  We develop a local spin model to explain the rich magnetic structures in the
iron-based superconductors $Fe_{1+y}Te_{1-x}Se_x$. 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.
