3D elastic modeling of switchable spin transition nanoparticles: finite size scaling and surface–bulk interplay effect on thermal hysteresis

Abstract

Spin-crossover (SCO) nanoparticles (NPs) hold remarkable promise for their integration in the development of multifunctional nanodevices thanks to their switchable electronic and structural properties. However, the cooperative mechanisms that govern their behavior within three-dimensional lattices remain largely underexplored, particularly regarding surface-to-core interactions and size-dependent dynamics. In the present study, we investigate the equilibrium and nonequilibrium thermodynamic properties of fully switchable 3D cubic lattices of cooperative SCO NPs using an electro–elastic model, with a focus on the interplay between electronic, structural degrees of freedom, on the one hand and surface effects on the other hand. Our simulations reveal how the high-spin fraction n_HS evolves in space and time with temperature T for various NP sizes N, displaying thermal hysteresis whose width varies with size. Spatiotemporal configurations further highlight the various features of nucleation, growth, and propagation mechanisms of spin domains along the spin transition. A phase diagram linking transition temperatures to NP size reveals three distinct regimes—non-cooperative, crossover, and cooperative—with a bifurcation emerging at the onset of cooperative behavior. We quantify the interaction between surface and bulk contributions, showing that the thermal hysteresis width follows a non-linear dependence with respect to the penetration depth from the NP surface. Thus, surface and bulk contributions to the thermal hysteresis could be derived and their effect identified with respect to the NP size. The analysis of the spin–spin correlation function reveals a unique characteristic length that governs the spatial organization of spin states, whose value depends on NP size. By addressing the complex interplay between electronic, structural, and cooperative effects in 3D nanoparticle lattices, this work aims to help bridge the gap between theoretical modeling and practical implementation, paving the way for broader implementation of SCO nanomaterials into multifunctional devices.