We consider the spin-1/2 antiferromagnetic Heisenberg model on three frustrated lattices (the diamond chain, the dimer-plaquette chain, and the two-dimensional square-kagome lattice) with almost dispersionless lowest magnon band. Eliminating high-energy degrees of freedom at high magnetic fields, we construct low-energy effective Hamiltonians, which are much simpler than the initial ones. These effective Hamiltonians allow a more extended analytical and numerical analysis. In addition to the standard strong-coupling perturbation theory, we also use a localized-magnon-based approach leading to a substantial improvement of the strong-coupling approximation. We perform extensive exact diagonalization calculations to check the quality of different effective Hamiltonians by comparison with the initial models. Based on the effective-model description, we examine the low-temperature properties of the considered frustrated quantum Heisenberg antiferromagnets in the high-field regime. We also apply our approach to explore thermodynamic properties for a generalized diamond spin chain model suitable to describe azurite at high magnetic fields. Interesting features of these highly frustrated spin models consist in a steep increase of the entropy at very small temperatures and a characteristic extra low-temperature peak in the specific heat. The most prominent effect is the existence of a magnetic-field-driven Berezinskii-Kosterlitz-Thouless phase transition occurring in the two-dimensional model.

• Received 15 April 2013

DOI:https://doi.org/10.1103/PhysRevB.88.094426