Enhanced Cooperative Interactions at the Nanoscale in Spin-crossover Materials with a First-order Phase Transition

We analyzed the size effect on a first-order spin transition governed by elastic interactions. This study was performed in the framework of a nonextensive thermodynamic core-shell model. When decreasing the particle size, differences in surface energies between the two phases lead to the shrinking of the thermal hysteresis width, the lowering of the transition temperature, and the increase of residual fractions at low temperature, in good agreement with recent experimental observations on spin transition nanomaterials. On the other hand, a modification of the particle-matrix interface may allow for the existence of the hysteresis loop even at very low sizes. In addition, an unexpected reopening of the hysteresis, when the size decreases, is also possible due to the hardening of the nanoparticles at very small sizes, which we deduced from the size dependence of the Debye temperature of a series of coordination nanoparticles.