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We revisit the fitting of the Fang-Bernevig-Hu model [Europhys. Lett. 86,67005 (2009)] to inelastic neutron scattering data carried out by Lipscombe etal. [Phys. Rev. Lett. 106, 057004 (2011)]. We demonstrate that there are manyquite different parameter choices within the experimentally observed phase(AFM3) that provide approximately equally good fits to the neutron data. Wenote that (a) all of these parameter sets lie very close to a point oftransition between the AFM3 phase and one of its neighbors in the classicalphase diagram, and (b) many of them involve rather large values of thethird-neighbor coupling $J_3$. In light of these observations, we discusswhether the modeling of FeTe may need revision to allow for a slightly non-AFM3ground state, orbital as well as spin physics on the Fe sites, the effects ofelectron itinerancy, or a combination of these.

Magnetic Order and Magnetic Excitations in FeTe: How Good is a Short-Range Heisenberg Model?