and below the Fe-layer, respectively. (a) The AF structure of La$_2$CuO$_4$, where the chemical unit cell is marked light green. (b) The collinear AF structure of nonsuperconducting iron pnictides in the FeAs-layer, where spins are aligned anti-parallel along the orthorhombic $a_o$-axis [@cruz; @qhuang; @slli09]. (c) The bi-collinear AF structure of FeTe [@webao08; @slli08]. (d) The block AF order of the insulating $A_y$Fe$_{1.6+x}$Se$_2$, where the $\sqrt{5}\times\sqrt{5}$ superlattice structure is marked by solid line with lattice parameter $a_s=8.663$ Å and the orthorhombic lattice cell is shaded green [@wbao1; @fye]. The iron vacancies are marked as yellow squares. (e) The wave vector dependence of the AF order in the $(H,K)$ plane of the reciprocal space for La$_2$CuO$_4$ [@coldea]; (f) BaFe$_2$As$_2$ [@qhuang]; (g) Fe$_{1.05}$Te [@webao08; @slli08]; and (h) the insulating $A_y$Fe$_{2-x}$Se$_2$ [@wbao1; @fye]. (i) Spin-wave dispersions along two high symmetry directions for La$_2$CuO$_4$ [@coldea]. The overall energy scale of spin waves for copper oxides is about $320$ meV and spin waves are instrumental resolution limited. (j) Spin-wave dispersions for BaFe$_2$As$_2$ and they broad considerably for energies above $\sim$100 meV [@lharriger]. (k) Spin-wave dispersions for Fe$_{1.05}$Te, and spin waves are very broad for energies above 30 meV [@lipscombe]. (l) Spin waves for the insulating Rb$_{0.89}$Fe$_{1.58}$Se$_2$ 