  In this paper, we perform a detail analysis on leptogenesis and dark matter
form low scale seesaw. In the framework of $\nu$2HDM, we further introduce one
scalar singlet $\phi$ and one Dirac fermion singlet $\chi$, which are charged
under a $Z_2$ symmetry. Assuming the coupling of $\chi$ is extremely small, it
serves as a FIMP dark matter. The heavy right hand neutrinos $N$ provide a
common origin for tiny neutrino mass (via seesaw mechanism), leptogenesis (via
$N\to \ell_L \Phi_\nu^*,\bar{\ell}_L \Phi_\nu$) and dark matter (via $N\to
\chi\phi$). With hierarchical right hand neutrino masses, the explicit
calculation shows that success thermal leptogenesis is viable even for TeV
scale $N_1$ with $0.4 \lesssim v_\nu\lesssim1$ GeV and lightest neutrino mass
$m_1\lesssim 10^{-11}$ eV. In such scenario, light FIMP dark matter in the keV
to MeV range is naturally expected. The common parameter space for neutrino
mass, natural leptogenesis and FIMP DM is also obtained in this paper.
