Simple Two-Dimensional Model for the Elastic Origin of Cooperativity among Spin States of Spin-Crossover Complexes

We study the origin of the cooperative nature of spin crossover (SC) between low spin (LS) and high spin (HS) states from the view point of elastic interactions among molecules. As the size of each molecule changes depending on its spin state, the elastic interaction among the lattice distortions provides the cooperative interaction of the spin states. We develop a simple model of SC with intra and intermolecular potentials which accounts for the elastic interaction including the effect of the inhomogeneity of the spin states, and apply constant temperature molecular dynamics based on the Nos\'e-Hoover formalism. We demonstrate that, with increase of the strength of the intermolecular interactions, the temperature dependence of the HS component changes from a gradual crossover to a first-order transition.Comment: 4 pages, 4 figure

A Unified Theoretical Description of the Thermodynamical Properties of Spin Crossover with Magnetic Interactions

After the discovery of the phenomena of light-induced excited spin state trapping (LIESST), the functional properties of metal complexes have been studied intensively. Among them, cooperative phenomena involving low spin-high spin (spin-crossover) transition and magnetic ordering have attracted interests, and it has become necessary to formulate a unified description of both phenomena. In this work, we propose a model in which they can be treated simultaneously by extending the Wajnflasz-Pick model including a magnetic interaction. We found that this new model is equivalent to Blume-Emery-Griffiths (BEG) Hamiltonian with degenerate levels. This model provides a unified description of the thermodynamic properties associated with various types of systems, such as spin-crossover (SC) solids and Prussian blue analogues (PBA). Here, the high spin fraction and the magnetization are the order parameters describing the cooperative phenomena of the model. We present several typical temperature dependences of the order parameters and we determine the phase diagram of the system using the mean-field theory and Monte Carlo simulations. We found that the magnetic interaction drives the SC transition leading to re-entrant magnetic and first-order SC transitions.Comment: 30pages, 11figure

Asymmetric self-organization accompanying a thermoinduced spin transition with symmetry breaking: Microscopic modeling

International audienceA microscopic elastic model allowing a symmetry breaking upon a spin transition is developed based on competing interactions between the nearest and next-nearest neighbors. The model yields a structurally degenerated high-spin state with a diamond-shaped cell and a nondegenerated low-spin state with a square-shaped cell. We investigated the effect of the symmetry change of the unit cell on the thermoinduced spin transition by monitoring the ratio of the elastic energies involved in the nearest and next-nearest neighbors. The simulations are performed on a deformable two-dimensional lattice made of spins S=±1 (representing the high-spin and low-spin molecules) coupled with springs. The numerical resolution of the model is based on the Monte Carlo metropolis approach, running on spins and positions variables. The simulations of the thermoinduced spin transition disclose asymmetric thermal hysteresis loops with quite different domain distributions on the heating and cooling branches. The analysis of the magnetic and structural properties pointed out that the spin transition with symmetry breaking is dependent on the sign of the thermal gradient. We demonstrated that the nucleation and growth process of spin domains might contrast with the structural self-organization of the lattice according to the energetic contribution of the symmetry breaking. Indeed, the examination of the spatial organization aspects revealed that the structural and elastic anisotropy in the lattice hinders the long-range character of the intermolecular interactions. The lattice configurations show a labyrinthlike structure during a transition from high-symmetry to low-symmetry phases and a multidomain structure upon a transition in the other way around regardless of the spin state in both phases. Furthermore, we found that thermal fluctuations have a crucial role depending on the thermal gradient and on the direction of evolution of the symmetry (reducing or increasing). We demonstrated that stepped and even incomplete spin transitions could be obtained by adjusting the elastic contribution responsible for the symmetry breaking

Aspects spatio-temporels de la transition de spin

Ce travail présente l'étude des aspects spatio-temporels de la transition de spin dans des monocristaux de composés du Fe(II). Les observations par microscopie optique ont permis de suivre en temps réel la germination et la croissance des domaines de spin ainsi que la propagation de l'interface macroscopique. L analyse de ces observations a permis de discuter les aspects spatiotemporels de cette propagation et de proposer un mécanisme multi-échelle pour décrire la transition. L étude d un système dinucléaire robuste a démontré la possibilité de créer et de contrôler le mouvement de l interface par des excitations extérieures et d établir un accès direct à la température d équilibre de la transition. Enfin, un modèle électro-élastique donnant accès à l étude des champs de déplacement et de déformations a été proposé et les premiers résultats sont encourageants et cohérents avec les résultats expérimentaux.This work presents the results of investigations of the spin transition on single crystals of iron(II) compounds. Observations by optical microscopy allowed to follow in real time the germination and growth of spin domains as well as the propagation of the macroscopic interface. A careful analysis of these observations allowed to discuss the spatiotemporal aspects of the interface propagation, and a multiscale mechanism of the transition was proposed. The study of a robust binuclear system provided the possibility of creating and controlling the motion of the interface by external excitations and gave a direct access to the equilibrium temperature. Finally, an electro-elastic model giving access to the displacement and deformation fields was proposed, the first results of which are encouraging, and consistent with the experimental data.VERSAILLES-BU Sciences et IUT (786462101) / SudocSudocFranceF

Pressure-induced multi-step and self-organized spin states in an electro-elastic model for spin-crossover solids

International audienceThe spin transition materials are known to exhibit a rich variety of behaviours under several stimuli, among which the pressure leads to major changes in their electronic and elastic properties. From the experimental point of view, thermal spin transitions under isotropic pressure showed transformations from (i) hysteretic to continuous transformations where the hysteresis width vanishes beyond some threshold pressure value; that is the conventional case. In several other cases very pathological and unexpected behaviours emerged, like (ii) persistent hysteresis under pressure; (iii) non uniform behavior of the thermal hysteresis width which first increases with pressure and then decreases and vanishes at higher pressures; (iv) also double step transitions induced by pressure are also often obtained, where the pressure triggers the appearance of a plateau during the thermal transition, leading to two-step transitions, and finally (v) other non-conventional re-entrant transitions, where the thermal hysteresis vanishes at some pressure and then reappears at higher pressure values are also observed. In the present theoretical study, we investigate this problem with an electro-elastic description of the spin-crossover phenomenon by solving the Hamiltonian by Monte Carlo technique. The pressure effect is here introduced directly in the lattice parameters, the elastic constants and ligand field energy. By considering spin state-dependence compressibility's, we demonstrate that a large panel of experimental observations can be qualitatively described with this model. Among them, we quote (i) the conventional pressure effect decreasing the hysteresis width, (ii) the unconventional cases with pressure causing a non-monotonous behaviour of the hysteresis width, (iii) re-entrant, as well as (iv) double step transitions accompanied with various types of spin state self-organization in the plateaus regions

Theoretical investigations on the pressure effects in spin-crossover materials: Reentrant phase transitions and other behavior

International audiencePressure effects have been widely studied in spin-crossover (SCO) solids due to their immediate influence on the thermal dependence of the high-spin (HS) fraction. In most of the cooperative SCO materials, the applied pressure shifts the transition temperatures upward and decreases the thermal hysteresis widths to such an extent that it vanishes at some critical pressure. However, several other unexpected experimental features were found in the literature, showing that the applied pressure may (i) induce an increase of the thermal hysteresis width or even (ii) lead to a reentrant behavior on the thermal hysteresis whose width first increases for low applied pressures and then decreases at high-pressure values. These nonstandard behaviors have been classified as anomalous, even though the transition temperature always increases under pressure. In this theoretical contribution, we rationalize all these behaviors by describing the spin-crossover system under pressure with an elastic description accounting for the difference of lattice parameters between the low-spin (LS) and HS phases including the pressure effects. The analytical study of this elastic model in the homogeneous mechanical system demonstrated its isomorphism with an Ising-like model with infinitely long-range interactions, in which the pressure acts linearly on the ligand field and nonlinearly on the strength of the interactions. The resolution of this model brings to light the existence of a pressure-induced interplay between these two contributions allowing one to recover a wide range of normal and abnormal observed experimental thermal dependences of the spin transition under pressure

Microscopic electroelastic modeling of a spin transition with symmetry breaking

International audienceA theoretical approach combining Monte-Carlo and molecular-dynamics techniques is developed to deal with the structural anisotropy upon the spin transition in molecular materials. The simulations were done on a 2D lattice, where the cells have two structural symmetries: square-shaped (non-degenerated) at a low spin (LS) state and a diamond-shaped (degenerated) at a high spin (HS) state. We investigated the thermally induced spin transition and the relaxation of a metastable HS state trapped at low temperatures. We demonstrated that the structural parameters have a crucial impact on the spin transition, and by adjusting the lattice and the elastic parameters, we were able to generate a two-step thermally induced spin transition. The analysis of magnetic and structural properties pointed out that the symmetry breaking reduces significantly the cooperativity between the lattice’s cells. The maps of the difference between cell diagonals reveal an auto-organized HS lattice with an alternation of different symmetries over the state, confirming the symmetry breaking when switching from an LS to HS state. The mechanical relaxation of an LS lattice containing HS defects shows an anisotropic distribution of the elastic energy, channelized over the shortest paths toward the borders of the lattice. The interaction between two HS defects placed in a LS lattice is as well investigated as a function of their separating distance for different symmetries of the HS state. We demonstrated that the HS symmetry impacts the HS/LS elastic barrier as well as the dependence of the relaxed elastic energy on the distance separating two HS defects introduced in an LS lattice