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The discovery of superconductivity in LaFeAsO introduced the ferropnictidesas a major new class of superconducting compounds with critical temperaturessecond only to cuprates. The presence of magnetic iron makes ferropnictidesradically different from cuprates. Antiferromagnetism of the parent compoundsstrongly suggests that superconductivity and magnetism are closely related.However, the character of magnetic interactions and spin fluctuations inferropnictides, in spite of vigorous efforts, has until now resistedunderstanding within any conventional model of magnetism. Here we show that themost puzzling features can be naturally reconciled within a rather simpleeffective spin model with biquadratic interactions, which is consistent withelectronic structure calculations. By going beyond the Heisenberg model, thisdescription explains numerous experimentally observed properties, including thepeculiarities of the spin wave spectrum, thin domain walls, crossover fromfirst to second order phase transition under doping in some compounds, andoffers new insight in the occurrence of the nematic phase above theantiferromagnetic phase transition.

Consistent model of magnetism in ferropnictides