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.

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.

We consider an open one-dimensional spin-crossover chain, in which each site can be in either a low spin (LS) or a high spin (HS) state. The sites interact elastically through nearest neighbor (nn) and next-nearest neighbor (nnn) springs with local equilibrium distances depending on the spin states. The system’s Hamiltonian is solved numerically using the Monte Carlo method, applied on both spin states and atomic displacements. This study focuses on the investigations of the isothermal relaxation of a photoinduced HS metastable chain, by analyzing the interplay between the electronic and structural properties along this process. The obtained results indicate that the nucleation and growth mechanisms of LS domains during relaxation are significantly influenced by the amplitude of the intermolecular interactions. Thus, increasing the latter reduces the number of HS/LS clusters due to the high cost of stored elastic energy at HS/LS interfaces. In the second part, we inject an elastic frustration between the equilibrium nn and nnn bond lengths, resulting in the emergence of two distinct relaxation regimes, which depend on the frustration rate, ξ. A detailed analysis of the effect of ξ on the isothermal HS to LS relaxation reveals the stabilization of rich intermediate self-organized electronic structures with long lifetime along this process. Thus, these results clearly demonstrate that the shape of the relaxation curves transforms from a continuous to a two-step behavior, which is reminiscent of the thermal dependence of the order parameters of such models in equilibrium thermodynamics.

This study investigates the thermal and spatiotemporal properties of a one-dimensional (1D) spin-crossover monoatomic chain using a homogeneous version of the electro-elastic model. This framework maps the original system initially defined by two degrees of freedom (atomic positions and spins) onto an effective Ising-like model. The resulting formulation combines infinite long-range ferroelastic interactions with short-range anti-ferroelastic interactions between nearest-neighbor and next-nearest-neighbor sites. The analytical treatment of this mapping enables the identification of all interaction parameters within the Ising-like model and establishes their direct physical relationship with the original elastic parameters. Consequently, this approach avoids the reliance on purely phenomenological interaction parameters commonly found in standard Ising-like models for spin transitions. The obtained results demonstrate the power of the present formalism and the key role of elastic frustration in stabilizing multi-step transitions in 1D spin-crossover materials.