  We investigate the magnetism of the
Co$^{II}_4$(OH)$_2$(C$_1$$_0$H$_1$$_6$O$_4$)$_3$ metal-organic framework which
displays complex inorganic chains separated from each other by distances of 1
to 2 nm, and which orders at ~5.4 K. The zero-field magnetic structure is
determined using neutron powder diffraction: it is mainly antiferromagnetic but
posseses a ferromagnetic component along the $\textbf{c}$-axis. This magnetic
structure persists in presence of a magnetic field. Ac susceptibility
measurements confirm the existence of a single thermally activated regime over
7 decades in frequency ($E/k_B\approx64 K$) whereas time-dependent relaxation
of the magnetization after saturation in an external field leads to a two times
smaller energy barrier. These experiments probe the slow dynamics of domain
walls within the chains: we propose that the ac measurements are sensitive to
the motion of existing domain walls within the chains, while the magnetization
measurements are governed by the creation of domain walls.
