Spin waves and magnetic exchange interactions in insulating Rb _0.89Fe_1.58Se₂

The parent compounds of iron pnictide superconductors are bad metals with a collinear antiferromagnetic structure and Néel temperatures below 220 K. Although alkaline iron selenide A_yFe_1.6+xSe₂ (A=K, Rb, Cs) superconductors are isostructural with iron pnictides, in the vicinity of the undoped limit they are insulators, forming a block antiferromagnetic order and having Néel temperatures of roughly 500 K. Here we show that the spin waves of the insulating antiferromagnet Rb _0.89Fe_1.58Se₂ can be accurately described by a local moment Heisenberg Hamiltonian. A fitting analysis of the spin wave spectra reveals that the next-nearest neighbour couplings in Rb_0.89Fe _1.58Se₂, (Ba,Ca,Sr)Fe₂As₂, and Fe_1.05 Te are of similar magnitude. Our results suggest a common origin for the magnetism of all the Fe-based superconductors, despite having different ground states and antiferromagnetic orderings.