Phenomenological modeling of molecular-based rings beyond the strong exchange limit: Bond alternation and single-ion anisotropy effects

Non-perturbative approaches, namely numerically exact diagonalization and quantum transfer matrix (QTM) technique, are applied to Heisenberg spin systems to model antiferromagnetic ring-shaped molecules. The Hamiltonian assumed includes the single-ion anisotropy and alternating nearest-neighbor exchange integrals (JoJo and Je=αJoJe=αJo for “odd” and “even” pairs, respectively). Using these techniques and exploiting the Hamiltonian symmetry group, we have been able to perform numerically exact calculations beyond the strong exchange limit for relatively large spin systems. Two antiferromagnetic spin systems have been considered: (i) 12 spins s=1s=1 and (ii) eight spins s=3/2s=3/2. In the first case, the energy spectra in the presence of single-ion anisotropy and magnetic field have been calculated using the results of the exact diagonalization. The anisotropy-dependent splitting and the field-dependent crossing of energy levels are presented and analyzed. The efficiency of QTM method is demonstrated for the spin s=3/2s=3/2 ring, corresponding to a Cr8 molecule. The susceptibility and specific heat have been found to depend mainly on the mean value of the exchange integrals J¯=(Jo+Je)/2. When J¯ is fixed, the alternation of the couplings is significant only when parameter αα is much larger or much smaller than 1.

Graphical abstractPerforming non-perturbative calculations we determined a dense structure of energy levels for a dozen antiferromagnetically-coupled s = 1 spins with the single-ion site-independent anisotropy. [Attached plot is made for J = 8.5 K, g = 2.13, D/J = 0.1.]Figure optionsDownload full-size imageDownload as PowerPoint slide