Magnetization Plateaux in the Antiferromagnetic Ising Chain with Single-Ion Anisotropy

Two one-dimensional spin-1 antiferromagnetic Ising models with a single-ion anisotropy under external magnetic field at low temperatures are exactly investigated by the transfer-matrix technique. The magnetization per spin ($m$) is obtained for the two types of models (denoted by model 1 and 2) as an explicit function of the magnetic field ($H$%) and of the anisotropy parameter ($D$). Model 1 is an extension of the recently one treated by Ohanyan and Ananikian [\emph{Phys. Lett. A} \textbf{% 307} (2003) 76]: we have generalized their model to the spin-1 case and a single-ion anisotropy term have been included. In the limit of positive (or null) anisotropy ($D\geq 0$) and strong antiferromagnetic coupling ($\alpha =J_{A}/J_{F}\geq 3$) the $m \times H$ curves are qualitatively the same as for the spin $S=1/2$ case, with the presence of only one plateau at $m/m_{sat}=1/3$. On the other hand, for negative anisotropy ($D<0$) we observe more plateaux ($m=1/6$ and 2/3), which depend on the values of $D$ and $% \alpha $. The second model (model 2) is the same as the one recently studied by Chen et al. [\emph{J. Mag. Mag. Mat. }\textbf{262} (2003) 258)] using Monte Carlo simulation; here, the model is treated within an exact transfer-matrix framework.