Search Results (12)

One-dimensional spin crossover (SCO) solids that convert between the low spin (LS) and the high spin (HS) states are widely studied in the literature due to their diverse thermal and optical characteristics which allow obtaining many original behaviors, such as large thermal hysteresis, incomplete spin transitions, as multi-step spin transitions with self-organized states. In the present work, we investigate the thermal behaviors of a system of two elastically coupled 1D mononuclear chains, using the electro-elastic model, by including an elastic frustration in the nearest neighbors (nn) bond length distances of each chain. The chains are made of SCO sites that are coupled elastically through springs with their nn and next-nearest neighbors. The elastic interchain coupling includes diagonal springs, while the nn inter-chain distance is fixed to that of the high spin state. The model is solved using MC simulations, performed on the spin states and the lattice distortions. When we only frustrate the first chain, we found a strong effect on the thermal dependence of the HS fraction of the second chain, which displays an incomplete spin transition with a significantly lowered transition temperature. In the second step, we frustrate both chains by imposing different frustration rates. Here, we demonstrate that for high frustration values, the thermal dependence of the total HS fraction exhibits multi-step spin transitions. The careful examination of the spin state structures in the plateau regions showed the coexistence of special dimerized ferro–antiferro patterns of type LL-HH-LL-HH along the first chain and HH-LL-HH-LL (H=HS and L=LS) along the second one, revealing that the two chains are antiferro-elastically coupled. This type of spatial modulation of the spin state and bond length distances is very attractive because it anticipates the possible existence of periodic structures in 2D lattices, made of alternate 1D SCO strings with HLHLHL structures, coupled in the ferro-like fashion along the interchain direction. Full article

We model the thermal effects in different 2D spin-crossover (SCO) square lattices within the frame of the Ising-like model using Monte Carlo entropic sampling (MCES) method to enhance the scan of macrostates beyond the most probable thermal ones. In fact, MCES allows access to the metastable states, and it is then well adapted to study thermal hysteresis properties. In this contribution, we distinguish, for the first time, the interaction between molecules located in bulk at the surface and those connecting the bulk and surface regions of an SCO lattice. In addition, an extra ligand field contribution is assigned to surface molecules through an interaction parameter $\mathrm{L}$. In the absence of environmental effects on surface nanoparticles, a single thermal hysteresis loop increasing with the lattice size is simulated with a unique bulk and surface equilibrium temperature $T_{eq}=T_{eq}^{bulk}= T_{eq}^{surf}$. When environmental effects are accounted for, a two-step behavior associated with two hysteresis loops of widths ΔT_S (for the surface) and ΔT_B (for the bulk) with an intermediate plateau 14 K wide is obtained in the thermal dependence of the high-spin (HS) fraction for the 6 × 6 lattice. The surface and bulk equilibrium temperatures are then different, both decreasing towards lower values, and the $\mathrm{L}$ parameter controls the three states’ behavior as well as the hysteresis loop interval. Size effects show that the equilibrium temperature is governed by the surface atoms for a small lattice size (5 × 5) and by the bulk atoms for a large lattice size (7 × 7). Moreover, a change in the size of the lattice results in a variation of the order–disorder (or Curie) temperature, T_O.D., and the surface equilibrium temperature, T_eq, while only T_O.D. changes in bulk. Full article

Spin-crossover solids have been studied for many years for their promising applications as optical switches and reversible high-density memories for information storage. This study reports the effect of random metal dilution on the thermal and structural properties of a spin-crossover single crystal. The analysis is performed on a 2D rectangular lattice using an electro-elastic model. The lattice is made of sites that can switch thermally between the low-spin and high-spin states, accompanied by local volume changes. The model is solved by Monte Carlo simulations, running on the spin states and atomic positions of this compressible 2D lattice. A detailed analysis of metal dilution on the magneto-structural properties allows us to address the following issues: (i) at low dilution rates, the transition is of the first order; (ii) increasing the concentration of dopant results in a decrease in cooperativity and leads to gradual transformations above a threshold concentration, while incomplete spin transitions are obtained for big dopant sizes. The effects of the metal dilution on the spatiotemporal aspects of the spin transition along the thermal transition and on the low-temperature relaxation of the photo-induced metastable high-spin states are also studied. Significant changes in the organization of the spin states are observed for the thermal transition, where the single-domain nucleation caused by the long-range elastic interactions is replaced by a multi-droplet nucleation. As to the issue of the relaxation curves: their shape transforms from a sigmoidal shape, characteristic of strong cooperative systems, into stretched exponentials for high dilution rates, which is the signature of a disordered system. Full article

Cooperative spin crossover (SCO) materials exhibit first-order phase transitions in the solid state, between the high-spin (HS) and low-spin (LS) states. Elastic long-range interactions are the basic mechanism for this particular behavior and are described well by the Ising-like model, which allows the reproduction of most of the experimental results in the literature. Until now, this model has been applied with an interaction parameter between the molecules, which is considered to be independent of the states. In this contribution, we extend the Ising-like model to include interaction energy that depends on the spin states and apply it to study SCO nanoparticles. Our research shows that following this new hypothesis, the equilibrium temperature shifts toward higher values. Full article

Among the large family of spin-crossover materials, binuclear systems play an important role due to their specific molecular configurations, allowing the presence of multi-step transitions and elastic frustration. Although this issue benefited from a significant number of spin-based theories, there is almost no elastic description of the spin transition phenomenon in binuclear systems. To overcome this deficiency, in this work we develop the first elastic modeling of thermal properties of binuclear spin-crossover solids. At this end, we investigated a finite spin-crossover open chain constituted of elastically coupled binuclear (A = B) blocks, $\cdots \left(\mathrm{A}=\mathrm{B}\right)-\left(\mathrm{A}=\mathrm{B}\right)-\left(\mathrm{A}=\mathrm{B}\right)\cdots$, in which the considered equivalent A and B sites may occupy two configurations, namely low-spin (LS) and high-spin (HS) states. The sites of the binuclear unit interact via an intramolecular spring and couple to the neighboring binuclear units via other springs. The model also includes the change of length inside and between the binuclear units subsequent to the spin state changes. When injecting an elastic frustration inside the binuclear unit in the LS state, competing interactions between the intra- and the inter-binuclear couplings emerge. The latter shows that according to the intra- and inter-binuclear elastic constants and the strength of the frustration, multi-step transitions are derived, for which a specific self-organization of type (HS = HS)-(LS-LS)-(HS = HS)⋯ is revealed and discussed. Finally, we have also studied the relaxation of the metastable photoinduced HS states at low temperature, in which two relaxation regimes with transient self-organized states were identified when monitoring the elastic frustration rate or the ratio of intra- and intermolecular elastic interactions. These behaviors are reminiscent of the thermal dependence of the order parameters of the system. The present model opens several possibilities of extensions of elastic frustrations acting in polynuclear spin-crossover systems, which may lead to other types of spin-state self-organizations and relaxation dynamics. Full article

The properties of spin crossover (SCO) nanoparticles were studied for five 2D hexagonal lattice structures of increasing sizes embedded in a matrix, thus affecting the thermal properties of the SCO region. These effects were modeled using the Ising-like model in the framework of local mean field approximation (LMFA). The systematic combined effect of the different types of couplings, consisting of (i) bulk short- and long-range interactions and (ii) edge and corner interactions at the surface mediated by the matrix environment, were investigated by using parameter values typical of SCO complexes. Gradual two and three hysteretic transition curves from the LS to HS states were obtained. The results were interpreted in terms of the competition between the structure-dependent order and disorder temperatures (T_O.D.) of internal coupling origin and the ligand field-dependent equilibrium temperatures (T_eq) of external origin. Full article

The jungle of experimental behaviors of spin-crossover materials contains a tremendous number of unexpected behaviors, among which, the unsymmetrical hysteresis loops having different shapes on heating and cooling, that we often encounter in literature. Excluding an extra effect of crystallographic phase transitions, we study here these phenomena from the point of view of elastic modeling and we demonstrate that a simple model accounting for the bond lengths misfits between the high-spin and low-spin states is sufficient to describe the situation of unsymmetrical hysteresis showing plateaus at the transition only on cooling or on heating branches. The idea behind this effect relates to the existence of a discriminant elastic frustration in the lattice, which expresses only along the high-spin to low-spin transition or in the opposite side. The obtained two-step transitions showed characteristics of self-organization of the spin states under the form of stripes, which we explain as an emergence process of antagonist directional elastic interactions inside the lattice. The analysis of the spin state transformation inside the plateau on cooling in terms of two sublattices demonstrated that the elastic-driven self-organization of the spin states is accompanied with a symmetry breaking. Full article

Two-dimensional (2D) square, rectangular and hexagonal lattices and 3D parallelepipedic lattices of spin crossover (SCO) compounds which represent typical examples of first order phase transitions compounds are studied in terms of their size, shape and model through an Ising-like Hamiltonian in which the fictitious spin states are coupled via the respective short and long-range interaction parameters J, and G. Furthermore, an environmental L parameter accounting for surface effects is also introduced. The wealth of SCO transition properties between its bi-stable low spin (LS) and high spin (HS) states are simulated using Monte Carlo Entropic Sampling (MCES) method which favors the scanning of macro states of weak probability occurrences. For given J and G, the focus is on surface effects through parameter L. It is shown that the combined first-order phase transition effects of the parameters of the Hamiltonian can be highlighted through two typical temperatures, T_O.D., the critical order-disorder temperature and T_eq the equilibrium temperature that is fixed at zero effective ligand field. The relative positions of T_O.D. and T_eq control the nature of the transition and mediate the width and position of the thermal hysteresis curves with size and shape. When surface effects are negligible (L = 0), the equilibrium transition temperature, T_eq. becomes constant, while the thermal hysteresis’ width increases with size. When surface effects are considered, L ≠ 0, T_eq. increases with size and the first order transition vanishes in favor of a gradual transition until reaching a threshold size, below which a reentrance phenomenon occurs and the thermal hysteresis reappears again, as shown for hexagonal configuration. Full article

We have investigated by means of optical microscopy and magnetic measurements the first-order thermal spin transition of the [{Fe(NCSe)(py)₂}₂(m-bpypz)] spin-crossover compound under various shining intensities, far from the light-induced spin-state trapping region. We found evidence of photo-heating effects on the thermally-induced hysteretic response of this spin-crossover material, thus causing the shift of the thermal hysteresis to lower temperature regions. The experimental results are discussed in terms of the apparent crystal temperature and are analyzed theoretically using two evolution equations of motion, written on the high-spin (HS) fraction and heat balance between the crystal and the thermal bath. A very good qualitative agreement was found between experiment and theory in the stationary regime, explaining the experimental observations well and identifying the key factors governing these photo-thermal effects. Full article

Optical microscopy technique is used to investigate the thermal and the spatio-temporal properties of the spin-crossover single crystal [Fe(2-pytrz) ${}_2$ {Pt(CN) ${}_4$ }]·3H ${}_2$ O, which exhibits a first-order spin transition from a full high-spin (HS) state at high temperature to an intermediate, high-spin low-spin (HS-LS) state, below 153 K, where only one of the two crystallographic Fe(II) centers switches from the HS to HS-LS state. In comparison with crystals undergoing a complete spin transition, the present transformation involves smaller volume changes at the transition, which helps to preserving the crystal’s integrity. By analyzing the spatio-temporal properties of this spin transition, we evidenced a direct correlation between the orientation and shape of HS/HS-LS domain wall with the crystal’s shape. Thanks to the small volume change accompanying this spin transition, the analysis of the experimental data by an anisotropic reaction-diffusion model becomes very relevant and leads to an excellent agreement with the experimental observations. Full article

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. Full article

We study the spatio-temporal formation and spreading of the low-spin state (LS) during the thermal spin transition and the cooperative relaxation of the photo-induced metastable high spin (HS) state at low temperature, in the presence of a structural defect. The model is made of a two-dimensional rectangular-shaped lattice with discrete spins coupled by springs. The investigations are performed for a perfect lattice and a lattice with a hole (simulating the defect) with a fixed size. We found that the presence of the defect affects the thermal equilibrium by reducing the size of the thermal hysteresis at the transition, although the transition temperature remains unchanged. The study of the low-temperature relaxation of the defect-free lattice from HS to LS state indicated the existence of three different regimes of the growth process: (i) a first regime of growth from one corner of the rectangle along the width, then followed by (ii) a second regime of longitudinal propagation at almost constant velocity, and (iii) a third rapid regime when the system feels the surface or the border of the crystal. When a hole is injected inside the lattice, it results in (i) the deformation of the HS/LS interface’s shape when it approaches the defect position; and (ii) the slowing down of its propagation velocity. These results, which are in good agreement with available experimental data, are discussed in terms of elastic energy stored in the system during the relaxation process. Full article