Magnetic frustration and iron-vacancy ordering in iron chalcogenide

Abstract

We study the spin- and vacancy-ordered states in 122 iron chalcogenides (${A}_{1\ensuremath{-}y}$Fe${}_{2\ensuremath{-}x}$Se${}_{2}$) by inspecting the magnetic ground states of a ${J}_{1}$-${J}_{2}$-${J}_{3}$ model on different vacancy-ordered lattices observed/conjectured in these compounds. A highly frustrated ${J}_{1}$-${J}_{2}$-${J}_{3}$ model was first applied to the study of magnetism in FeTe and was reported to explain the inelastic neutron-scattering data qualitatively. We find that the vacancy-ordered states are generally energetically favored for their reduction of magnetic frustration inherent to the spin-exchange model and, especially, that the 245 vacancy-spin-ordered state minimizes the magnetic exchange energy among all known vacancy-ordered states, in line with the fact that it has the highest vacancy-ordering phase transition temperature and the largest ordered moment in all iron-based superconductors. Thus, our study provides an electronic perspective for understanding the various vacancy orderings in these compounds. Then we focus on the experimentally well-studied 245 state and calculate the spin-wave spectrum and dynamic spin susceptibility. Finding that the key features of these calculated quantities are consistent with a recent inelastic neutron-scattering experiment, we conclude that we have obtained a qualitative local spin model for the 245 state. We also discuss the possibility of a unified local-moment description for all iron chalcogenides based on our result.