  We consider a spin chain of fermionic atoms in an optical lattice,
interacting with each other by super-exchange interactions. We theoretically
investigate the dissipative evolution of the spin chain when it is coupled by
magnetic dipole-dipole interaction to a bath consisting of atoms with a strong
magnetic moment. Dipolar interactions with the bath allow for a dynamical
evolution of the collective spin of the spin chain. Starting from an
uncorrelated thermal sample, we demonstrate that the dissipative cooling
produces highly entangled low energy spin states of the chain in a timescale of
a few seconds. In practice, the lowest energy singlet state driven by
super-exchange interactions is efficiently produced. This dissipative approach
is a promising alternative to cool spin-full atoms in spin-independent
lattices. It provides direct thermalization of the spin degrees of freedom,
while traditional approaches are plagued by the inherently long timescale
associated to the necessary spatial redistribution of spins under the effect of
super-exchange interactions.
