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arXiv:cond-mat/0409311 · Journal of Statistical Mechanics Theory and Experiment

Thermal and magnetic properties of integrable spin-1 and spin-3/2chains with applications to real compounds

Murray T. Batchelor, X-W Guan, N. Oelkers, Angela Foerster

Published Oct 30, 2004• 12 citations
arXivHTMLPDF

Abstract

The ground state and thermodynamic properties of spin-1 and spin- chains are investigated via exactly solved su (3) and su (4) models with physically motivated chemical potential terms. The analysis involves the thermodynamic Bethe ansatz and the high temperature expansion (HTE) methods. For the spin-1 chain with large single-ion anisotropy, a gapped phase occurs which is significantly different from the valence-bond-solid Haldane phase. The theoretical curves for the magnetization, susceptibility and specific heat are favourably compared with experimental data for a number of spin-1 chain compounds. For the spin- chain a degenerate gapped phase exists starting at zero external magnetic field. A middle magnetization plateau can be triggered by the single-ion anisotropy term. Overall, our results lend further weight to the applicability of integrable models to the physics of low-dimensional quantum spin systems. They also highlight the utility of the exact HTE method.

DOI
10.1088/1742-5468/2004/10/p10017

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The ground state and thermodynamic properties of spin-1 and spin- chains are investigated via exactly solved su (3) and su (4) models with physically motivated chemical potential terms. The analysis involves the thermodynamic Bethe ansatz and the high temperature expansion (HTE) methods. For the spin-1 chain with large single-ion anisotropy, a gapped phase occurs which is significantly different from the valence-bond-solid Haldane phase. The theoretical curves for the magnetization, susceptibility and specific heat are favourably compared with experimental data for a number of spin-1 chain compounds. For the spin- chain a degenerate gapped phase exists starting at zero external magnetic field. A middle magnetization plateau can be triggered by the single-ion anisotropy term. Overall, our results lend further weight to the applicability of integrable models to the physics of low-dimensional quantum spin systems. They also highlight the utility of the exact HTE method.
The thermal and magnetic properties of spin-1 magnetic chain compounds with large single-ion and in-plane anisotropies are investigated via the integrable su(3)su(3)su(3) model in terms of the quantum transfer matrix method and the recently developed high temperature expansion method for exactly solved models. It is shown that large single-ion anisotropy may result in a singlet gapped phase in the spin-111 chain which is significantly different from the standard Haldane phase. A large in-plane anisotropy may destroy the gapped phase. On the other hand, in the vicinity of the critical point a weak in-plane anisotropy leads to a different phase transition than the Pokrovsky-Talapov transition. The magnetic susceptibility, specific heat, and magnetization evaluated from the free energy are in excellent agreement with the experimental data for the compounds Ni(C2H8N2)2Ni(CN)4{\mathrm{Ni}(\mathrm{C}}_{2}{\mathrm{H}}_{8}{\mathrm{N}}_{2}{)}_{2}\mathrm{Ni}{(\mathrm{CN})}_{4}Ni(C2​H8​N2​)2​Ni(CN)4​ and ${\mathrm{Ni}(\mathrm{C}}_{10}{\mathrm{H}}_{8}{\mathrm{N}}_{2}{)}_{2}\mathrm{Ni}{(\mathrm{CN})}_{4}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{H}}_{2}\mathrm{O}$.
This chapter reviews the various techniques developed for the study of the thermodynamics of integrable systems at the example of the simplest one, namely the spin-12 Heisenberg chain. As a matter of fact, the strict ground state is inaccessible due to the very fundamentals of thermodynamics. The minimization of the free energy functional yields what is known as the thermodynamical Bethe ansatz. Application of thermodynamical data of quantum spin chains is the microscopic modelling of magnetic systems such as spin-Peierls compounds and ladder systems. The microscopic interactions of a given substance are determined by a comparative analysis of the experimental results for the susceptibility and the theoretical data obtained for a model. Lowering the temperature, the systems enter a large regime with non-universal correlations and finally approach the quantum critical point at exactly zero temperature showing again universal yet nontrivial properties with divergent correlation lengths governed by conformal field theory.
This article considers recent advances in the investigation of the thermal and magnetic properties of integrable spin ladder models and their applicability to the physics of strong coupling ladder compounds. For this class of compounds the rung coupling J ⊥ is much stronger than the coupling J ∥ along the ladder legs. The ground state properties of the integrable two-leg spin- and the mixed spin-() ladder models at zero temperature are analysed by means of the Thermodynamic Bethe Ansatz (TBA). Solving the TBA equations yields exact results for the critical fields and critical behaviour. The thermal and magnetic properties of the models are discussed in terms of the recently introduced High Temperature Expansion (HTE) method, which is reviewed in detail. In the strong coupling region the integrable spin- ladder model exhibits three quantum phases: (i) a gapped phase in the regime , (ii) a fully polarized phase for , and (iii) a Luttinger liquid magnetic phase in the regime H c1<H<H c2. The critical behaviour in the vicinity of the critical points H c1 and H c2 is of Pokrovsky-Talapov type. The temperature-dependent thermal and magnetic properties are directly evaluated from the exact free energy expression and compared to known experimental results for the strong coupling ladder compounds (5IAP)2CuBr4· 2H2O, Cu2(C5H12N2)2Cl4, (C5H12N)2CuBr4, BIP-BNO and [Cu2(C2\O 2)(C10H8N2)2)](NO3)2. Similar analysis of the mixed spin-() ladder model reveals a rich phase diagram, with a and a full saturation magnetization plateau within the strong antiferromagnetic rung coupling regime. For weak rung coupling, the fractional magnetization plateau is diminished and a new quantum phase transition occurs. The phase diagram can be directly deduced from the magnetization curve obtained from the exact result derived from the TBA and HTE. The results are applied to the mixed ferrimagnetic ladder compound PNNBNO. The thermodynamics of the spin-orbital model with different single-ion anisotropies is also discussed. For this model single-ion anisotropy can trigger different quantum phase transitions within the spin and orbital degrees of freedom, with magnetization plateaux arising from different spin and orbit Landé g-factors.
By the numerical transfer-matrix method we have computed several thermal properties for a Heisenberg chain of 150 antiferromagnetically coupled spins with quantum number s = 1. We dispensed with any extrapolation to the infinite chain, because the results for the magnetization, the susceptibility, the correlation length, and the static structure factor at wave number q = π have been found to be insensitive to a further increase of the chain length in the temperature regime considered. The characteristic features of our results, that occur at sufficiently low temperatures and low applied fields, can convincingly be explained by the existence of a gap in the excitation spectrum of the order of 0.4 coupling constants and, therefore, nicely complement previous numerical results for corresponding ground-state properties. We have also performed computations for a chain with an additional single-site anisotropy. We find, for appropriate parameter values, excellent agreement with experimental data for the quasi-one-dimensional model compound NENP.
We investigate the thermal and magnetic properties of the integrable su(4)su(4)su(4) ladder model by means of the quantum transfer matrix method. The magnetic susceptibility, specific heat, magnetic entropy, and high field magnetization are evaluated from the free energy derived via the recently proposed method of high temperature expansion for exactly solved models. We show that the integrable model can be used to describe the physics of the strong coupling ladder compounds. Excellent agreement is seen between the theoretical results and the experimental data for the known ladder compounds $(5\mathrm{I}\mathrm{A}\mathrm{P}{)}_{2}{\mathrm{C}\mathrm{u}\mathrm{B}\mathrm{r}}_{4}\ifmmode\cdot\else\textperiodcentered\fi{}2{\mathrm{H}}_{2}\mathrm{O}$, Cu2(C5H12N2)2Cl4{\mathrm{C}\mathrm{u}}_{2}({\mathrm{C}}_{5}{\mathrm{H}}_{12}{\mathrm{N}}_{2}{)}_{2}{\mathrm{C}\mathrm{l}}_{4}Cu2​(C5​H12​N2​)2​Cl4​, etc.