Homospin dinuclear systems

For the exchange coupling of homospin systems the allowed molecular states lie between 

In this fortunate case the zero-field Hamiltonian is diagonal, giving rise to energy levels 

Since the (spin) Zeeman operator in the basis set of coupled spin angular momenta functions S Ms) is diagonal as well, then the magnetic energy levels are easy to generate (Table 10.8) 

Energy levels es for a dinuclear homospin system in zero field 

In evaluating the magnetic susceptibility one can apply the magnetisation formula (Chapter 2). Because the second-order derivatives are zero for the isotropic exchange model, a simplification is obtained 

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There are 21 combinations of heterospin dinuclear systems between SA = 1/2 and SB = 7/2 local spins. The zero-field energy levels of the coupled systems can be generated in the same way as in the previous case of homospin systems. The result is... 

Fig. 10.6. Magnetisation per dimer versus the applied field for dinuclear homospin systems at T = 4.2K J/k = — 5K (solid), J/k— — 10K (long dashed), J/k = —20K (medium dashed), J/k = — 30 K (short dashed).

Characteristic susceptibility functions for dinuclear homospin systems SA = SB SA F(x)... 

Isotropic exchange in heterospin dinuclear complexes differs from the homospin case in that the second-order van Vleck coefficients are also non-zero. The final formula for the magnetic susceptibility resembles the case of the narrow multiplets for mononuclear systems spin-orbit coupling can be formally substituted by spin-spin (exchange) coupling. However, the local atomic g-tensors should be properly combined into the molecular-state g-tensor. 

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