Magnetism and its microscopic origin in iron-based high-temperature superconductors

High-temperature superconductivity in the iron-based materials emerges from, or sometimes coexists with, their metallic or insulating parent compound states. This is surprising, as these undoped states exhibit dramatically different antiferromagnetic spin arrangements and Neel temperatures. Although there is a general consensus that magnetic interactions are important for superconductivity, much remains unknown concerning the microscopic origin of the magnetic states. In this review, we summarize the progress in this area, focusing on recent experimental and theoretical results, and their microscopic implications. We conclude that the parent compounds are in a state that is more complex than that implied by a simple Fermi surface nesting scenario, and a dual description including both itinerant and localized degrees of freedom is needed to properly describe these fascinating materials.