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 one recently treated by Ohanyan and Ananikian [V.R. Ohanyan, N.S. Ananikian, Phys. Lett. A 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 ≥ 0 ) and strong antiferromagnetic coupling ( α = J A / J F ≥ 3 ) the m × H curves are qualitatively the same as for the spin S = 1 / 2 case, with the presence of only one plateau at m / m s a t = 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 α . The second model (model 2) is the same as the one recently studied by Chen et al. [X.Y. Chen, Q. Jiang, W.Z. Shen, C.G. Zhang, J. Mag. Mag. Mat. 262 (2003) 258] using Monte Carlo simulation; here, the model is treated within an exact transfer-matrix framework.