Study of spin-conversion compound nanoparticles in the atom- phonon coupling model including a surface effect

We discuss a two dimensional model that is capable of reproducing, 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 crystal's phonon branches 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 = Δb for molecules within the bulk, and Δ = Δse < Δb for molecules on the boundary. These values are compound-dependent, but independent of the crystal's size. Our model reproduces qualitatively two seemingly contradictory experimental results as well as the disappearance and reappearance of the hysteresis loop that is observed when the number N of crystal's molecules is very small. Our model explains why the width of the hysteresis loop decreases with decreasing N. We find that for any N the crystal's entropy vanish at 0K, in accordance with the third law of thermodynamics.