Unified Spin Model for Magnetic Excitations in Iron Chalcogenides

Recent inelastic neutron scattering (INS) measurements on the iron chalcogenides FeSe and Fe(Te$_{1-x}$Se$_{x}$) have sparked intense debate over the role of magnetism in these materials. We will argue that magnetic frustrations of the underlying Fe spin-1 degrees of freedom are the key to understanding the nature of the ground states. We propose an effective bilinear-biquadratic spin model which is shown to consistently describe the evolution of low-energy spin excitations in FeSe, both under applied pressure and upon Se/Te substitution. The phase diagram, studied using a combination of variational mean-field, flavor-wave, and density-matrix renormalization group (DMRG) calculations, exhibits a sequence of transitions between the non-magnetic ferroquadrupolar phase attributed to FeSe and several other magnetically ordered phases{[1]}. The calculated spin structure factors mimic closely those observed with INS in FeSe and in the Fe(Te$_{1-x}$Se$_x$) series{[2]}. In addition to the experimentally established phases, the possibility of incommensurate magnetic order is also predicted.\\ {[1]} P. Bilbao Ergueta, Z. Wang, W.-J. Hu, and A. H. Nevidomskyy, arXiv: 1607.05295.\\ {[2]} Z. Xu \emph{et al.}, Phys. Rev. B. \textbf{93}, 104517 (2016).