Spin Waves and Spatially Anisotropic Exchange Interactions in the $\mathrm{S}=2$ Stripe Antiferromagnet Rb${}_{0.8}$Fe${}_{1.5}$S${}_2$

An inelastic neutron scattering study of the spin waves corresponding to the stripe antiferromagnetic order in insulating Rb${}_{0.8}$Fe${}_{1.5}$S${}_2$ throughout the Brillouin zone is reported. The spin wave spectra are well described by a Heisenberg Hamiltonian with anisotropic in-plane exchange interactions. Integrating the ordered moment and the spin fluctuations results in a total moment squared of $27.6\pm 4.2{\mu }_B^2$/Fe, consistent with $\mathrm{S \approx 2}$\mathrm{.}Unlike$X$Fe$_2$As$_2$($X=$ Ca, Sr, and Ba), where the itinerant electrons have a significant contribution, our data suggest that this stripe antiferromagnetically ordered phase in Rb${}_{0.8}$Fe${}_{1.5}$S${}_2$ is a Mott-like insulator with fully localized $3d$ electrons and a high-spin ground state configuration. Nevertheless, the anisotropic exchange couplings appear to be universal in the stripe phase of Fe pnictides and chalcogenides.