The static and dynamic properties of the single-chain molecular magnet [Co(hfac)$_2$NITPhOMe] are investigated in the framework of the Ising model with Glauber dynamics, in order to take into account both the effect of an applied magnetic field and a
finite size of the chains. For static fields of moderate intensity and short chain lengths, the approximation of a mono-exponential decay of the magnetization fluctuations is found to be valid at low temperatures; for strong fields and long chains, a multi-exponential decay should rather be assumed. The effect of an oscillating magnetic field, with intensity much smaller than that of the static one, is included in the theory in order to obtain the dynamic susceptibility $chi(omega)$. We find that, for an open chain with $N$ spins, $chi(omega)$ can be written as a weighted sum of $N$ frequency contributions, with a sum rule relating the frequency weights to the static susceptibility of the chain. Very good agreement is found between the theoretical dynamic susceptibility and the ac susceptibility measured in moderate static fields ($H_{rm dc}le 2$ kOe), where the approximation of a single dominating frequency turns out to be valid. For static fields in this range, new data for the relaxation time, $tau$ versus $H_{rm dc}$, of the magnetization of CoPhOMe at low temperature are also well reproduced by theory, provided that finite-size effects are included.
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 organi
c 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.
