Utilization of the Spin Symmetry in Fitting the Magnetic Data lor Large Exchange Clusters

Abstract

The Heisenberg Hamiltonian appropriate to exchange clusters commutes with the square of the total spin ant its third component. Therefore in studying the exchange coupled clusters of medium/high nuclearity the spin quantum number S can be utilized in factoring of large interaction matrices (dimension of which is 10⁴ - 10⁵). Then the blocks of much lower size can be diagonalized using the desktop computers. To this end, the eigenvalues form the partition function Z(T,B) from which all thermodynamic properties, including the magnetization M(B,T₀) and the magnetic susceptibility _χ(T,B₀), can be reconstructed. The matrix elements of the interaction operators in the coupled basis set of spin kets have been generated with the help of the irreducible tensor operators for a loop for S = S_min until S = S_max. In addition to the modelling of energy levels for different topologies, a fitting of magnetic data is exemplified by a number of examples like [Fe₆] and [Mn₃Cr₄] systems.