Minimal effective Hamiltonian for spin-crossover materials

My colleagues and I just put a preprint on the arXiv. I am particularly proud of it.  As always, comments would be appreciated.

Equivalence of elastic and Ising models for spin-crossover materials

Gian Ruzzi, Jace Cruddas, Ross H. McKenzie, Ben J. Powell 

Spin crossover (SCO) materials are reversible molecular switches; and occur in a wide range of near octahedral transition metal complexes and frameworks with d4−d7 electron configurations. SCO systems present collective spin-state phase transitions that show hysteresis, multistep transitions, gradual transitions, and anti-ferroelastic phases. Ising models have often been employed to model these behaviors, as they are far easier to solve than more realistic elastic models. However, previously Ising models have required phenomenological parameters that do not have a clear physical origin. 

We present an exact mapping from an elastic model of balls and springs to the Ising model. The resulting Ising coupling constants arise only from the elastic interactions, and are independent of the lattice dynamics, i.e., there are no isotope effects. The elastic interactions, and hence the Ising coupling constants can be determined from the measurements of the bulk and shear moduli. The Ising coupling constants can be frustrated, their signs can be negative or positive, and their magnitude agrees well with previous estimates from fits of experimental spin-transition curves. The Ising coupling constants follow a power law for large separations between metal centers, in particular an inverse square law for the square lattice. For the square lattice with nearest neighbor elastic interactions this model predicts a diverse range of spin-state orders including multistep transitions.

 


Comments

  1. AnonymousAugust 27, 2020 at 9:59 PM

    Nice paper- I have two questions (from a chemistry point of view). Hopefully not too dumb :-)

    1) Imagine we are dealing with a pressure-induced spin-state transition in a molecule based material. I'd expect a huge difference in stiffness between the metal-ligand bonds and the intermolecular contacts. The former (stiff) control the crystal-field and hence spin-state, and the latter (soft) control the percolation of order between sites. I don't quite understand how your model accounts for the very different responses of these to the 'control' parameter? This actually gets more complicated in materials which dimerise at a pressure-induced spin-state transition.

    2) What is the relevance (if any) of your model to materials which also undergo metallisation at the spin-state transition?

    ReplyDelete
  2. Ross H. McKenzieSeptember 7, 2020 at 10:45 AM

    Thanks for your interest and your excellent questions.

    1) Our model is specifically for metal-organic frameworks (where there is only one type of bond M-L-M, i.e. the ligand is shared between two metals). This different from the (more common) class of materials you describe, which might be represented M-L...L-M. We also working on a model for them.

    Nevertheless, some of the physics may be similar. Delta H (and probably Delta S) in our model should have some pressure dependence – which would account for the changes in the inner coordination sphere whereas competition between k and the external pressure would account for changes in the outer coordination sphere.

    2) Are you thinking about Prussian blue analogues or similar materials? The microscopic physics is importantly different – so our model is not directly relevant.

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