  Direct dark matter detection experiments based on a liquid xenon target are
leading the search for dark matter particles with masses above $\sim$ 5
GeV/c$^2$, but have limited sensitivity to lighter masses because of the small
momentum transfer in dark matter-nucleus elastic scattering. However, there is
an irreducible contribution from inelastic processes accompanying the elastic
scattering, which leads to the excitation and ionization of the recoiling atom
(the Migdal effect) or the emission of a Bremsstrahlung photon. In this letter,
we report on a probe of low-mass dark matter with masses down to about 85
MeV/c$^2$ by looking for electronic recoils induced by the Migdal effect and
Bremsstrahlung, using data from the XENON1T experiment. Besides the approach of
detecting both scintillation and ionization signals, we exploit an approach
that uses ionization signals only, which allows for a lower detection
threshold. This analysis significantly enhances the sensitivity of XENON1T to
light dark matter previously beyond its reach.
