Surface Effects Leading to Unusual Size Dependence of the Thermal Hysteresis Behavior in Spin-Crossover Nanoparticles

Jorge Linares,Kamel Boukheddaden,Catalin Jureschi

doi:10.3390/magnetochemistry2020024

Abstract

We analyze the size effect on spin-crossover transition nanoparticles in a 2D Ising-like model subject to a specific ligand-field at the surface. By anisotropic sampling method applied to the finite 2D square Ising lattices with various sizes, we determined the density of macro states by scanning the spin configurations. This information, which is independent on the system parameters, is used to exactly calculate the thermal behavior of spin-crossover nanoparticles whose ligand-field of the atoms at the surface is lower than those of the bulk. We found that decreasing the size of the nanoparticles leads to a global increase of the effective interaction, which has the consequence to enhance the width of the thermal hysteresis. This unusual behavior opens a new avenue in controlling the bistability characteristics at small scale, one of the important conditions of applicability of these materials at the nanometric scale.

Highlights

In recent years, there has been a growing interest in the field of spin-crossover (SCO) solids
E(HS) – E(LS) between the spin states of isolated molecules, and J is the coupling parameter accounting for short-range ferroelastic interactions between spin states, here limited to first-neighboring molecules; and G is the long-range part of the interaction, which is identified as due to lattice phonons and volume change accompanying the transition
The energetic contribution L (>0), limited to surface atoms, Magnetochemistry 2016, 2, 24 describes the additional “negative” ligand-field felt by the surface atoms. This contribution may arise from coordinated water molecules which substitute to one or several nitrogen atoms linked to the Fe center, or may be due to the elastic effect of the surrounding polymeric matrix

Summary

Introduction

There has been a growing interest in the field of spin-crossover (SCO) solids. The samples usually present a rather wide distribution of sizes, various shapes, and particles were often aggregated in various manners All of these features obviously impact the switching behavior of the SCO nanoparticles and made the investigation on the properties of a unique nanoparticle a very challenging goal. We introduce an additional aspect, which is the specific electronic state of the atoms located at the surface of the nanoparticle This was suggested by a recent experimental investigation [26], on SCO nano-particles of Fe(pyrazine)[Pt(CN)4], with well-controlled sizes above and below the critical size. In addition to the expected narrowing of the hysteresis loop upon decreasing size, this system displayed a sizable lowering of the transition temperature and an increase of the residual HS fraction The latter features are explained by the different coordination of the surface atoms, including water molecules instead of the organic ligands. The paper is organized as follows: Section 2 is devoted to the model; Section 3 to the results and their discussion; Section 4 is dedicated to a detailed comparison to experimental data, including the impact of size distributions, and Section 5, to our conclusion

Results

TGp h f mi

Monte Carlo Entropic Sampling

Results and Discussion

Size Dependence of the Equilibrium Temperature