The nucleation and growth properties of domains of molecules of the same state in open boundary three-dimensional (3D) spin-crossover systems of various shapes are discussed within the framework of the mechanoelastic model. The molecules are situated on face-centered-cubic lattices and are linked by springs through which they interact. Monte Carlo simulations imply that clusters nucleate from corners in the case of systems having well-developed faces and from kinks in the case of spherical samples, in accordance with available experimental data. In addition, a method to characterize the cooperativity in these systems is proposed, which by scanning the fluctuations in the 3D samples can be related directly to powder x-ray-diffraction experiments.

Here we reproduce the static and dynamical properties of spin-crossover complexes in the framework of the mechanoelastic model applied to triangular lattices. The switching processes between the high-spin and low-spin states are studied by combining the Monte Carlo method with the elastic lattice relaxation. The transition probabilities between the two states take into account intrinsic parameters, the values of which are approximated from experimental quantities (e.g., the energy gap, and the degeneracy ratio from the thermodynamic enthalpy and the entropy difference between the states), and the elastic force or elastic energy stored in the springs connecting the spin-changing centres. The value of the corresponding spring constant is estimated from the experimentally determined variation of the ligand-field strengths in the two spin states due to the cooperativity and the bulk modulus. Both simulated hysteresis loops and relaxation curves are in agreement with experimental data. Cooperativity related phenomena such as like-spin domain formation and the evolution of the interaction distribution with the HS fraction are also analysed.

The recently obtained spin-crossover nanoparticles are possible candidates for applications in the recording media industry as materials for data storage, or as pressure and temperature sensors. For these applications, the intermolecular interactions and interactions between spin-crossover nanoparticles are extremely important, as they may be essential factors in triggering the transition between the two stable phases: the high-spin and low-spin ones. In order to find correlations between the distributions in size and interactions and the transition temperatures distribution, we apply the FORC (First Order Reversal Curves) method, using simulations based on a mechanoelastic model applied to 2D triangular lattices composed of molecules linked by springs and embedded in a surfactant. We consider two Gaussian distributions: one is the size of the nanoparticles and another is the elastic interactions between edge spin-crossover molecules and the surfactant molecules. In order to disentangle the kinetic and non-kinetic parts of the FORC distributions, we compare the results obtained for different temperature sweeping rates. We also show that the presence of few larger particles in a distribution centered around much smaller particles dramatically increases the hysteresis width.

Depending on the iron(II) concentration, the mixed crystals of {[Zn_1-xFe_x(bbtr)₃](BF₄)₂}∞, bbtr = 1,4-di(1,2,3-triazol-1-yl)butane, 0.01 ≤ x ≤ 1, show macroscopic light-induced bistability between the high-spin and the low-spin state. In the highly diluted system with x = 0.01 and up to x = 0.31, the photoinduced low-spin state always relaxes back to the high-spin state independent of the initial light-induced low-spin fraction. In the highly concentrated mixed crystals with x = 0.67, 0.87 and 1, the strong cooperative effects coupled to a crystallographic phase transition result in light-induced bistability with decreasing critical light-induced low-spin fraction and increasing hysteresis width for increasing iron(II) concentrations. The lower limit for the light-induced bistability is estimated at x ≈ 0.5.

Whereas the neat polymeric Fe(II) compound {[Fe(bbtr)₃](ClO₄)₂}_∞ (bbtr=1,4-di(1,2,3-triazol-1-yl)butane) shows an abrupt spin transition centered at 107 K facilitated by a crystallographic symmetry breaking, in the covalently linked 2D coordination network of {[Fe(bbtr)₃](BF₄)₂}_∞, Fe(II) stays in the high-spin state down to 10 K. However, strong cooperative effects of elastic origin result in reversible, persistent and wavelength-selective photoswitching between the low-spin and high-spin manifolds. This compound thus shows true light-induced bistability below 100 K. The persistent bidirectional optical switching behavior is discussed as a function of temperature, irradiation time and intensity. Crystallographic studies reveal a photo-induced symmetry breaking and serve to establish the correlation between structure and cooperative effects. The static and kinetic behavior is explicated within the framework of the mean-field approximation.

The mechanoelastic model is applied to reproduce the experimental relaxation and thermal transition curves as determined for crystals of pure and diluted {[Fe_xZn_1–x(bbtr)₃](ClO₄)₂}_∞ [bbtr = 1,4-di(1,2,3-triazol-1-yl)butane] spin-crossover systems. In the mechanoelastic model, the spin-crossover complexes are situated in a hexagonal planar lattice, which is similar to the 2D coordination polymer with (3,6) network topology of [Fe(bbtr)₃](ClO₄)₂. These complexes are linked by springs, which simulate the elastic interactions between them. Owing to the change in volume of the complexes during the spin transition, an elastic force accompanies the switch of every complex. This force propagates through the entire lattice and causes a shift of all molecules in the system and thus results in a new nuclear configuration. First, the ability of the model to reproduce various shapes of thermal transition and relaxation curves in pure compounds is analyzed; these range from gradual to very steep and include hysteresis behavior for the former and from single exponential to sigmoidal or with several steps for the latter. A structural phase transition can also be accounted for by changing the shape of the sample at a fixed temperature from a regular to an elongated hexagon. Furthermore, the effect of adding Zn as a dopant in a mixed crystal series is discussed. The role of dopants on the cluster evolution is also analyzed directly and by using the correlation factor.

The thermal spin transition, the photoexcitation, and the subsequent spin relaxation in the mixed crystal series of the covalently linked two-dimensional network {[Zn_1-xFe_x(bbtr)₃](ClO₄)₂}_∞ (x = 0.02–1, bbtr =1,4-di(1,2,3-triazol-1-yl)-butane) are discussed. In the neat compound, the thermal spin transition with a hysteresis of 13 K is accompanied by a crystallographic phase transition (Kusz, J.; Bronisz, R.; Zubko, M.; Bednarek, H. Chem. Eur. J.2011, 17, 6807). In contrast, the diluted crystals with x ≤ 0.1 stay essentially in the high-spin state down to low temperatures and show typical first order relaxation kinetics upon photoexcitation, and the structural phase transition is well separated from the spin transition. With increasing Fe(II) concentration, steeper thermal transitions and sigmoidal relaxation curves indicate increasingly important cooperative effects. Already at x = 0.38, the spin relaxation is governed by cooperative interactions between Fe(II) centers, and the crystallographic phase transition begins to influence the spin transition. The kinetic behavior of the thermal spin transition is reproduced within the framework of a dynamic mean-field model.

The recently developed mechanoelastic model is applied to characterize the thermal transition in spin-crossover complexes, with special attention given to the case of spin-crossover nanoparticles. In a two-dimensional system, hexagonal-shaped samples with open boundary conditions are composed of individual molecules that are linked by springs and can switch between two states, namely, the high-spin (HS) and the low-spin (LS) states. The switching of an individual molecule during the spin transition is decided by way of a Monte Carlo standard procedure, using transition probabilities depending on the temperature, the energy gap between the two states, the enthalpy difference, the degeneracy ratio, and the local pressure determined by the elongation or compression of its closest springs. The influence of external parameters, such as temperature sweeping rate and pressure, or intrinsic features of the system, such as the value of its spring constant, on the width of the thermal hysteresis, its shape, and its position are discussed. The particular case of spin-crossover nanoparticles is treated by considering them embedded into a polymer environment, which essentially affects the molecules situated at the edges and faces by decreasing their transition probabilities from HS to LS. Finally, the pressure hysteresis, obtained by varying the external pressure at constant temperature is discussed.

We model here the behavior of spin transition compounds, considering molecules arranged in a 2D hexagonal lattice and interacting via springs. The role of impurities in the clustering and nucleation phenomena is analyzed, as well as the manner in which the impurities affect the relaxation curves. The switching of the individual molecules is checked using a Monte Carlo procedure. When a molecule changes its state, it also modifies its volume, and the new equilibrium positions of all the molecules are calculated. As in previously reported experiments, it is found here that bigger impurities slow down the relaxation from the metastable high-spin state to the low-spin state, while smaller impurities act in an opposite way. It is shown that if the concentration of the impurities is higher than a certain threshold, then they act as a barrier, trammeling the fast evolution of domains developing from the edges.

Whereas the neat polymeric iron(II) compound [Fe(bbtr)₃](ClO₄)₂, bbtr = 1,4-di(1,2,3-triazol-1-yl)butane, shows a quantitative spin transition triggered by a crystallographic phase transition centered at 107 K with a 13 K wide hysteresis, the iron(II) complexes in the diluted mixed crystals [Fe_xZn_1−x(bbtr)₃](ClO₄)₂, x = 0.02 and 0.1, stay predominantly in the ⁵T₂ high-spin state down to cryogenic temperatures. However, the ¹A₁ low-spin state can be populated as metastable state via irradiation into the spin-allowed ⁵T₂→⁵E ligand-field transition of the high-spin species in the near-infrared. The quantum efficiency of the light-induced conversion is approximately 10% at low temperatures and decreases rapidly above 160 K. The lifetime of the light-induced low-spin state decreases from 15 days at 40 K to 30 ns at 220 K, that is, by 14 orders of magnitude. In the high-temperature regime the activation energy for the low-spin→high-spin relaxation is 1840(20) cm^−1.

In the dilute mixed-crystal system [Zn_1−xFe_x(bbtr)₃](ClO₄)₂, x=2 % (bbtr=1,4-di(1,2,3-triazol-1-yl)butane), the iron(II) centers are predominantly in the high-spin state. The low-spin state can be populated as a metastable state by irradiation with near-IR light; the rate constant of the low-spin→high-spin relaxation spans 14 orders of magnitude between 40 and 220 K

In this paper we use a recently proposed elastic model in order to study the competition between linear photoexcitation and cooperative relaxation in spin-crossover molecular magnets. The difference in molecular size between the two possible spin states, that is, the high-spin and the low-spin states, respectively, induces distortions of the crystal lattice. These determine the elastic interactions between molecules, treated here as connecting springs that are either compressed or extended from their equilibrium length, thus modulating the local probability for the high-spin→low-spin relaxation. The crossover of individual molecules within the lattice is checked by a standard Monte Carlo procedure. Using very simple assumptions and a minimum number of parameters, photoexcitation curves and hysteresis loops under continuous irradiation below the thermal transition temperature can thus be simulated. The formation of clusters is analyzed and the presence of inhomogeneities in the system is investigated.

In this paper we study the cluster formation and evolution in spin crossover systems during the thermal transition in the frame of a mechano-elastic model applied to open boundary hexagonal lattices. The switching processes between the high-spin (HS) and low-spin (LS) state are studied by a method combining a Monte Carlo standard procedure on the spin state and the lattice relaxation. In the present study, we adopt the transition probabilities of the spin state taking into account the energy gap between the two states, the degeneracy ratio and the local pressure determined by the elongations of the closest springs. It is found that clusters of molecules in the same state tend to grow starting from corners, as in available experimental data. Some qualitative differences between the processes of cluster formation for the two hysteresis branches, i.e., HS to LS and LS to HS are pointed out. Moreover, we have studied the dependence of cluster formation on the strength of the elastic interactions, and also on the system size. The size dependence of the ratio between the system size and the maximum cluster length is very weak, which indicates the appearance of macroscopic domains.

The relaxation in a spin transition compound is modeled on the basis of molecules interacting by theway of connecting springs and situated in a bidimensional open boundary hexagonal lattice. The switch ofindividual molecules is randomly checked using a standard Monte Carlo procedure. The switchingprobability depends on the energy gap between the two states in the absence of interactions and on theelongations of the nearest springs. The main characteristics of the experimental relaxation curves arereproduced and clustering and nucleation phenomena are detected.

The thermal and the light-induced spin transition in [Fe(bbtr)₃](ClO₄)₂ (bbtr = 1,4-di(1,2,3-triazol-1-yl)) as well as the high-spin → low-spin relaxation following the light-induced population of the high-spin state below the thermal transition temperature are discussed in relation to the accompanying crystallographic phase transition. The experimental data have exclusively been obtained using optical single crystal absorption spectroscopy.

The spin-crossover compound [Fe(bbtr)₃](ClO₄)₂ (bbtr = 1,4-di(1,2,3-triazol-1-yl)butane) forms a polymeric hexagonal sheet structure. It shows an abrupt thermal spin transition with 13 K wide hysteresis around 105 K, as evidenced by single crystal optical spectroscopy. The transition temperature for the thermal high-spin→low-spin transition on cooling as well as the relaxation kinetics just below T_c^↓ depend upon the history of the sample. This is typical for a nucleation and growth mechanism and domain formation. In contrast, the high-spin→low-spin relaxation following the light-induced population of the high-spin state at low temperatures is governed by the intersystem crossing process.

The spin transition of the [Co(terpy)₂]²⁺ complex (terpy = 2,2′:6′,2″-terpyridine) is analysed based on experimental data from optical spectroscopy and magnetic susceptibility measurements. The single crystal absorption spectrum of [Co(terpy)₂](ClO₄)₂ shows an asymmetric absorption band at 14 400 cm^−1 with an intensity typical for a spin-allowed d–d transition and a temperature behaviour typical for a thermal spin transition. The single crystal absorption spectra of suggest that in this compound, the complex is essentially in the high-spin state at all temperatures. However, the increase in intensity observed in the region of the low-spin MLCT transition with increasing temperature implies an unusual partial thermal population of the low-spin state of up to about 10% at room temperature. Finally, high-spin → low-spin relaxation curves following pulsed laser excitation for [Co(terpy)₂](ClO₄)₂ dispersed in KBr discs, and as a comparison for the closely related [Co(4-terpyridone)₂](ClO₄)₂ spin-crossover compound are given.

Whereas there are hundreds of known iron(II) spin-crossover compounds, only a handful of cobalt(II) spin-crossover compounds have been discovered to date, and hardly an in depth study on any of them exists. This review begins with an introduction into the theoretical aspects to be considered when discussing spin-crossover compounds in general and cobalt(II) systems in particular. It is followed by case studies on [Co(bpy)₃]²⁺ and [Co(terpy)₂]²⁺ (bpy = 2,2′-bipyridine, terpy = 2,2′:6′,2″-terpyridine) presenting and discussing results from magnetic susceptibility measurements, X-ray crystallography, optical spectroscopy, and EPR spectroscopy.

The photophysical properties of the ferric catecholate spin-crossover compounds [(TPA)Fe(R-Cat)]X (TPA=tris(2-pyridylmethyl)amine; X=PF₆^-, BPh₄^-; R-Cat=catecholate dianion substituted by R=NO₂, Cl, or H) are investigated in the solid state. The catecholate-to-iron(III) charge-transfer bands are sensitive both to the spin state of the metal ion and the charge-transfer interactions associated with the different catecholate substituents. Vibronic progressions are identified in the near-infrared (NIR) absorption of the low-spin species. Evidence for a low-temperature photoexcitation process is provided. The relaxation dynamics between 10 and 100 K indicate a pure tunneling process below ≈40 K, and a thermally activated region at higher temperatures. The relaxation rate constants in the tunneling regime at low temperature, k_HL(T→0), vary in the range from 0.58 to 8.84 s^-1. These values are in qualitative agreement with the inverse energy-gap law and with structural parameters. A comparison with ferrous spin-crossover complexes shows that the high-spin to low-spin relaxation is generally faster for ferric complexes, owing to the smaller bond length changes for the latter. However, in the present case the corresponding rate constants are smaller than expected based on the single configurational coordinate model. This is attributed to the combined influence of the electronic configuration and the molecular geometry.

The high-spin → low-spin relaxation in spin-crossover compounds can be described as non-adiabatic multi-phonon process in the strong coupling limit, in which the low-temperature tunnelling rate increases exponentially with the zero-point energy difference between the two states. Based on the hypothesis that the experimental bond length difference between the high-spin and the low-spin state of ~0.2 Å is also valid for low-spin iron(II) complexes, extrapolation of the single configurational coordinate model allows an estimate of the zero-point energy difference for low-spin complexes from kinetic data. DFT calculations on low-spin [Fe(bpy)₃]²⁺ support the structural assumption. However, for low-spin [Fe(terpy)₂]²⁺ the relaxation rate constant shows an anomalous behaviour in so far as it is more in line with spin-crossover systems. This is attributed to very anisotropic bond length changes associated with the spin state change, and the subsequent breakdown of the single mode model.

The compound {Fe(pmd)[Ag(CN)₂][Ag₂(CN)₃]} (pmd=pyrimidine) was synthesized and characterized. Magnetic, calorimetric and single crystal visible spectroscopic studies demonstrate the occurrence of a two-step high-spin (HS) ↔ low-spin (LS) transition. The critical temperatures are T_c1=185 and T_c2=148 K. Each step involves ~50 % of the iron centers, with the low-temperature step showing a hysteresis of 2.5 K. The enthalpy and entropy variations associated with the two steps are ΔH₁=3.6±0.4 kJ mol^-1 and ΔS₁=19.5±3 J K^-1 mol^-1; ΔH₂=4.8±0.4 kJ mol^-1 and ΔS₂=33.5±3 J K^-1 mol^-1. Photomagnetic and visible spectroscopy experiments show that below 50 K, where the LS state is the thermodynamically stable state, the compound can be switched quantitatively to the HS state using green-red light (550-650 nm). HS-to-LS relaxation experiments in the dark at temperatures between 15 and 55 K show that the relaxation takes place via a two-step cooperative process, which was analyzed in the context of the mean field theory. The crystal structure has been studied at 290, 220, 170, 90 and 30 K together with 30 K after irradiation. The compound adopts monoclinic symmetry (P2₁/c, Z=16) at all temperatures. There are five [FeN₆] pseudo-octahedral sites linked by pmd, [Ag(CN)₂]^- and [Ag₂(CN)₃]^- bridging ligands to form an unprecedented three-dimensional (6,6) topology. The structural analysis allows for an understanding of the microscopic mechanism of the two-step behavior of the thermally induced spin transition as well as the corresponding relaxation of the photoexcited compound based on the individual changes of the five sites. Synergy between metallophilic interactions and the spin transition is also shown by the variation of the Ag^…Ag distances. Correlations between the variation of the unit-cell volume and the change of Ag^…Ag interactions within each step with the asymmetric change of the anomalous heat capacity have also been inferred.

In this paper we discuss on the quantum efficiency in spin crossover compounds. Spin crossover solids are text-book examples of photo switchable materials that present a thermal spin transition from the diamagnetic low-spin state, thermodynamically stable at low temperatures, to the paramagnetic high-spin state becoming the thermodynamically stable state at elevated temperature. By irradiating them with an appropriate wavelength, they can pass from the stable low spin state to the metastable high spin state at temperatures below the thermal transition temperature. For the compound [Fe(pic)₃]Cl₂·EtOH, the question regarding the quantum efficiency of the photo-conversion process that is the number of molecules converted by one single photon and its possible dependency on irradiation intensity gave rise to a controversy. The experimental results presented in this paper demonstrate that the quantum efficiency of the photo-conversion at 11 K is on the order of unity, with no noticeable dependency of the quantum efficiency on light intensity. It does, however, depend to a small extent on the fraction of complexes already converted to the high-spin state.

[Fe(pic)₃]Cl₂·EtOH (pic = 2-picolylamine) is a spin-crossover compound that can be converted from the low-spin state to the high-spin state at temperatures below the thermal transition temperature by way of light irradiation in the visible part of the electromagnetic spectrum. For this compound, the question regarding the quantum efficiency of this photoconversion process and its possible dependence on irradiation intensity gave rise to some controversy. The experimental results presented in this paper demonstrate that the quantum efficiency of the photoconversion at 11 K is on the order of unity, with no noticeable dependence on irradiation intensity. It does, however, depend to some extent on the fraction of complexes already converted to the high-spin state.