  We report the search results of light dark matter through its interactions
with shell electrons and nuclei, using the commissioning data from the
PandaX-4T liquid xenon detector. Low energy events are selected to have an
ionization-only signal between 60 to 200 photoelectrons, corresponding to a
mean nuclear recoil energy from 0.77 to 2.54 keV and electronic recoil energy
from 0.07 to 0.23 keV. With an effective exposure of 0.55 tonne$\cdot$year, we
set the most stringent limits within a mass range from 40 $\rm{MeV/c^2}$ to 10
$\rm{GeV/c^2}$ for point-like dark matter-electron interaction, 100 MeV/c$^2$
to 10 GeV/c$^2$ for dark matter-electron interaction via a light mediator, and
3.2 to 4 $\rm{GeV/c^2}$ for dark matter-nucleon spin-independent interaction.
For DM interaction with electrons, our limits are closing in on the parameter
space predicted by the freeze-in and freeze-out mechanisms in the early
Universe.
