Spin transition materials: Molecular and solid-state

Today, material science is an interdisciplinary area at the interface between physics, chemistry, and biology focusing on new materials with novel and/or multi-functionalities that are quite promising for future development of high-tech applications. Current miniaturization techniques may reach their limitations in a few decades; hence, molecular electronics form a powerful research area to propose alternative solutions, well-adapted to the constant need for highly efficient devices at very small scales. The advent of the nano-era will not be genuinely feasible until we can formulate methods to assert power over nanomaterials and devices and harness useful work from them. However, these objectives based only on performances are insufficient, and the environmental impacts of the developed technologies must be integrated among the selection criteria. Thus, the need for ecofriendly multifunctional systems is more urgent than ever. Spin-crossover (SCO) materials (among other iron-based molecular systems) have a low environmental impact, which makes them interesting candidates for applications in several areas, including high-density non-volatile memories, spintronics, actuation, and energy harvesting. Current microelectronics represent an important part of the overall consumption of electricity, and the proliferation of microelectronics consumes a growing number of rare materials such as indium, gallium, and germanium, requiring heavy investments for the recycling and decontamination of the resulting electronic waste.

Molecular materials, among others, constitute an interesting alternative to today's energy-intensive electronics. Molecular systems like SCO materials are based on the use of abundant organic and inorganic ecofriendly elements, and they are free from any toxic characteristics. Furthermore, the searched physical property is already present at the molecular scale, e.g., spin switching or molecular electron transfer; this character remains present at the nanoscopic (nanoparticle) and mesoscopic scale, while the ultimate size reduction in the electronic circuits poses fundamental challenges related to the emergence of quantum effects that create a paradigm shift, requiring new electronics. Unlike the usual top-down approaches constituted by lithography techniques, the molecular electronic is based on a bottom-up approach going from the molecule to the functionalized solid. As mentioned above, such research areas aim to replace the current technologies based on silicon with new ones based on molecules. However, the integration of molecular materials in miniaturized electronic devices presents the most exciting and challenging goal for scientists, as they should be able to reproduce the functionalities at low dimensionality. In this context, the SCO materials (although many of their fundamental aspects remain to be clarified) present serious potentialities in the development of new generation electronic devices,^1–5 but also as very accurate sensors,¹ displays, as well as optical memories.^2–4 These materials combine both thermo-, piezo-, magneto-, and photo-switching features, leading to original physical properties. At the solid state, however, all these properties remain quite slow, complicated to control, and so incite research devoted to (i) the synthesis of new systems with better performances and (ii) deeper investigations of the physical and chemical properties of SCO at several size scales, particularly at very small scales. Prior to the development of the associated chemistry, the idea was that very small particles would present very short switching times when addressing the information as well as when reading it. However, this naïve picture faced the serious problem of understanding the non-linear changes produced on the physical (magnetic, elastic, and optical) properties of SCO solids when reducing the size. The transition from the solid state to a nanoparticle is indeed not continuous, and the nanoparticle itself is an intriguing object that merits to be studied for its own rights. The molecular and thermodynamic properties of SCO compounds are well-documented in literature, and there is no need to recall them from the basis of ligand theory. Readers can consult reference books and articles on the subject^6–14 as well several tutorial references included in the present special topic, where the global aspects of this phenomenon are introduced to be accessible for a non-specialized reader. In particular, the magnetic properties of molecular SCO solids are reviewed and the difference with ordered magnetic systems is discussed, in order to avoid the usual confusion between both topics. Several types of spin-crossover transitions are presented, covering a wide range of behaviors, without pretending to cover all SCO literature and experimental data.

In general, SCO behavior occurs for the first-row transition metal complexes of d⁴–d⁷ electronic configurations [chromium (II), manganese (III), iron (II, III), and cobalt (II)] in octahedral symmetry, surrounded by donor atoms (N, O, S, etc.).^6–10 The case of Fe(II)-based SCO materials, with 3d⁶ configuration, is the most common in the literature, with a total spin of $S=2$ and $S=0$⁠, in high-spin (HS) and low-spin (LS) states, respectively. In these ferrous SCO compounds, the five d-orbitals of iron (II) are then split into three $t2g$⁠, and two anti-bonding, $eg$⁠, orbitals. According to the strength of the ligand field, $Δ=E(t2g)−E(eg)$⁠, the metal ion can be in the LS (HS) state when $Δ$ is much stronger (weaker) than the electrons pairing energy. The resulting spin state then emerges from the delicate balance between the energy of orbital, needed to occupy all of the 3d levels in order to maximize the spin state and the average energy of the Coulomb repulsion of the d-electrons. 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 hysteretic¹¹ 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. The spin transition of the metal ion, which redistributes the electrons occupancy between the $t2g$⁠, and the anti-bonding, $eg$⁠, orbitals is accompanied by a huge relative change of the molecular volume by about 30%,^7,13 while the volume change of the unit cell is only 3%–5%.¹⁴ This difference is due to the existence of a structural reorganization at the molecular level involving the reorientation and/or distortion of the ligands. Overall, these magneto-structural changes also affect the vibrational and the optical properties of these materials. Beside such SCO thermal behavior, photo-conversion [light-induced excited spin-state trapping (LIESST) and reverse-LIESST effects] of the LS stable state into the HS metastable state can occur reversibly at low temperature for some complexes. This allows a bidirectional photo-switching between a reference and an excited spin states with a long lifetime, as long as the experiment is performed at low temperature.

The present special topic addresses several aspects of SCO materials from both experimental and theoretical aspects. It includes their fundamental property of bistability in the macroscopic and microscopic states. In the former, they manifest in the change of the continuum mechanics properties of the materials as a result of the important role of the elastic energy in the course of the transition between the LS and the HS states. From the experimental side, these aspects are examined through crystallographic studies to which several papers have been dedicated. 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.

Even if the scope of this topic is essentially dedicated to the physical and theoretical investigations of the switchable systems, we cannot omit, however, the contribution of molecular synthetic chemistry and the coordination chemistry in the design of new systems and functional ligands helping to anticipate the coordination environment of the active metal center and strong intermolecular contacts, including covalent links. These chemical aspects are then coupled to the x-ray diffraction technique to control or to tune, in the crystal packing, the intermolecular interactions at the origin of the cooperative effects. Benmansour et al.¹⁵ and Charytanowicz et al.¹⁶ show the crucial role of the crystallization solvent on the SCO characteristics (transition temperature, co-operativity, multi-step behaviors, and the possibility to tune such characteristics through desolvation process or by reversible solvent exchanges). In addition to this solvent effect, these SCO characteristics could also be modulated by the introduction of functional groups such as sulfur rich ligand backbones introduced by Schönfeld et al.¹⁷ in a series of two SCO Fe(II) coordination compounds based on Schiff base-like N₂O₂ ligands. Garcia-López et al.¹⁸ relate a new type of SCO 1D-coordination polymer based on a unidendate pyridine ligand containing a bulky t-butyl substituent. This compound displays abrupt spin transition with hysteresis and light-induced excited spin-state trapping. Cuza et al.¹⁹ report another series of three mononuclear Fe(II) SCO complexes based on sophisticated cyanocarbanion anionic ligands. The transition temperature can be finely tuned by acting on the coordination isomerism of the terminal cyanocarbanion anion involving four different nitrile donor groups. A new system from Kühne et al.²⁰ concerns an uncommon series of SCO Mn(III) cationic complexes with different counterions for which the position of the nitro substituent out-of-plane to the benzene ring of the Schiff base tends to stabilize the triplet spin state, while the spin-quintet form is favored for a nitro group in-plane with the benzene ring. The crucial effect of guest molecules on the spin transition characteristics, in particular, in the 3D Hoffman framework Fe(pyrazine)[Pt(CN)₄] is widely investigated in the literature. In this topic, Sawczak et al.²¹ investigate the spin transition in thin films of the 3D Hoffman framework nanocrystalline material Fe(pyrazine)[Pt(CN)₄] deposited by nanosecond laser ablation. The observed laser induced host–guest exchange indicates the possibility of selective modification of thin layers of SCO materials to obtain their desired characteristics. In Pillet,²² a tutorial surveys the practical use of x-ray crystallography, notably in cryogenic conditions, highlighting the crucial role of x-ray measurements in providing a privileged access to the physical mechanisms operating in SCO materials from bulk single crystals to nanocrystals. An exhaustive review of selected examples illustrates the most important recent advanced x-ray crystallography methods used in investigating the various physical properties of bistable SCO molecular solids. SCO materials are also known for their sensitivity to pressure effect. Indeed, the volume change accompanying the spin transition make them good candidates for mechanical stimuli, such as hydrostatic pressure, stress, or acoustic wave. Rusu et al.²³ study the effect of an applied non-uniform hydrostatic pressure on the shape of the thermal hysteresis in spin-crossover complexes, using a first-order reversal curve (FORC) diagram showing that high pressure gradients distort the shape of the thermal hysteresis loop in good agreement with experimental data.

An interesting and well-known property of Prussian blue analog (PBA) materials is their ability to switch under light excitation at low temperature between the LS diamagnetic state [Co(III, LS)–NC–Fe(II, LS)] to the electronic state [Co(II, HS, S = 3/2)–NC–Fe(III, LS, S = 1/2)], which leads to creation of a cold and raw (non-relaxed) frustrated ferrimagnetic structure. The presence of electronic transfer and SCO in the same material makes these systems rather original from both experimental and theoretical point of views. In this context, Stefańczyk and Ohkoshi²⁴ proposed a perspective on the photoswitchable two- and three-dimensional cyanido-bridged Co^II–[W^V(CN)₈] networks exhibiting electron-transfer-coupled spin transition with broad hysteresis and photo-induced spontaneous magnetization and humidity sensitivity for some of them. A second contribution related to a similar parent system concerns a three-dimensional Fe^II–[W^V(CN)₈] assembly exhibiting a SCO incomplete gradual behavior that is attributed to the elastic frustration between the HS and the LS Fe(II) centers.²⁵ The analysis of the effect of the strain in altering spin-crossover properties is studied by Cain et al.²⁶ This is indeed remarkable given that spin transitions are accompanied by volume changes in the solid state and are then excellent candidates for actuation as a source of mechanical strain inducible by light and pressure. This work highlights the progress using cobalt hexacyanoferrate network solids, or Prussian blue analogs (CoFe PBA), as a framework for investigating spin transition induced strain in nano- and hetero-structures, focusing on their response to strain generated by the thermally or optically induced spin-state change of the core. Pressure effect is also important in Co–NC–Fe PBA compounds where the charge transfer is delayed by the stress. Consequently, the photomagnetic and the thermal transitions are also strongly affected, as demonstrated by Maurin et al.,²⁷ where the effect of high pressure is studied on heteroepitaxial core–shell particles made of Co–Fe and Ni–Cr PBAs. The compressibility of these two PBAs is studied under hydrostatic pressure, and the modification of their elastic properties when the two lattices is coupled within a heteroepitaxial core–shell structure are analyzed in detail.

Understanding and predicting the behavior of these materials is critical for optimizing operation and necessitates a thorough understanding of structure–property relationships. During the last decades, various studies have been conducted in order to establish the intimate connection between the electronic and the elastic properties of the SCO materials, including their nonequilibrium properties. Ising-like models are also still very popular due to their diversity and efficiency in describing the tremendous number of experimental situations emerging from experimental data. They are often a source of inspiration since they present the advantage of catching the essential physics of the SCO phenomenon and are still capable of achieving impressive results. In all two-levels models, the first-order thermal transition is obtained through a phenomenological interaction parameter. 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. Gudyma and Gudyma²⁸ investigate an example of the use of spin models for the modeling 1D SCO chain made of interacting binuclear units using an Ising-like model, where an exact resolution of the spin Hamiltonian is proposed allowing one to determine the thermal behavior of the HS fraction and correlation function for this type of strongly anisotropic systems. In the second example provided by Das et al.,²⁹ a quantum phase transition of a frustrated antiferromagnetic Heisenberg mixed spin-1 system on the 3/4 and 3/5 skewed two-leg ladder geometries is investigated. The system's phase diagram in the ground state is calculated as a function of the interaction and system's size. An example of spin models accounting for the effect of vibrations is provided by Klokishner and Ostrovsky³⁰ in a theoretical description of the charge transfer-induced spin transition in crystalline cyanide-bridged binuclear Co–Fe clusters. The proposed Hamiltonian accounts for both charge transfers between the two metal ions, accompanied with the spin transition of Co and the cooperative interactions mediated by the acoustic waves. Recently, discrete atomistic models based on deformable lattices have been developed with the aim to mimic the spatiotemporal features of spin phases at the thermal transition. These models combining electronic and elastic degrees of freedom, allowing one to discriminate these two contributions, are revisited by Popa et al.³¹ and Nishino et al.³² with valuable developments on the physics of nucleation, growth, and propagation of the elastic domains along the spin-crossover transition in single crystals. Ndiaye et al.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. In the same spirit, a general macroscopic Landau theory of non-symmetry-breaking and symmetry-breaking spin transition materials is proposed by Azzolina et al.,³⁴ considering a model combing two order parameters associated with the electronic and structural changes, respectively. This topic of SCO transition with symmetry breaking is also analyzed by Slimani and Boukheddaden³⁵ using a microscopic elastic model in which the unit cell geometry of the HS states is twofold degenerate. Very recently, the elastic frustration concept has been introduced in these atomistic models, which also helped to explain the role of the elastic interactions in the occurrence of multi-step and incomplete spin transitions as well as that of the existence of experimentally observed HS/LS modulated structures. Here, the competition ferroelastic and antiferroelastic interactions are recognized as key factors from which originate this complexity. In this context, Cruddas et al.³⁶ address the question of original organizations of the spin states in SCO materials. Here, spin-state smectic phases are analyzed in a 2D network showing HS and LS patterns breaking spontaneously rotational symmetry and translational symmetry in one direction only. Overall, these new treatments undoubtedly mark a turning point in the better understanding of the leading role of the mechanical stresses in the mechanism of emergence of the SCO transition and its dynamics. They also clarify the macroscopic nucleation nature of the SCO phenomenon and hence the important role of the global shape of the material on these mechanisms. Thus, these theoretical investigations brought to light the interplay between the electronic and mechanical degrees of freedom of SCO systems opening the route for new types of control of this phenomenon.

Finally, from the point of view of applications, SCO materials can be of substantial help to the field of molecular actuators, for example, as they can add a variety of smart features (e.g., shape memory), a high degree of synthetic versatility, and multifunctionality such as the coupling of optical, electrical, magnetic, and mechanical properties since the SCO molecules have the ability to be operated via different stimuli routes as already mentioned. Furthermore, SCO complexes or molecules can exhibit useful mechanical response, which range from microscopic crystal to the single-molecule level, implying that there are no fundamental limitations to their functionality at the nano-scale. Clearly, there are several challenges and bottlenecks to overcome, primarily enhancing synergy between molecules and their surroundings to produce useful output while maintaining or devising possibilities for reversible external control, and we have yet to reckon in terms of strain, efficiency, durability, scaling, and control for their effective deployment in these disruptive applications. From the theoretical point of view, although a great step has been made in the fundamental understanding of the SCO phenomenon at the molecular level, there are still gray areas concerning the mode of interactions between the molecules, which clearly involve electrostatic, electronic, and elastic couplings. The molecular structure of each system is unique in its packing mode with its own structural anisotropies, affecting the global response of the SCO phenomenon. This means that we still do not have a clear grasp and control of all the factors governing the intimate nature of the SCO transition, which promises that this research still has its best days ahead it.

The authors acknowledge the editors of Journal of Applied Physics, particularly Dr. Christian Brosseau for his encouraging and enthusiastic support. We also acknowledge the staff of the Journal of Applied Physics, among whom Dr. Brian Solis, Brontë Brecht, Jessica Trudeau, and others, for organizing the “Spin Transition Materials: Molecular and Solid-State” Special Topic. We also acknowledge the authors and reviewers for contributing with their work to the success of this Special Issue. Financial support from CNRS (MITI program) and ANR (Mol-CoSM ANR Project No. ANR-20-CE07-0028-01) are gratefully acknowledged.

The authors have no conflicts to disclose.