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Among the large family of spin-crossover (SCO) solids, recent investigations focused on polynuclear SCO materials, whose specific molecular configurations allow the presence of multi-step transitions and elastic frustration. In this contribution, we develop the first elastic modeling of thermal and dynamical properties of trinuclear SCO solids. For that, we study a finite SCO open chain constituted of successive elastically coupled trinuclear (A=B=C) blocks, in which each site (A, B, and C) may occupy two electronic configurations, namely, low-spin (LS) and high-spin (HS) states, accompanied with structural changes. Intra- and inter-molecular springs couple the sites inside and between trimers. The model also includes the change of length inside and between the trinuclear units subsequent to the spin states changes. First, we studied the mechanical relaxation of a LS chain initially prepared with HS distances, from which we dissected the dynamics of the atomic displacements for various strengths of intra- and inter-molecular elastic constants. Second, we investigated the thermal properties of the chain at equilibrium, which revealed the existence of a rich variety of behaviors, going from: gradual LS to HS transition to multiple spin transitions with the presence of self-organized spin state structures in the plateaus. The latter were identified as emerging from antagonist short- and long-range elastic interactions between intra- and inter-block size changes. The present model opens several possible extensions, among which are the cases of coupled non-linear trimer molecules as well as that of inter-chain interactions with block–block interactions, leading to unexpected hysteretic spin transitions. [ABSTRACT FROM AUTHOR]

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 JCC, JSS and JCS 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 (N×N≤92 ${N\times N\ \le {9}^{2}}$) (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. [ABSTRACT FROM AUTHOR]

In the solid state, the thermal properties of SCO materials give rise to a rich variety of behaviors, ranging from (i) simple continuous gradual spin transitions, corresponding to a Boltzmann population of two degenerate states to (ii) sharp first-order hysteretic[11] transitions, including (iii) incomplete transitions and (iv) two-step or multi-step spin transitions,[12] characterized by the presence of a macroscopic intermediate state in the course of the transition between the LS and the HS states. Ndiaye I et al i .[33] establish the existence of an isomorphism between the electro-elastic models developed for the spin transition and Ising-like models including competing interactions, which confirms the relevance of the spin models in describing the multi-step spin transitions. Indeed, due to the volume change accompanying the spin transition between the LS and the HS states, crystallography appears as a direct probe of the spin transition at several scales, giving information about the deformation of the molecular structure and its consequence on the expansion/contraction of the lattice along the spin transformation. Later on, new interesting initiatives emerge through the introduction of spin-phonon models and elastic models in which the spin states were coupled to the atomic displacements of the SCO lattice, renormalizing the ligand field to which an elastic contribution arising from the lattice is added. [Extracted from the article]

Metastable phases of the photoswitchable molecular magnet K0.3Co[Fe(CN)6]0.77 ⋅ nH2O in sub-micrometer particles have been structurally investigated by synchrotron powder x-ray diffraction (PXRD) measurements. The K0.3Co[Fe(CN)6]0.77 ⋅ nH2O bulk compound (studied here with a sample having average particle size of 500 nm) undergoes a charge transfer coupled spin transition (CTCST), where spin configurations change between a paramagnetic CoII (S = 3/2) –FeIII (S = 1/2) high-temperature (HT) state and a diamagnetic CoIII (S = 0) –FeII (S = 0) low-temperature (LT) state. The bulk compound exhibits a unique intermediate (IM) phase, which corresponds to a mixture of HT and LT spin states that depend on the cooling rate. Several hidden metastable HT states emerge as a function of thermal and photo stimuli, namely: (1) a quench (Q) state generated from the HT state by flash cooling, (2) a LTPX state obtained by photoexcitation from the LT state derived by thermal relaxation from the Q state, and (3) an IMPX state accessed by photo-irradiation from the IM state. A sample with a smaller particle size, 135 nm, is investigated for which the particles are on the scale of the coherent LT domains in the IM phase within the larger 500 nm sample. PXRD studies under controlled thermal and/or optical excitations have clarified that the reduction of the particle size profoundly affects the structural changes associated with the CTCST. The unusual IM state is also observed as segregated domains in the 135 nm particle, but the collective structural transformations are more hindered in small particles. The volume change decreases to 2%–3%, almost half the value found for 500 nm particles (5%–8%), even though the linear thermal expansion coefficients are larger for the smaller particles. Furthermore, photoexcitation from the IM and LT states does not turn into single phases in the smaller particles, presumably because of the multiple interfaces and/or internal stress generated by the coexistence of small CoII–FeIII and CoIII–FeII domains in the lattice. Since the reduced particle size limits cooperativity and domain growth in the lattice, CTCST in the small particle sample becomes less sensitive to external stimuli. [ABSTRACT FROM AUTHOR]

Spin-crossover (SC) compounds are fascinating materials that exhibit colorful phase transitions induced by temperature, pressure, photoirradiation, etc. From the microscopic point of view, the electronic (spin) state of a molecule changes between the low-spin (LS) and high-spin (HS) states by such stimuli, and a variation of the molecular size follows through the vibronic coupling between the electronic state and structure in the molecule. This causes an elastic distortion and then an elastic interaction. The elastic interaction is essential in cooperative properties of SC phenomena. In this paper, we present a tutorial study on elastic interaction models for SC phenomena, which are the recent trend of modeling of SC compounds. We focus on multistep transitions, which are a topic of SC phenomena. We analyze the phase diagrams including the metastable phases for several SC systems, in which antiferromagnetic-like and ferrimagnetic-like phases are associated in addition to the LS and HS phases. Making use of the phase diagrams, we show various patterns of thermally induced SC transition with steps. We also investigate SC transitions with steps in a core-shell SC nanocomposite composed of two different SC compounds. We focus on two cases: the core has a lower transition temperature than the shell, and the core has a higher transition temperature. We show characteristic features of difference in the two systems. [ABSTRACT FROM AUTHOR]

We report the compressibility of two Prussian blue analogs (PBAs) under hydrostatic pressure, one with small and one with a relatively large cubic unit cell among PBAs, and investigate the modification of their elastic properties when the two lattices are coupled within a heteroepitaxial core–shell structure. Bulk modulus (K0) values are derived from x-ray powder diffraction experiments using a diamond anvil cell with silicone oil as a pressure-transmitting medium. The pressure–volume curves fitted to Murnaghan equations of states show that K0 inversely scales with the crystal packing for the rubidium cobalt hexacyanoferrate and rubidium nickel hexacyanochromate samples (K0 ∼ 29 GPa for Co-Fe PBA, a0 = 9.95 Å and ∼20 GPa for Ni-Cr PBA, a0 = 10.48 Å with a0 being the lattice constant at ambient pressure). The two single-phase samples undergo a cubic-to-rhombohedral phase transition above ∼0.8 GPa, which correlates fairly well with the build-up of nonhydrostatic pressure contributions in the cell. Within the core–shell structure, the volume change observed for the core scales with that of the shell because of the configuration close to the case of a solid pressure-transmitting medium. The Ni-Cr PBA shell layer exhibits an increased rhombohedral distortion with respect to the single-phase reference possibly associated with shearing at the core–shell interface. Its bulk modulus is not significantly modified with respect to that of the single-phase sample despite the presence of defects associated with the growth mode, whereas the P-V curve of the core suggests a stiffening of the Co-Fe PBA lattice. [ABSTRACT FROM AUTHOR]

A 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. [ABSTRACT FROM AUTHOR]

Elastic modeling of spin-crossover materials has boomed remarkably these last years. Among these models, the electro-elastic model combining spin and lattice degrees of freedom showed good abilities of fair description of the thermodynamics and spin-crossover solids. In the present work, we explore a new treatment of this model based on a homogeneous description of the lattice spacing with well separate relaxation timescales for the lattice and spin state degrees of freedom. This description is analogous to the Born–Oppenheimer approximation and allows analytic treatment of the elastic part of the model, thus simplifying considerably the model resolution. As a result, we have been able to demonstrate the equivalence between the genuine electro-elastic model and an Ising-like Hamiltonian with competing long-range ferro-like and short-range (nearest neighbors and next-nearest neighbors along diagonals) antiferro-like interactions, whose relationship with the high-spin to low-spin misfit elastic energy has been established. This model generates intrinsic elastic frustration in the lattice, which leads to a rich variety of hysteretic first-order transitions made of one- two-, three-, or four-step behaviors. Complex self-organizations of the spin states are evidenced in the plateau regions in the form of checkerboard-like, stripes-like patterns, constituted of alternate high-spin and low-spin ferro-like stripes or alternate ferro high-spin (or low-spin) and antiferro-like chains, as well labyrinth structures. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]