An Efficient Analytical Method for Determining Transition Temperatures in Core-Shell Spin Crossover Nanoparticles Described by an Extended Ising-Like Model

Abstract

This contribution is dedicated to the analysis of the size and interaction parameters effects on the thermal properties of square-shaped cross-spin transition core-shell nanoparticles. The present study is carried out by varying the shell size at fixed core size and vice versa. In this problem, the core and shell are active from the spin transition point of view, while having different properties in terms of ligand field (transition temperatures) and interactions. The resulting nanoparticle is described by an Ising-type model including the three interaction parameters J_CC, J_SS and J_CS coupling core-core, shell-shell and core-shell sites, respectively. The thermodynamic investigations have been carried out in 3 different ways: (i) by Monte Carlo Entropic Sampling (MCES) for small size nanoparticles ($$ ) (ii) by usual Monte Carlo Metropolis for higher dimensions (iii) by an analytical method deducing the equilibrium temperature of the system from the various local environments. We demonstrate that, as long as a clear plateau region occurs in the thermal-dependence of the high-spin fraction, an excellent agreement is obtained, allowing to predict analytically the evolution of the transition temperatures. The limitations of the method are discussed in the case of strong interference between the thermal dependences of the core and shell.