Abstract

We observed in superconducting (Tl,Rb)${}_{2}$Fe${}_{4}$Se${}_{5}$ spin-wave branches that span an energy range from 6.5 to 209 meV. Spin dynamics are successfully described by a Heisenberg localized spin model whose dominant in-plane interactions include only the nearest (${J}_{1}$ and ${J}_{1}^{\ensuremath{'}}$) and next nearest neighbor (${J}_{2}$ and ${J}_{2}^{\ensuremath{'}}$) exchange terms within and between the tetramer spin blocks, respectively. These experimentally determined exchange constants would crucially constrain the theoretical viewpoints on magnetism and superconductivity in the Fe-based materials.

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