Magnetism in iron-based superconductors and their parent compounds

In this dissertation, I study the magnetism of iron-based superconductors and their parent compounds using local spin models. The study is focused on two major types of iron-based superconductors: the iron-pnictides and iron-chalcogenides. A 3D Heisenberg model on a layered lattice with nearest neighbor, next nearest neighbor and inter-layer exchanges (the J 1- J2- Jz model) is argued to have captured the qualitative features of the phase diagrams of the 1111-family and 122-family iron-pnictides. In an analysis, an emergent Ising degree of freedom named the nematic field is found stabilized by quantum fluctuation and plays a key role in explaining the separation of lattice distortion transition and Neel order transition. A modifiedJ1- J2 model, i.e., the J1- J2- J3 model is shown to exhibit magnetic ground state consistent with experiments on the 11-family of iron-chalcogenides. In the recently discovered 122-family of iron-chalcogenides, the J1- J2- J 3 model explains the magnetic structure in the vacancy ordered compounds A0.8Fe1.6Se2, but also suggests a magnetic origin of the vacancy ordering. Besides producing phase diagrams, the local spin models also give predictions on dynamic properties such as dynamic spin susceptibility. They are studied using spin wave theory for the magnetically ordered states. The results are compared with recent neutron experiments on various materials in iron-pnictides and iron-chalcogenides. Inhomogeneity in the spin models is also studied. It is found that a small concentration of static spin vacancies in a frustrated 2D model ( J1- J2 model) can drive the ground state from collinear antiferromagnet to anticollinear antiferromagnet through a quantum phase transition