Estimating the Ising interaction in spin-crossover compounds

I previously discussed how one of the simplest model effective Hamiltonians that can describe many physical properties of spin-crossover compounds is an Ising model in an external "field". The s_i=+/-1 is a pseudo-spin denoting the low-spin (LS) and high-spin (HS) states of a transition metal molecular complex at site i.
The ``external field" is one half of the Gibbs free energy difference between the LS and HS states. The physical origin of the J interaction is ``believed to be'' elastic, not magnetic interactions. A short and helpful review of the literature is by Pavlik and Boca.

Important questions are:

1. What is a realistic model that can explain how J arises due to elastic interactions?
2. How does one calculate J from quantum chemistry calculations?
3. How does one estimate J for a specific material from experimental data?
4. What are typical values of J?

I will focus on the last two questions.
One can do a mean-field treatment of the Ising model, leading to a model free energy for the whole system that has the same form as that of an ideal binary mixture of two fluids where
x = (1 + av(s_i))/2, is the relative fraction of low spins. 
This model free energy was proposed in 1972 by Slichter and Drickmamer.
The free energy of interaction between the two "fluids" is of the form -Gamma x^2.
Gamma is often referred to as the ``co-operativity" parameter.
Minimising the free energy versus x gives a self-consistent equation for x(T).
This can be compared to experimental data for x vs T, e.g. from the magnetic susceptibility, and a Gamma value extracted for a specific material.

Values for Gamma obtained in this way for a wide-range of quasi-one-dimensional materials [with covalent bonding (i.e. strong elastic interactions) between spin centres] are given in Tables 1 and 2 of Roubeau et al. The values of Gamma are in the range 2-10 kJ/mol. In temperature units this corresponds to 240-1200 K.

My calculations [which may be wrong] give that Gamma = 4 J z, where z is the number of nearest neighbours in the Ising model. This means that (for a 1d chain with z=2) that J is in the range of 0.3-1.5 kJ/mol, or 30-150 K.

In many spin-crossover materials, the elastic interactions are via van der Waals, hydrogen bonding, or pi-stacking interactions. In that case, we would expect smaller values of J.
This is consistent with the following.
An analysis of a family of alloys by Jakobi et al. leads to a value of Gamma of 2 kJ/mol.
[See equation 9b. Note B=Gamma=150 cm^-1.  Also in this paper x is actually denoted gamma and x denotes the fraction of Zn in the material.].

I thank members of the UQ SCO group for all they are teaching me and the questions they keep asking.

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