Critical temperature and correlation length of an elastic interaction model for spin-crossover materials

Abstract

It has previously been pointed out that the coexistence of infinite-range and short-range interactions causes a system to have a phase transition of the mean-field universality class, in which the cluster size is finite even at the critical point. In the present paper, we study this property in a model of bistable molecules, whose size changes depending on the bistable states. The molecules can move in space, interacting via an elastic interaction. It is known that due to the different sizes, an effective long-range interaction between the spins appears, and thus this model has a mean-field type of phase transition. It is found that the scaling properties of the shift of the critical temperature from the pure short-range limit in the model with infinite-range and short-range interactions hold also in the present model, regarding the ratio of the size of the two states as a control parameter for the strength of the long-range interaction. By studying the structure factor, it is shown that the dependence of the cluster size at the critical temperature also shows the same scaling properties as a previously studied model with both infinite-range and short-range interactions. We therefore conclude that these scaling relations hold universally in hybrid models with both short-range and weak long-range interactions.

Spatially Resolved Investigation and Control of the Bistability in Single Crystals of the [Fe(bbpya) (NCS)2] Spin Crossover Complex

“…This behavior was considered from the early stages of SCO research, [2][3][4] but it was first explicitly demonstrated using single crystal X-ray diffraction only in 2004. [5][6] Recently, these phenomena have been studied in detail by optical microscopy in some SCO crystals and several theoretical models [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] have also been proposed to describe the experimental observations.…”

Cooperative phenomena in spin crossover systems

“…For example, if we consider the usual Lennard-Jones potential between molecules which depends on the spin states, the model has both elastic and short-range interactions [72]. Competition and interplay between the short-range and long-range interactions are interesting topics in phase transitions [73][74][75][76][77][78][79][80]. In the pure short-range model, clustering of the ordered phase takes place near the critical temperature, leading to the divergence of the correlation length of the order parameter.…”

“…However, the long-range interaction suppresses the generation of domains, and the configuration is uniform even at the critical temperature [43]. This effect should be experimentally observable as an absence of critical opalescence [43,79,80]. Phase transitions in such systems belong to the mean-field universality class.…”

Consequences of Lattice Mismatch for Phase Equilibrium in Heterostructured Solids

“…Thermodynamic potentials with indefinite convexity, and their implications for phase coexistence, are similarly anticipated as generic consequences of the elastic forces attending lattice mismatch. Testing these predictions in the laboratory may be most straightforward for materials that can be manipulated more readily than the internal structure of nanocrystals, for instance assemblies of DNA-coated nanoparticles [28] or spin-crossover compounds [29][30][31][32][33][34], where elasticity is known to play a significant role.…”