Interplay Between Heisenberg and Anderson Models

Consider a dimeric unit built up from two ions in octahedral sites, with the overall symmetry D3h. We assume on each site one unpaired electron corresponding to the 2T2g ground-term. Further, only exchange mechanisms involving similar t2g orbitals for both ions are considered. Direct or superexchange-like 

A tedious though straightforward calculation thus leads to the expression of the exchange Hamiltonian  

The first term of this operator describes the exchange when one neglects the intra-ionic spin-spin coupling while the second one takes it into account precisely ( extended Anderson model). 

Obviously, this Hamiltonian shows drastic differences with the Heisenberg expression. To compare the results of this approach, for = J2 and Jj =t= J2, to those of the Heisenberg Hamiltonian, we define a new set of parameters  

From the respective energy diagrams (Fig. 2), it can be emphasized that  

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