We have calculated the local magnetic susceptibility of one of the prototypical Fe-based superconductors (LaFeAsO) by means of the local density approximation + dynamical mean field theory as a function of both (imaginary) time and real frequencies with and without vertex corrections. Vertex corrections are essential for obtaining the correct $omega$-dependence, in particular a pronounced low-energy peak at $omega sim 0.2 $eV, which constitutes the hallmark of the dynamical screening of a large instantaneous magnetic moment on the Fe atoms. In experiments, however, except for the case of x-ray absorption spectroscopy (XAS), the magnetic moment or the susceptibility represent typically the average over long time scales. In this respect, the frequency range of typical neutron experiments would be too limited to directly estimate the magnitude of the short-time moment.
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