Ising-like Model Hasn't Yet Said its Last Word: Exact and Mean-Field Investigations of 2, 3 and 4-Body Interactions in 1D Ising Chain of Binuclear Spin-Crossover Solids.

We investigate the static properties of a new class of 1D Ising-like Hamiltonian for binuclear spin-crossover materials accounting for two-, three-, and four-body short-range interactions between binuclear units of spins [[EQUATION]] and [[EQUATION]]. The following 2-, 3- , and 4-body [[EQUATION]], [[EQUATION]], and [[EQUATION]] terms are considered, in addition to intra-binuclear interactions, such as effective ligand-field energy and exchange-like coupling. An exact treatment is carried out within the frame of the transfer matrix method, leading to a [[EQUATION]] matrix from which, we obtained the thermal evolution of the thermodynamic quantities. Several situations of model parameter values were tested, among which that of competing intra- and inter-molecular interactions, leading to the occurrence of (i) one-step spin transition, (ii) two-, three-, and four-step transitions, obtained with a reasonable number of parameters. To reproduce first-order phase transitions, we accounted for inter-chains interactions, treated in the mean-field approach. Hysteretic multi-step transitions, recalling experimental observations, are then achieved. Overall, the present model not only suggests new landscapes of interaction configurations between SCO molecules but also opens new avenues to tackle the complex behaviors often observed in the properties of SCO materials.

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

Spin transition materials are known to exhibit a rich variety of behaviors under several stimuli, among which pressure leads to major changes in their electronic and elastic properties. From an 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; this 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) furthermore, 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 using a 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-dependent compressibility, 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 behavior 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 plateau regions.

Optical microscopy imaging of the thermally-induced spin transition and isothermal multi-stepped relaxation in a low-spin stabilized spin-crossover material.

The thermal spin transition and the photo-induced high-spin → low-spin relaxation of the prototypical [Fe(ptz)6](BF4)2 spin-crossover compound (ptz = 1-propyltetrazole) diluted in the isostructural ruthenium host lattice [Ru(ptz)6](BF4)2, which stabilizes the Fe(II) low-spin state, have been investigated. We demonstrate the presence of a crystallographic phase transition around 145 K (i.e. from the high-temperature ordered high-spin phase to a low-temperature disordered low-spin phase) upon slow cooling from room temperature. This crystallographic phase transition is decoupled from the thermal spin transition. A supercooled ordered low-spin phase is observed as in the pure Fe(II) analogue upon fast cooling. A similar order-disorder phase transition is also observed for pure [Ru(ptz)6](BF4)2 but at relatively higher temperature (i.e. at around 150 K) without involving any spin transition. For Ru-diluted [Fe(ptz)6]2+, the crystallographic phase transition as well as strong cooperative effects involving various degrees of elastic frustration are at the origin of stepped sigmoidal high-spin → low-spin relaxation curves, which are modelled in the framework of a classical mean field model, considering both the tunnelling and thermally activated regimes. Optical microscopy studies performed on two different single crystals showed the existence of hysteretic thermal transitions with slight domain formation, hardly visible in the static crystal images. This behavior is attributed to the double effect upon Ru dilution, which decreases the cooperative character of the transition and simultaneously reduces the optical contrast between the LS and HS states. Moreover, the transition temperature revealed to be slightly crystal dependent, highlighting the crucial role of the spatial distribution of Ru from one crystal to another, in addition to the well-known effects of crystal shape and size.

Electro-Elastic Modeling of Thermal Spin Transition in Diluted Spin-Crossover Single Crystals.

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.

Downsizing of Nanocrystals While Retaining Bistable Spin Crossover Properties in Three-Dimensional Hofmann-Type {Fe(pz)[Pt(CN)4]}-Iodine Adducts.

Mastering nanostructuration of functional materials into electronic devices is presently an essential task in materials science. This is particularly relevant for spin crossover (SCO) compounds, whose properties are extremely sensitive to size reduction. Indeed, the search for materials displaying strong cooperative hysteretic SCO properties operative at the nanoscale close near room temperature is extremely challenging. In this context, we describe here the synthesis and characterization of 20-30 nm surfactant-free nanocrystals of the FeII Hofmann-type polymer {FeII(pz)[PtII,IVIx(CN)4]} (pz = pyrazine), which affords the first example of a robust three-dimensional coordination polymer, substantially keeping operational thermally induced SCO bistability at such a scale.

Pressure-Induced Conversion of a Paramagnetic FeCo Complex into a Molecular Magnetic Switch with Tuneable Hysteresis.

A key challenge in the design of magnetic molecular switches is to obtain bistability at room temperature. Here, we show that application of moderate pressure makes it possible to convert a paramagnetic FeIII 2 CoII 2 square complex into a molecular switch exhibiting a full dia- to paramagnetic transition: FeII CoIII ⇔ FeIII CoII . Moreover, the complex follows a rare behavior: the higher the pressure, the broader the magnetic hysteresis. Thus, the application of an adequate pressure allows inducing a magnetic bistability at room temperature with predictable hysteresis width. The structural studies at different pressures suggest that the pressure-enhanced bistability is due to the strengthening of intermolecular interactions upon pressure increase. An original microscopic Ising-like model including pressure effects is developed to simulate this unprecedented behavior. Overall, this study shows that FeCo complexes could be very sensitive piezo switches with potential use as sensors.

Unprecedented Bistability in Spin-Crossover Solids Based on the Retroaction of the High Spin Low-Spin Interface with the Crystal Bending.

There has been in recent years a continuous increase in spatiotemporal investigations of the dynamics of the first-order transitions in spin-crossover (SCO) solids. In single crystals, this phenomenon proceeds via a single domain nucleation and propagation, characterized in some systems with the presence of two equivalent and symmetric interface orientations, between the high-spin (HS) and low-spin (LS) phases, due to the anisotropic structural change of the unit cell at the transition. The present investigations bring an experimental evidence of the reversible driving of the translational and rotational degrees of freedom of the HS-LS interface. In addition to its rectilinear displacement, the interface rotates between two stable angles, 60o and 120o. It is demonstrated that while the translation motion is accompanied by a crystal's length change, the interface rotation is controlled by the crystal's bending. These results are well-explained in the frame of an elastic theoretical description in which the effect of the crystal bending, on the stability of the interface's orientation, is simulated by applying a moment of forces on the crystal. It is found that the interface orientation becomes unstable beyond a threshold load value, announcing the emergence of a bistability in SCO solids, taking place at constant HS fraction and volume. This work underlines the sensitive character of the interface orientation to any macroscopic crystal bending, an idea that can be used to develop a new generation of robust stress sensors, working at constant volume, thus avoiding deterioration problems due to crystal fatigue.

Control of the Speed of a Light-Induced Spin Transition through Mesoscale Core-Shell Architecture.

The rate of the light-induced spin transition in a coordination polymer network solid dramatically increases when included as the core in mesoscale core-shell particles. A series of photomagnetic coordination polymer core-shell heterostructures, based on the light-switchable Rb aCo b[Fe(CN)6] c· mH2O (RbCoFe-PBA) as core with the isostructural K jNi k[Cr(CN)6] l· nH2O (KNiCr-PBA) as shell, are studied using temperature-dependent powder X-ray diffraction and SQUID magnetometry. The core RbCoFe-PBA exhibits a charge transfer-induced spin transition (CTIST), which can be thermally and optically induced. When coupled to the shell, the rate of the optically induced transition from low spin to high spin increases. Isothermal relaxation from the optically induced high spin state of the core back to the low spin state and activation energies associated with the transition between these states were measured. The presence of a shell decreases the activation energy, which is associated with the elastic properties of the core. Numerical simulations using an electro-elastic model for the spin transition in core-shell particles supports the findings, demonstrating how coupling of the core to the shell changes the elastic properties of the system. The ability to tune the rate of optically induced magnetic and structural phase transitions through control of mesoscale architecture presents a new approach to the development of photoswitchable materials with tailored properties.

Structural Insight into Order-Disorder Transition and Charge-Transfer Phase Transition in an Iron Mixed-Valence Complex (n-C3H7)4N[FeIIFeIII(dto)3] with a Two-Dimensional Honeycomb Network.

The structural properties of the iron mixed-valence complex ( n-C3H7)4N[FeIIFeIII(dto)3] (dto = dithiooxalato, C2O2S2) have been investigated by single-crystal X-ray diffraction (SCXRD) at low temperatures. ( n-C3H7)4N[FeIIFeIII(dto)3] has two-dimensional (2D) honeycomb layers consisting of alternating FeII and FeIII arrays bonded by bis-bidentate dithiooxalato ligands. Upon cooling, a superlattice structure with q = (1/3, 1/3, 0) was observed below 260 K, which corresponds to an order-disorder transition of the ( n-C3H7)4N+ ions between the honeycomb layers. The charge-transfer phase transition (CTPT) occurs at TC↑1/2 ∼ 120 K and TC↓1/2 ∼ 90 K upon heating and cooling, respectively, with an electron transfer between the FeII and FeIII ions, accompanied by a spin-state change, FeII ( S = 2; HS)-O2C2S2-FeIII ( S = 1/2; LS) ↔ FeIII ( S = 5/2; HS)-O2C2S2-FeII ( S = 0; LS). During the CTPT, the intersheet [FeIIFeIII(dto)3] distance decreased monotonously upon cooling, and an abrupt structural contraction was observed in the hexagonal 2D network. The volume contraction during the CTPT was quite small (∼0.7%), and differences in the structural distortions at the FeS6 and FeO6 sites were not found in the vicinity of the CTPT. We also calculated the orbital energies and the occupied spin states for the [Fe(O2C2S2)3] and [Fe(S2C2O2)3] octahedra in the vicinity of the CTPT by density functional theory (DFT). Because the local symmetry around the two coordinating iron ions is already lowered to trigonal symmetry, the CTPT did not cause any further deformation. This symmetry invariance resulted in an absence of orbital contributions to the total entropy change (Δ S) in the CTPT, which is in agreement with the previous heat capacity measurements. [Nakamoto, T; Miyazaki, Y; Itoi, M; Ono, Y; Kojima, N; Sorai, M. Heat Capacity of the Mixed-Valence Complex {[( n-C3H7)4N][FeIIFeIII(dto)3]}∞, Phase Transition because of Electron Transfer, and a Change in Spin-State of the Whole System. Angew. Chem., Int. Ed. 2001, 40, 4716-4719.].

An electro-elastic theory for the mechanically-assisted photo-induced spin transition in core-shell spin-crossover nanoparticles.

The development of heterostructure materials may lead to new features that cannot be obtained with natural materials. Here we simulate a model structurally hybrid core-shell nanoparticle with different lattice parameters between an electronically inert shell and an active spin crossover core. The nanoparticle consists of a 2D core with 20 × 20 size with square symmetry, surrounded by a shell made of 10 atomic layers. The low temperature photoexcitation of the core shows a significant environment-dependent behavior. In particular, we demonstrate that a shell with a large lattice parameter accelerates the low-spin to high-spin photoexcitation process of the core through the single domain nucleation mechanism while a moderate shell lattice parameter leads to spatially-homogeneous growth of the high-spin fraction. We found that the mechanical retro-action of the shell may cause elastic instability of the core leading to efficient control and manipulation of its photo-conversion.

Interplay between a crystal's shape and spatiotemporal dynamics in a spin transition material.

We investigated by means of optical microscopy (OM) the spatiotemporal features of the thermo-induced spin transition of [Fe(2-pytrz)2{Pd(CN)4}]·3H2O (1) (2-pytrz = 4-(2-pyridyl)-1,2,4,4H-triazole) single crystals having two different shapes (triangle and rectangle). While magnetic and calorimetric measurements, performed on a polycrystalline material, showed the respective average heating and cooling transition temperatures of (Tdown1/2 ∼ 152 K, Tup1/2 ∼ 154 K) and (Tdown1/2 ∼ 160.0 K, Tup1/2 ∼ 163.5 K), OM studies performed on a unique single crystal revealed significantly different switching temperatures (Tdown1/2 ∼ 152 K and Tup1/2 ∼ 162 K). OM investigations showed an interface spreading over all crystals during the spin transition. Thanks to the color contrast between the low-spin (LS) and the high-spin (HS) states, we have been able to follow the real time dynamics of the spin transition between these two spin states, as well as access the thermal hysteresis loop of each single crystal. After image processing, the HS-LS interface's velocity was carefully estimated in the ranges [4.4-8.5] µm s-1 and [2.5-5.5] µm s-1 on cooling and heating, respectively. In addition, we found that the velocity of the interface is shape-dependent, and accelerates nearby the crystal's borders. Interestingly, we observed that during the propagation process, the interface optimizes its shape so as to minimize the excess of elastic energy arising from the lattice parameter misfit between the LS and HS phases. All of these original experimental results are well reproduced using a spatiotemporal model based on the description of the spin-crossover problem as a reaction diffusion phenomenon.

Elastic Frustration Causing Two-Step and Multistep Transitions in Spin-Crossover Solids: Emergence of Complex Antiferroelastic Structures.

Two-step and multistep spin transitions are frequently observed in switchable cooperative molecular solids. They present the advantage to open the way for three- or several-bit electronics. Despite extensive experimental studies, their theoretical description was to date only phenomenological, based on Ising models including competing ferro- and antiferro-magnetic interactions, even though it is recognized that the elastic interactions are at the heart of the spin transition phenomenon, due to the volume change between the low- and high-temperature phases. To remedy this shortcoming, we designed the first consistent elastic model, taking into account both volume change upon spin transition and elastic frustration. This ingredient was revealed to be powerful, since it was able to obtain all observed experimental configurations in a consistent way. Thus, according to the strength of the elastic frustration, the system may undergo first-order transition with hysteresis, gradual, hysteretic two-step or multistep transitions, and incomplete transitions. Furthermore, the analysis of the spatial organization of the HS and LS species in the plateau regions revealed the emergence of complex antiferro-elastic patterns going from simple antiferro-magnetic-like order to long-range spatial modulations of the high-spin fraction. These results enabled us to identify the elastic frustration as the fundamental mechanism at the origin of the very recent experimental observations showing the existence of organized spatial modulations of the high-spin fraction inside the plateau of two-step spin transitions.

Elastic Frustration Triggering Photoinduced Hidden Hysteresis and Multistability in a Two-Dimensional Photoswitchable Hofmann-Like Spin-Crossover Metal-Organic Framework.

We report a two-dimensional Hofmann-like spin-crossover (SCO) material, [Fe(trz-py)2{Pt(CN)4}]·3H2O, built from [FePt(CN)4] layers separated by interdigitated 4-(2-pyridyl)-1,2,4,4H-triazole (trz-py) ligands with two symmetrically inequivalent FeII sites. This compound exhibits an incomplete first-order spin transition at 153 K between fully high-spin (HS-HS) and intermediate high-spin low-spin (HS-LS) ordered states. At low temperature, it undergoes a bidirectional photoswitching to HS-HS and fully low-spin (LS-LS) states with green and near-IR light irradiation, respectively, with associated T(LIESST = Light-Induced Excited Spin-State Trapping) and T(reverse-LIESST) values of 52 and 85 K, respectively. Photomagnetic investigations show that the reverse-LIESST process, performed from either HS-HS or HS-LS states, enables access to a hidden stable LS-LS state, revealing the existence of a hidden thermal hysteresis. Crystallographic investigations allowed to identify that the strong metastability of the HS-LS state originates from the existence of a strong elastic frustration causing antiferroelastic interactions within the [FePt(CN)4] layers, through the rigid NC-Pt-CN bridges connecting the inequivalent FeII sites. The existence of the stable LS-LS state paves the way for a multidirectional photoswitching and allows potential applications for electronic devices based on ternary digits.

Reversible Control by Light of the High-Spin Low-Spin Elastic Interface inside the Bistable Region of a Robust Spin-Transition Single Crystal.

By using a weak modulated laser intensity we have succeeded in reversibly controlling the dynamics of the spin-crossover (SC) single crystal [{Fe(NCSe)(py)2 }2 (m-bpypz)] inside the thermal hysteresis. The experiment could be repeated several times with a reproducible response of the high-spin low-spin interface and without crystal damage. In-depth investigations as a function of the amplitude and frequency of the excitation brought to light the existence of a cut-off frequency ca. 1.5 Hz. The results not only document the applicability of SC materials as actuators, memory devices, or switches, but also open a new avenue for the reversible photo-control of the spin transition inside the thermal hysteresis.

Direct Observation of Short-Range Structural Coherence During a Charge Transfer Induced Spin Transition in a CoFe Prussian Blue Analogue by Transmission Electron Microscopy.

The local structure within the Co-Fe atomic array of the photoswitchable coordination polymer magnet, K0.3Co[Fe(CN)6]0.77·nH2O, is directly observed during charge transfer induced spin transition (CTIST), a solid-solid phase change, using high-resolution transmission electron microscopy (HRTEM). Along with the low-spin (LS) or thermally quenched high-spin (HS) states normally observed in CTIST solids at low temperature, slow cooling of K0.3Co[Fe(CN)6]0.77·nH2O results in an intermediate phase containing both HS and LS domains with short coherence length. By mapping individual metal-metal distances, the nanometer-scale HS domains are directly visualized within the LS array. Temperature-dependent analyses allow monitoring of HS domain coarsening along the warming branch of the CTIST, providing direct visualization of the elastic process and insight into the mechanism of phase propagation. Normally sensitive to electron beam damage, the low-temperature TEM measurements of the porous coordination polymer are enabled by using appropriate ionic liquids instead of usual conductive thin-film coatings, an approach that should find general utility in related classes of materials.

Reparametrization approach of DFT functionals based on the equilibrium temperature of spin-crossover compounds.

The required approach to investigate the electronic properties of spin-crossover (SCO) compounds needs to be able to provide a reliable estimate of high-spin/low-spin (HS/LS) energy gaps while retaining an accurate and efficient computation of the ground-state energy. We propose a reparametrization approach of the density functional theory (DFT) functionals to adjust the exact exchange admixture that governs the HS/LS energy splitting. Through the investigation of the thermodynamic properties of two typical SCO compounds, we demonstrate that the computed equilibrium temperature depends linearly, like the HS/LS energy gap, on the coefficient of the exact exchange admixture. We show that by taking the experimental value of the equilibrium temperature of the studied SCO compound as a reference, different hybrid functionals converge to comparable and realistic HS/LS energy gaps as well as enthalpy and entropy differences that agree well with the prior experimental investigations.

Structure-driven orientation of the high-spin-low-spin interface in a spin-crossover single crystal.

The orientation of the high-spin (HS)-low-spin (LS) macroscopic interface at the thermal transition of thin [{Fe(NCSe)(py)2}2(m-bpypz)] crystals is explained by considering the possible vanishing of the structural mismatch between the coexisting phases. The structural property which allows mismatch-free interfaces is characterized. The observed orientations of the interface and the tilt angle between the HS and LS domains are accurately reproduced by a two-dimensional continuous medium model, based on the structural data. Simulations using an atomistic electro-elastic model meet the predictions of the macroscopic analysis and provide information on the distribution of the elastic energy density in the biphasic state. The presence of mismatch-free domain structures can explain the exceptional resilience of these crystals upon repeated switching.

Velocity of the high-spin low-spin interface inside the thermal hysteresis loop of a spin-crossover crystal, via photothermal control of the interface motion.

We investigated by optical microscopy the thermal transition of the spin-crossover dinuclear iron(II) compound [(Fe(NCSe)(py)(2))(2)(m-bpypz)]. In a high-quality crystal the high-spin (HS) low-spin (LS) thermal transition took place with a sizable hysteresis, at ~108 K and ~116 K on cooling and heating, respectively, through the growth of a single macroscopic domain with a straight LS and HS interface. The interface orientation was almost constant and its propagation velocity was close to ~6 and 26 µ m s(-1) for the on-cooling and on-heating processes, respectively. We found that the motion of the interface was sensitive to the intensity of the irradiation beam of the microscope, through a photothermal effect. By fine-tuning the intensity we could stop and even reverse the interface motion. This way we stabilized a biphasic state of the crystal, and we followed the spontaneous motion of the interface at different temperatures inside the thermal hysteresis loop. This experiment gives access for the first time to an accurate determination of the equilibrium temperature in the case of thermal hysteresis--which was not accessible by the usual quasistatic investigations. The temperature dependence of the propagation velocity inside the hysteretic interval was revealed to be highly nonlinear, and it was quantitatively reproduced by a dynamical mean-field theory, which made possible an estimate of the macroscopic energy barrier.

BEG spin-1 model with random exchange magnetic interactions for spin-crossover solids.

We have investigated magnetic phase diagrams of spin-crossover (SCO) solids throughout the Blume-Emery-Griffiths spin-1 model where the spin states ±1 and 0 are associated to high-spin state and low-spin states respectively. In the present work, the quadrupolar interaction,K, parameter depends linearly on temperature and accounts for the role of the lattice phonons in the elastic interactions between the SCO units. Magnetic interactions are randomly distributed in the system and are controlled by a factorγ=Jij/Ksuch that forγ = 0 (Jij=0), magnetic ordering is not expected. The crystal-field that acts on SCO sites depends both on the ligand-field strength and the degeneracy ratio between HS and LS states as in some previous works. The system is also under the effect of a random local magnetic fieldhiacting on each sitei. The model is solved using a homogeneous mean field theory. Our investigations reveal the occurrence of thermally-induced gradual, and first-order spin-transitions by varying the model parameters. At vicinity of first-order transition, various types of isothermal magnetic hysteresis loops are obtained and their corresponding coercive field and loop patterns are discussed as function of temperature.

Electric-field-induced charge-transfer phase transition: a promising approach toward electrically switchable devices.

Much research has been directed toward the development of electrically switchable optical materials for applications in memory and display devices. Here we present experimental evidence for an electric-field-induced charge-transfer phase transition in two cyanometalate complexes: Rb(0.8)Mn[Fe(CN)(6)](0.93).1.62H(2)O and Co(3)[W(CN)(8)](2)(pyrimidine)(4).6H(2)O, involving changes in their magnetic, optical, and electronic properties as well. Application of an electric field above a threshold value and within the thermal hysteresis region leads to a transition from the high- to the low-temperature phase in these compounds. A model is proposed to explain the main observations on the basis of a para-ferroelectric transition. Our observations suggest that this new concept of electrical switching, based on materials exhibiting charge-transfer phase transitions with large thermal hysteresis loops, may open up doors for novel electro-optical devices.