  We consider searches for the inelastic scattering of low-mass dark matter at
direct detection experiments, using the Migdal effect. We find that there are
degeneracies between the dark matter mass and the mass splitting that are
difficult to break. Using XENON1T data we set bounds on a previously unexplored
region of the inelastic dark matter parameter space. For the case of exothermic
scattering, we find that the Migdal effect allows xenon-based detectors to have
sensitivity to dark matter with ${\cal O}(\mathrm{MeV})$ mass, far beyond what
can be obtained with nuclear recoils alone.
