Two major themes in the physics of condensed matter are quantum critical phenomena and unconventional superconductivity. These usually occur in the context of competing interactions in systems of strongly correlated electrons. All this interesting physics comes together in the behavior of the recently discovered iron pnictide compounds that have generated enormous interest because of their moderately high-temperature superconductivity. The ubiquity of antiferromagnetic ordering in their phase diagrams naturally raises the question of the relevance of magnetic quantum criticality, but the answer remains uncertain both theoretically and experimentally. Here, we show that the undoped iron pnictides feature a unique type of magnetic quantum critical point, which results from a competition between electronic localization and itinerancy. Our theory provides a mechanism to understand the experimentally observed variation of the ordered moment among the undoped iron pnictides. We suggest P substitution for As in the undoped iron pnictides as a means to access this example of magnetic quantum criticality in an unmasked fashion. Our findings point to the iron pnictides as a much-needed setting for quantum criticality, one that offers a unique set of control parameters
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