  The framework for soft leptogenesis minimally extended with a DM sector is
studied. A heavy singlet neutrino superfield acts as the source for (s)lepton
asymmetry and by coupling to the singlet DM superfield it produces a DM
particle density through decays. The nature of DM generated is twofold
depending on whether the Yukawa and DM couplings are either small or large.
With sufficiently small Yukawa and DM couplings DM annihilations into MSSM
particles are slow and as a consequence all DM particles form the DM component.
The solutions to Boltzmann equations are given and the dependence between the
DM masses and coupling are presented in this weak coupling regime. Also, the
behavior of the efficiency of producing asymmetric DM is determined with weak
couplings. We note that a different outcome arises if the couplings are larger
because then the ADM component is dominant due to the effectiveness of DM
decays into the MSSM sector.
