Molecules with Two Electronic Energy Levels: Study of Nanoparticles in the Atom-Phonon Coupling Model Including a Surface Effect

We discuss a two-dimensional model that leads to results which reproduce, at least qualitatively, some of the experimentally observed features of spin-conversion compounds. The molecules of these compounds have two electronic energy levels separated by Δ. The values of the elastic constants of the springs contained in the molecules are lower in the upper level. Consequently, the phonon branches of the crystal depend on the electronic states of the molecules. The fundamental level is a low spin (LS) state and the excited one is a high spin (HS) state. We study the thermal variation of the high spin fraction, i.e., the fraction of molecules in the (HS) level by using a model of atom-phonon coupling with a boundary effect: Δ = Δ_b for molecules within the bulk, and Δ = Δ_se < Δ_b for molecules on the boundary. These values are compound-dependent, but independent of the size of the crystal. Our results qualitatively reproduce two seemingly contradictory experimental results as well as the disappearance and reappearance of the hysteresis loop that is observed when the number N of molecules of the crystal is very small. Our model explains why the width of the hysteresis loop decreases with decreasing N. We find that, for any number of molecules, the entropy of the crystal vanishes at 0 K, in accordance with the third law of thermodynamics.