jzhao], SrFe$_2$As$_2$ [@raewings], and BaFe$_2$As$_2$ [@lharriger] throughout the Brillouin zone. Although there are still debates concerning whether spin waves in these materials can be described by a pure itinerant picture [@diallo09; @raewings] or require local moments [@jzhao; @lharriger], the overall spin-wave energy scales are around 220 meV. Therefore, magnetic exchange couplings in iron pnictides are clearly smaller than those of copper oxides (Figs. 1i and 1j). Although spin waves are broadened at high energies, the spin-wave dispersion curves (Fig. 1j) can still be described by a Heisenberg Hamiltonian with strong anisotropic NN exchange couplings ($J_{1a}\gg J_{1b}$) and fairly large NNN exchange coupling ($J_2$) [@jzhao; @lharriger]. This large in-plane magnetic exchange coupling anisotropy has been interpreted as due to possible electronic nematic phase and/or orbital ordering [@jzhao; @lharriger]. Table I compares the effective magnetic exchange couplings of the Fe-based systems studied thus far against those of the insulating copper-oxide La$_2$CuO$_4$.

For the chalcogenides Fe$_{1+y}$Te, the commensurate bi-collinear AF spin structure in Fig. 1c becomes incommensurate for concentration $y>0.12$ [@rodriguez]. The overall spin-waves energy scale (Fig. 1k) is similar to those of the iron pnictides. Although the large static ordered 