Spin waves in the $(\pi ,0)$ magnetically ordered iron chalcogenide Fe${}_{1.05}$Te

We use inelastic neutron scattering to show that the spin waves in the iron chalcogenide Fe${}_{1.05}$Te display novel dispersion clearly different from those in the related iron pnictide systems. By fitting the spin waves to a Heisenberg Hamiltonian, we extract magnetic exchange couplings that are dramatically different from both predictions by density functional calculations and measurements on the iron pnictide CaFe${}_2$As${}_2$. While the nearest-neighbor exchange couplings in CaFe${}_2$As${}_2$ and Fe${}_{1.05}$Te are quite different, their next-nearest-neighbor exchange couplings are similar. These results suggest that superconductivity in the pnictides and chalcogenides share a common magnetic origin that is intimately associated with the next-nearest-neighbor magnetic coupling between the irons.