  We investigate theoretically and experimentally the static magnetic
properties of single crystals of the molecular-based Single-Chain Magnet (SCM)
of formula [Dy(hfac)$_{3}$NIT(C$_{6}$H$_{4}$OPh)]$_{\infty}$ comprising
alternating Dy$^{3+}$ and organic radicals. A peculiar inversion between maxima
and minima in the angular dependence of the magnetic molar susceptibility
$\chi_{M}$ occurs on increasing temperature. Using information regarding the
monomeric building block as well as an {\it ab initio} estimation of the
magnetic anisotropy of the Dy$^{3+}$ ion, this anisotropy-inversion phenomenon
can be assigned to weak one-dimensional ferromagnetism along the chain axis.
This indicates that antiferromagnetic next-nearest-neighbor interactions
between Dy$^{3+}$ ions dominate, despite the large Dy-Dy separation, over the
nearest-neighbor interactions between the radicals and the Dy$^{3+}$ ions.
Measurements of the field dependence of the magnetization, both along and
perpendicularly to the chain, and of the angular dependence of $\chi_{M}$ in a
strong magnetic field confirm such an interpretation. Transfer matrix
simulations of the experimental measurements are performed using a classical
one-dimensional spin model with antiferromagnetic Heisenberg exchange
interaction and non-collinear uniaxial single-ion anisotropies favoring a
canted antiferromagnetic spin arrangement, with a net magnetic moment along the
chain axis. The fine agreement obtained with experimental data provides
estimates of the Hamiltonian parameters, essential for further study of the
dynamics of rare-earths based molecular chains.
