Integrable Models and Quantum Spin Ladders: Comparison Between Theory and Experiment for the Strong Coupling Ladder Compounds

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-[image omitted] and the mixed spin-([image omitted]) 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-[image omitted] ladder model exhibits three quantum phases: (i) a gapped phase in the regime [image omitted], (ii) a fully polarized phase for [image omitted], and (iii) a Luttinger liquid magnetic phase in the regime Hc1HHc2. The critical behaviour in the vicinity of the critical points Hc1 and Hc2 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\O2)(C10H8N2)2)](NO3)2. Similar analysis of the mixed spin-([image omitted]) ladder model reveals a rich phase diagram, with a [image omitted] 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 Land g-factors