Anisotropic planar Heisenberg model of the quantum heterobimetallic zigzag chains with bridged ReIV-CuIImagnetic complexes

Abstract

An anisotropic quantum planar Heisenberg model is proposed and thoroughly analyzed within the numerical density-matrix renormalization group approach. The model takes into account the site-dependent alternating directions of the local coordination system for the Re${}^{\mathit{IV}}$ ions and both the axial and the rhombic single-ion anisotropy terms. Thermodynamic properties of a simpler collinear model without the rhombic term and its Ising counterpart as well as some previous approximations for Re${}^{\mathit{IV}}$-ion-containing compounds are discussed to point out the importance of quantum effects and deficiencies of classical approaches. For the noncollinear model with the alternating uniaxial local $z$ axis tilted by the angle $\ensuremath{\theta}$ from the global chain axis formed by copper ions, some symmetries for the single-crystal susceptibilities are found. In the strong-anisotropy limit some striking maxima in the corresponding single-crystal $\ensuremath{\chi}T$ products are revealed and their relation to the experimental determination of the anisotropy parameters is emphasized. Some cases to which the collinear model for zigzag chains is fully applicable are indicated. Finally, fitting the reference experimental data for a powder sample of given chloro- and cyanobridged zigzag chains, the weaker magnetic coupling and the uniaxial single-ion anisotropy term parameters have been found. The corrected value of the ferromagnetic interaction parameter implies that for the cyanobridge compound the record of the highest superexchange through cyanide has not been beaten.