Coupling of the lattice to spin-crossover transitions

There is a very nice paper
Complete Set of Elastic Moduli of a Spin-Crossover Solid: Spin-State Dependence and Mechanical Actuation 
Mirko Mikolasek, Maria D. Manrique-Juarez, Helena J. Shepherd, Karl Ridier, Sylvain Rat, Victoria Shalabaeva, Alin-Ciprian Bas, Ines E. Collings, Fabrice Mathieu, Jean Cacheux, Thierry Leichle, Liviu Nicu, William Nicolazzi, Lionel Salmon, Gábor Molnár, and Azzedine Bousseksou

It investigates the spin-crossover in a specific compound with a suite of techniques, including x-ray diffraction, inelastic neutron scattering, and micro-electromechanical systems (MEMS).

The nice results reflect significant advances over the past few decades in neutron scattering and microfabrication.

The graph below shows the vibrational density of states of the Fe nuclei and the low-spin (LS) and high-spin (HS) states. Note how the LS modes around 50 meV (400 cm-1) soften significantly in the HS state. These modes are the Fe-N stretches in the octahedron. This softening is associated with a significant increase in entropy which helps drive the spin-crossover transition.
Note that there is a small parabolic part at low energies of a few meV.


The figure below is a "blow up" of the low energy data. 
The energy resolution is amazing! 
The graph shows the density of states divided by E^2. 
Why?
In an isotropic solid (or a powder such as used here) in the Debye model for phonons, the density of states is proportional to E^2 and the proportionality is determined by the speed of sound, v_D.



One clearly sees several things.
1. For E less than about 3 meV, the DOS is quadratic in E, as predicted by Debye.
2. The lattice softens with the spin-crossover.
3. The deviation from quadratic occurs at a smaller E for HS than LS.

The values of the speed of sound can be combined with the lattice constant to estimate the Debye frequency, which is roughly where the deviation from quadratic dependence should occur.
I have done this (since the authors don't appear to have) and one gets values of the order of a few meV, consistent with experiment.

From the speed of sound, one can also determine the Young's modulus. This can then be compared to the bulk modulus, which can be determined from MEMS. The values obtained by these different methods are consistent with one another.
Overall, the values of the bulk modulus for different spin-crossover complexes, of order 5-10 GPa, are comparable to those for organic molecular crystals.

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