Simple Two-Dimensional Model for the Elastic Origin of Cooperativity among Spin States of Spin-Crossover Complexes

We study the origin of the cooperative nature of spin crossover (SC) between low-spin and high-spin (HS) states from the viewpoint of elastic interactions among molecules. As the size of each molecule changes depending on its spin state, the elastic interaction among the lattice distortions provides the cooperative interaction of the spin states. We develop a simple model of SC with intra and intermolecular potentials which accounts for the elastic interaction including the effect of the inhomogeneity of the spin states and apply constant temperature molecular dynamics based on the Nosé-Hoover formalism. We demonstrate that, with increase of the strength of the intermolecular interactions, the temperature dependence of the HS component changes from a gradual crossover to a first-order transition.

Figure 1

(a) A schematic picture of the LS molecule and the HS molecule. The HS molecule is bigger than the LS molecule. (b) [(c)] shows a schematic picture of the lattice distortion for a HS (LS) molecule and surrounding LS (HS) molecules.

Figure 2

(a) A schematic picture of the model. ($X$, $Y$) is the coordinate of the center of each molecule and $r$ is its radius. (b) Intramolecular potential, where $x$ is the growth of $r$ from $r_{\mathrm{LS}}$. (c) Temperature dependence of $⟨x⟩$ without intermolecular interactions.

Figure 3

Temperature dependences of $⟨x⟩$ for the values of (a) $D=10$, (b) $D=20$, (c) $D=28$, and (d) $D=42$. The open red circles (blue squares) denote $⟨x⟩$ in the warming (cooling) process.

Figure 4

Snapshots of configurations. HS molecules (red circles) are allocated when $r$ is larger than $r=r_{\mathrm{LS}}+x_c$. LS molecules are drawn by blue circles. (a) Complete LS phase. (b) Complete HS phase. (c) A snapshot of configuration at $T=0.6$ in the system of $D=10$ ($L^2={16}^2$), where 80 molecules are in the HS state. (d) A snapshot of configuration at $T=1.0$ in the system of $D=42$ ($L^2={16}^2$), where 79 molecules are in the HS state.