  Detectors with low thresholds for electron recoil open a new window to direct
searches of sub-GeV dark matter (DM) candidates. In the past decade, many
strong limits on DM-electron interactions have been set, but most on the one
which is spin-independent (SI) of both dark matter and electron spins. In this
work, we study DM-atom scattering through a spin-dependent (SD) interaction at
leading order (LO), using well-benchmarked, state-of-the-art atomic many-body
calculations. Exclusion limits on the SD DM-electron cross section are derived
with data taken from experiments with xenon and germanium detectors at leading
sensitivities. In the DM mass range of 0.1 - 10 GeV, the best limits set by the
XENON1T experiment: $\sigma_e^{\textrm{(SD)}}<10^{-41}-10^{-40}\,\textrm{cm}^2$
are comparable to the ones drawn on DM-neutron and DM-proton at slightly bigger
DM masses. The detector's responses to the LO SD and SI interactions are
analyzed. In nonrelativistic limit, a constant ratio between them leads to an
indistinguishability of the SD and SI recoil energy spectra. Relativistic
calculations however show the scaling starts to break down at a few hundreds of
eV, where spin-orbit effects become sizable. We discuss the prospects of
disentangling the SI and SD components in DM-electron interactions via spectral
shape measurements, as well as having spin-sensitive experimental signatures
without SI background.
