Integrable models and quantum spin ladders: comparison between theory and experiment for the strong coupling ladder compounds

Abstract

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.

Acknowledgements

This work has been supported by the Australian Research Council through the Discovery and Linkage International programs and the Japanese Society for the Promotion of Science (JSPS) Bilateral Joint Project “Solvable models and their thermodynamics in statistical mechanics and field theory”. Z. Tsuboi was partially supported by a JSPS Grant-in-Aid for Scientific Research (no. 16914018). N. Oelkers has also been supported by DAAD during the early stages of this work. We thank A. Foerster, M. Orendáč, M. Shiroishi, Z.-J. Ying and H.-Q. Zhou for helpful discussions. The authors thank M. Takahashi and M. Shiroishi for their kind hospitality at the Institute for Solid State Physics at the University of Tokyo where part of this work was undertaken.