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In this paper we review our results of comprehensive study of molecular nanomagnets recently synthesized in the form of the chromium-based molecules and bimetallic copper-containing chains as well as we present some new findings. We focus on effects of anisotropy, geometry and frustration appearing in various thermodynamic properties of the nanoscale magnets which are described by Heisenberg-like spin models and simulated by accurate numerical methods. We show that bond-dependent exchange anisotropy is needed to model magnetic torque in the Cd-doped chromium ring. We argue that only in the limit of infinite rings (n → ∞) frustration can be considered as the opposite to bipartiteness in the odd numbered (3 ⩽ n ⩽ 9) s = 3=2 quantum spin rings. We analyse the influence of exchange interactions and anisotropy on magnetic susceptibility of bimetallic (S = 3=2, s = 1=2) chains composed of Cu ions linked to di_erent 3d ions by _tting experimental data. We reach the remarkable consistency of the density functional theory estimates of the magnetic couplings in Cr8 molecule and provide strong support to the spin models exploited in the literature. [ABSTRACT FROM AUTHOR]

Quantum transfer matrix technique and numerically exact diagonalization method are applied to the Heisenberg spin systems to model ring-shaped molecules. Two cases are investigated: (i) a dozen of S = 1 spins with additional biquadratic exchange and (ii) a dimetallic molecule Cr7Cd, where it is assumed that exchange anisotropy is determined in a local coordination system. In the latter case the calculated susceptibility is compared with experimental results. [ABSTRACT FROM AUTHOR]

Abstract: We fitted the data obtained from the susceptibility measurement performed on polycrystalline samples with two different sets of microscopic parameters. One set (a) contains only single ion anisotropy and the other (b) both single ion and exchange anisotropy. None of them can be favored on the basis of powder experiment. We demonstrated by means of quantum transfer matrix and exact diagonalization calculations that parameters with only one type and those comprising two types of anisotropy lead to qualitatively different behavior of magnetic susceptibility and torque calculated for a mono crystal. On the microscopic level me observe that the first anti-crossing gap between the ground and first exited states vanishes when two types of anisotropies (single ion and exchange) of different orientation (easy axis and easy plane) and similar magnitude are present in the system. [Copyright &y& Elsevier]

Abstract: 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 ( and 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 and (ii) eight spins . 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 ring, corresponding to a molecule. The susceptibility and specific heat have been found to depend mainly on the mean value of the exchange integrals . When is fixed, the alternation of the couplings is significant only when parameter is much larger or much smaller than 1. [Copyright &y& Elsevier]