Spin waves and magnetic exchange interactions in the spin-ladder compounds BaFe$_{\mathrm{2}}$S$_{\mathrm{3}}$ and RbFe$_{\mathrm{2}}$Se$_{\mathrm{3}}$.*

We report inelastic neutron scattering studies on the spin waves of BaFe$_{\mathrm{2}}$S$_{\mathrm{3}}$ and RbFe$_{\mathrm{2}}$Se$_{\mathrm{3}}$. Both of them exhibit similar stripe antiferromagnetic (AF) orders as that of BaFe$_{\mathrm{2}}$As$_{\mathrm{2}}$. At ambient pressure BaFe$_{\mathrm{2}}$S$_{\mathrm{3}}$ can be viewed as the parent state of the superconductivity discovered under pressure. Fitting the spin wave spectra to a Heisenberg Hamiltonian reveals a strong ferromagnetic (FM) exchange interaction (SJ$_{\mathrm{R}}$\textasciitilde 71 meV) along the rung direction, an AF SJ$_{\mathrm{L}}$\textasciitilde 49 meV along the leg direction, and a FM SJ$_{\mathrm{2}}$\textasciitilde 15 meV along the diagonal direction. The results are in clear contrast to the exchange interactions of the parent compounds of the other iron-based superconductors, suggesting that specific relative values for the exchange interactions do not appear to be unique for the parent states of the superconducting materials. However, identical measurements for insulating RbFe$_{\mathrm{2}}$Se$_{\mathrm{3}}$ reveal comparable exchange interactions as that of BaFe$_{\mathrm{2}}$As$_{\mathrm{2}}$, indicating the irrelevance of the fermiology for the existence of the stripe AF order among various Fe-based materials. arXiv:1609.00465, PRB 94,041111(R)(2016).