  The Migdal effect predicts that a nuclear recoil interaction can be
accompanied by atomic ionization, allowing many dark matter direct detection
experiments to gain sensitivity to sub-GeV masses. We report the first direct
search for the Migdal effect for M- and L-shell electrons in liquid xenon using
7.0$\pm$1.6 keV nuclear recoils produced by tagged neutron scatters. Despite an
observed background rate lower than that of expected signals in the region of
interest, we do not observe a signal consistent with predictions. We discuss
possible explanations, including inaccurate predictions for either the Migdal
rate or the signal response in liquid xenon. We comment on the implications for
direct dark-matter searches and future Migdal characterization efforts.
