Unified Spin Model for Magnetic Excitations in Iron Chalcogenides

Recent inelastic neutron scattering (INS) measurements on FeSe and Fe(Te$_{1-x}$Se$_x$), have sparked intense debate over the nature of the ground state in these materials. Here 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 calculations, and density-matrix renormalization group (DMRG), exhibits a sequence of transitions between the columnar antiferromagnet common to the iron pnictides, the non-magnetic ferroquadrupolar phase attributed to FeSe, and the double-stripe antiferromagnetic order known to exist in Fe$_{1+y}$Te. The calculated spin structure factor in these phases mimics closely that observed with INS in the Fe(Te$_{1-x}$Se$_x$), series. In addition to the experimentally established phases, the possibility of incommensurate magnetic order is also predicted.