Theory of magnetic order in Fe_1+yTe_{1- x}Se_x

We develop a local spin model to explain the rich magnetic structures in the iron-based superconductors Fe_1+yTe_1-xSe_x. We show that our model exhibits both commensurate antiferromagnetic and incommensurate magnetic order along the crystal a-axis. The transition from the commensurate to the incommensurate phase is induced when the concentration of excess Fe atoms is larger than a critical value. Experimentally measurable spin-wave features are calculated, and the mean-field phase diagram of the model is obtained. Our model also suggests the existence of a large quantum critical region due to strong spin frustration upon increasing Se concentration.