Interplay between elastic interactions in a core-shell model for spin-crossover nanoparticles

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A coupled spin deformation model for spin-crossover (SC) materials, consisting of distortable 2D square-shaped lattices, whose sites may be occupied by high-spin $(\mathrm{HS})$ or low-spin $(\mathrm{LS})$ atoms, is studied by Monte Carlo simulations. To be consistent with the experimental studies, we have studied shell-free and core-shell nanoparticles. In the case of shell-free nanoparticles, we constrained the surface of the nanoparticle (one layer) to be in the $\mathrm{HS}$ state from the electronic and the elastic point of view because the surface atoms have weaker ligand-field energy than those of the bulk. We then investigated the size effects and found that the thermal hysteresis width $\ensuremath{\Delta}T$ and the transition temperature ${T}_{\mathrm{eq}}$ follow the respective universal laws, $\ensuremath{\Delta}T\ensuremath{\propto}\sqrt{(L\ensuremath{-}{L}_{0})}$ and ${T}_{\mathrm{eq}}\ensuremath{\propto}\sqrt{\mathrm{ln}(L\ensuremath{-}{L}_{c})}$, where $L$ is the nanoparticle size. These laws hold independently of the sweeping rate of temperature. In a second stage, we studied the effect of a soft shell on the thermal properties of the core shell nanoparticle for which we have investigated the thermodynamic properties at various sizes of the shell. We find that the thermal hysteresis shifts downwards and the corresponding width increases; a result that contrasts with that of shell-free nanoparticles. In addition, we have observed that large shell size widths hinder the domain formation upon the first-order transition, although the transition is still of first order. These behaviors originate from the elastic stress produced by the shell on the bulk of the nanoparticle, and are identified through the spatial distribution of the internal stress upon the thermal transition. Moreover, we studied the effect of the shell size on the relaxation of the photoinduced metastable HS fraction at low temperature. At this end, a preliminary optimization of the structure of the nanoparticle is performed. We then evidenced that increasing the size of the shell results in an acceleration of the relaxation process. This behavior is in excellent agreement with recent data reported on core shell nanoparticles of Prussian Blue analogs.