Magnetisation of a zero-field splitting system

For a low temperature and high fields the zero-field splitting systems are no longer linear magnetics. The thermal energy kT is of the order of the 

Formulae for the susceptibility contributions of zero-field splitting systems 

Let us consider an S = 2 system under the constraint of E = 0. The energy levels (Table 8.22) can be substituted into the partition function so that 

No expansions of the exponentials are permitted. The approximation for the mean susceptibility 

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