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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 since these undoped states display dramatically different antiferromagnetic (AF) spin arrangements and N$\rm \acute{e}$el temperatures. Although there is general consensus that magnetic interactions are important for superconductivity, much is still unknown concerning the microscopic origin of the magnetic states. In this review, progress in this area is summarized, focusing on recent experimental and theoretical results and discussing their microscopic implications. It is concluded that the parent compounds are in a state that is more complex than 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.