Magnetic and Thermal Behaviour of One-Dimensional Antiferromagnetic Spin-1 Ising Chain at Low Temperatures

Abstract

In this study, we have investigated ground state properties of one-dimensional antiferromagnetic spin-1 chain with single-ion anisotropy at very low temperatures using the Transfer Matrix method. Magnetic plateaus, phase diagram, specific heat, susceptibility of the spin chain have been evaluated numerically from the free energy. Results are in good agreement with the experimental data for the spin-1 compounds [Ni2(Medpt)2(µ-ox)(H2O)2](ClO4)22H2O, [Ni2(Medpt)2(µ-ox)(µ-N3)](ClO4)0.5H2O, Ni(C2H8N2)Ni(CN)4 and Ni(C10H8N2)2Ni(CN)4.H2O. However, spin-Peierls transition have not been observed in the temperature dependence of specific heat and magnetic susceptibility. The physics of low-dimensional i.e., one-dimensional (1D) or quasi-one-dimensional (Q1D) spin-S (S≥ 1) chains has attracted a considerable amount of attention after the prediction by Haldane 1 that a 1D Heisenberg antiferromagnet should have an energy gap between the singlet ground state and the first excited triplet states in the case of an integer spin quantum number, while the energy levels are gapless in the case of a half integer spin quantum number. The most fascinating characteristic of these low-dimensional systems is that they show magnetic plateaus i.e., quantization of magnetization at low temperatures near the ground state. This phenomenon has been observed not only in Haldane spin systems but also in other spin gapped systems for instance; spinPeierls and spin ladders systems. A general condition of quantization of the magnetization was derived from the Lieb-Schultz-Mattis theorem 2 for low-dimensional magnetic systems. The fact that, Oshikawa, Yamanaka and Affleck (OYA) 3 discussed this plateau problem and derived a condition p(S − m) = integer, necessary for the appearance of the plateau in the magnetization curve of one-dimensional spin system, where S is the magnitude of spin, m is the magnetization per site and p is the spatial period of the ground state, respectively. The 2S + 1 magnetization plateaus (contained the saturated magnetization m = S) can appear when the magnetic field increases from zero to its saturation value h s . Theoretical studies have suggested the realization of quantization of magnetization in various systems, 3,4,5,6,7,8,9,10,11,12,13,14 and it has been observed in experimental studies. 15,16,17,18,19 Recent years, antiferromagnetic (AF) spin-1 systems among the other low-dimensional gapped spin-S systems have drawn attention from both theorists and experimentalists in literature. So far, many Q1D gapped AF spin-1 systems, which are called Haldane systems, spin-Peierls and ladder compounds, were synthesized and to understand the ground state behaviors of the spin-1 AF Heisenberg chain have been extensively studied. The first Q1D spin-1 Haldane gap compound was Ni(C 2 H 8 N 2 ) 2 NO 2 (ClO 4 ) (abbreviated NENP) which was synthesized by Meyer et al. 20 in 1981, just before the Haldane's prediction appeared. Renard et al. 21 showed that NENP had the energy spectrum predicted by Haldane; the magnetic susceptibility ...

Magnetization and quadrupolar plateaus in the one‐dimensional antiferromagnetic spin‐3/2 and spin‐2 Blume–Capel model

“…Our results strongly suggest that the single-ion anisotropy play crucial role for plateaus in magnetization formation in one-dimensional antiferromagnetic spin-3/2 and spin-2 Ising chains. The plateau predictions in present study are compatible with previous theoretical studies [4,10,[13][14][15][16]. Therefore, the present results provide that there is a class of onedimensional spin systems which in terms of Heisenberg and Ising spins lead to the qualitatively similar structures of the magnetization profiles, particularly to the formation of magnetization plateaus.…”

“…Indeed, single-ion anisotropy is one of the necessary ingredient to plateau mechanism for the present system. Previous theoretical studies [13][14][15] also provide that single-ion anisotropy plays a crucial role to appear magnetization plateaus for classical Ising chains.…”

“…For instance; Chen et al [13] employed the classical Monte Carlo technique to investigate the magnetization plateaus of 1D classic spin-1 and spin-3/2 AF Ising chain with a single-ion anisotropy under the external field at low temperatures, and they showed that the systems have 2 1 S + magnetic plateaus. Aydıner and Akyüz obtained magnetization plateaus for spin-1 using classical transfer matrix technique [14]. Aydıner observed the plateaus in the classical mixed spin chain using Monte Carlo simulation technique [15].…”

“…Another mechanism lies in so-called crystallization of the magnetic particles [22,23]. Meanwhile, even though the phenomenon of magnetization plateaus are often regarded to have purely quantum origin, it is obviously not clear since one-dimensional [13][14][15][16] and two dimensional [24,25] quasi-classical spin models which exhibit a magnetization plateaus at zero temperature or near the ground state. In fact, these studies show to us that Heisenberg and Ising spins leads to the qualitatively similar structures of the magnetization profiles, particularly to the formation of magnetization plateaus.…”

Lattice distortions in a sawtooth chain with Heisenberg and Ising bonds

“…Despite great successes in exact describing of thermodynamic functions for integrable models by TBA and especially by QTM 25,26 , for many other physically and principally important low-dimensional strongly correlated lattice models only laborious numerical calculations provide more or less reliable results for finite T thermodynamics. Recently, many papers have been devoted to exact solution of the low-dimensional lattice spin models with mixed Ising and Heisenberg bonds [27][28][29][30][31][32][33][34][35][36][37] or just to pure Ising counterparts of known Heisenberg models with various one-dimensional topologies of bonds [38][39][40][41][42] . These exact solutions for modified models have much in common with the numerical and experimental results obtained for their Heisenberg counterparts.…”