First order high-spin/low-spin phase transition induced by acoustic-phonons

A model for high spin/ low spin transitions in solid is presented. It is assumed that interaction between molecules is only due to the dependence of the crystal elastic constants on the electronic states of the molecules. This work is performed for a linear chain of molecules modeled as atoms each with two electronic states. Only adjacent atoms are linked by springs. We suppose that the elastic force constant of the springs can have three values, corresponding to the electronic states of the particular atoms. In this article, we obtain the exact expression for the Hamiltonian of the atom-phonon coupling assumed. We then deduce that this coupling creates an effective field on each atom and an exchange-like interaction between the two first neighbouring atoms. Here we only study the effect of the field. The phase diagram for the chain is established. We show that the chain does or does not exhibit a first order transition, depending on the elastic force constant values. The results obtained in this study could be used for chain-like spin conversion compounds, or for any spin conversion compound if we assume that only one type of spring (e.g. those linking nn, or nnn, etc.) have an elastic force constant which varys with the electronic states of atoms linked by such springs.