Two-variable anharmonic model for spin-crossover solids: A like-spin domains interpretation

Abstract

Spin-crossover (SC) complexes are one of the most fascinating examples of molecular bistability, whose solid-state properties are tightly connected to cooperative interactions within the crystal lattice. A variety of macroscopic and microscopic models have been developed to explore the cooperative nature of the SC phenomenon. We present here a two-variable microscopic Ising-like model for SC solids, accounting for the elastic origin of the cooperativity using coupled spin and translational (lattice) degrees of freedom. Within our model, the interaction between a pair of neighboring molecules in the crystal is dependent not only on their spin states but also on their separation distance, modeled by spin-dependent Lennard-Jones (LJ) potentials. This scheme leads explicitly to local variations in the interactions, associated to the local strain induced by the molecules changing their spin state. In essence, the LJ potentials provide the anharmonicity of the crystal lattice. The equilibrium (quasistatic) properties of the proposed Hamiltonian are analyzed by Monte Carlo simulations on a regular deformable square lattice. We show that the spin dependence of the LJ potentials breaks the spin-state symmetry in the free energy. The interplay between spin and lattice degrees of freedom shows itself in the temperature evolution of the fraction of high-spin molecules and the mean lattice spacing, as a function of the intersite coupling. For strong coupling, like-spin domains nucleate and develop, evidenced by a double structure in the distribution of lattice spacings; structural relaxation occurs at the domain walls. In the weakly cooperative situation, the mean lattice constant scales directly with the fraction of high-spin species; structural relaxation spans the entire system.