High-spin Fraction Research Articles

Nonequivalent Antiferromagnetically Coupled Sublattices Induce Two-Step Spin-Crossover Transitions: Equilibrium and Nonequilibrium Aspects

As a continuation to the previously published work (Yalçın et al. (2022)), we investigate the equilibrium and nonequilibrium properties of the spin-crossover systems, with a specific focus on the nonequivalent sublattice, and compare these properties with those of the equivalent sublattices. We used the lowest approximation of the cluster variation method (LACVM) to derive the static equations for the order parameters of the two sublattices and determine high-spin fraction in relation to temperature and external magnetic field in a spin-crossover system. At a low temperature, the transition from stable high-spin (HS) state where nHS=1 occurs in the plateau region, where nHS=0.5 for nonequivalent sublattices. The order parameters for non-equivalent sublattices exhibit different states at the transition temperature. Also, we study the nonequilibrium properties of the order parameters and high-spin fraction using the path probability method (PPM). With the current model, we obtain and analyze the relaxation curves for the order parameters Sa, Sb, and high-spin fraction. These curves demonstrate the existence of bistability at low temperatures. At the end of this study, we present the flow diagram that shows the order parameters for different temperature values. The diagram exhibits states that are stable, metastable, and unstable.

The role of anharmonicity in single-molecule spin-crossover

We exploit the system-bath paradigm to investigate vibrational-anharmonicity effects on spin-crossover in a single molecule. Focusing on weak coupling, we use the linear response approximation to deal with the nonlinear vibrational bath and propagate the Redfield master equation to obtain the equilibrium high spin fraction. We take both the anharmonicity in the bath potentials and the nonlinearity in the spin-vibration coupling into account and find a strong interplay between these two effects. Further, we show that the spin-crossover in a single molecule is always a gradual transition and the anharmonicity-induced phonon drag greatly affects the transition behavior.

Spin crossover in dinuclear iron(II) complexes bridged by bis-bipyridine ligands: dimer effects on electronic structure, spectroscopic properties and spin-state switching.

Inspired by the well-studied mononuclear spin crossover compound [Fe(H2B(pz)2)2(bipy)], the bipyridine-based bisbidentate ligands 1,2-di(2,2'-bipyridin-5-yl)ethyne (ac(bipy)2) and 1,4-di(2,2'-bipyridine-5-yl)-3,5-dimethoxybenzene (Ph(OMe)2(bipy)2) are used to bridge two [Fe(H2B(pz)2)2] units, leading to the charge-neutral dinuclear iron(II) compounds [{Fe(H2B(pz)2)2}2 μ-(ac(bipy)2)] (1) and [{Fe(H2B(pz)2)2}2 μ-(Ph(OMe)2(bipy)2)] (2), respectively. The spin-crossover properties of these molecules are investigated by temperature-dependent PPMS measurements, Mössbauer, vibrational and UV/Vis spectroscopy as well as X-ray absorption spectroscopy. While compound 1 undergoes complete SCO with T1/2 = 125 K, an incomplete spin transition is observed for 2 with an inflection point at 152 K and a remaining high-spin fraction of 40% below 65 K. The spin transitions of the dinuclear compounds are also more gradual than for the parent compound [Fe(H2B(pz)2)2(bipy)]. This is attributed to steric hindrance between the molecules, limiting intermolecular interactions such as π-π-stacking.

Electro-Elastic Modeling of Multi-Step Transitions in Two Elastically Coupled and Sterically Frustrated 1D Spin Crossover Chains

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.

Surface-Bulk 2D Spin-Crossover Nanoparticles within Ising-like Model Solved by Using Entropic Sampling Technique

We model the thermal effects in different 2D spin-crossover (SCO) square lattices within the frame of the Ising-like model using Monte Carlo entropic sampling (MCES) method to enhance the scan of macrostates beyond the most probable thermal ones. In fact, MCES allows access to the metastable states, and it is then well adapted to study thermal hysteresis properties. In this contribution, we distinguish, for the first time, the interaction between molecules located in bulk at the surface and those connecting the bulk and surface regions of an SCO lattice. In addition, an extra ligand field contribution is assigned to surface molecules through an interaction parameter L. In the absence of environmental effects on surface nanoparticles, a single thermal hysteresis loop increasing with the lattice size is simulated with a unique bulk and surface equilibrium temperature Teq=Teqbulk= Teqsurf. When environmental effects are accounted for, a two-step behavior associated with two hysteresis loops of widths ΔTS (for the surface) and ΔTB (for the bulk) with an intermediate plateau 14 K wide is obtained in the thermal dependence of the high-spin (HS) fraction for the 6 × 6 lattice. The surface and bulk equilibrium temperatures are then different, both decreasing towards lower values, and the L parameter controls the three states’ behavior as well as the hysteresis loop interval. Size effects show that the equilibrium temperature is governed by the surface atoms for a small lattice size (5 × 5) and by the bulk atoms for a large lattice size (7 × 7). Moreover, a change in the size of the lattice results in a variation of the order–disorder (or Curie) temperature, TO.D., and the surface equilibrium temperature, Teq, while only TO.D. changes in bulk.

Is the surface of Hofmann-like spin-crossover {Fe(pz)[Pt(CN)4]} the same as its bulk?

Temperature dependent X-ray photoemission spectroscopy (XPS) has been employed to examine the spin-crossover (SCO) transition in the nanocrystals of 3D Hoffman-like {Fe(pz)[Pt(CN)4]}. Consistent with the existing literature, the temperature-dependent variations in the Fe 2p core-level spectrum provide unambiguous evidence of the spin-state transition in this SCO complex. One of the many possible reasons behind a lack of discernible temperature-driven shifts in the binding energies of both the N 1s core-level components could be the immunity of its HS electronic configuration to thermal fluctuations. The high-spin fraction versus temperature plot, extrapolated from the XPS measurements, reveals that the surface of the nanocrystals of {Fe(pz)[Pt(CN)4]} is in the high-spin state at room temperature, rendering it promising for room-temperature spintronics and quantum information science applications.

Surface stabilisation of the high-spin state of Fe(II) spin-crossover complexes.

Temperature dependent X-ray photoemission spectroscopy (XPS) has been employed to examine the Fe 2p and N 1s core levels of the studied Fe(II) spin crossover (SCO) complexes of interest, namely: Fe(phen)2(NCS)2, [Fe(3-Fpy)2{Ni(CN)4}], and [Fe(3-Fpy)2{Pt(CN)4}]. The changes in the Fe 2p core-level spectra with temperature indicate spin state transitions in these SCO complexes, which are consistent with one's expectations and the existing literature. Additionally, the temperature dependence of the binding energy of the N 1s core-level provides further physical insights into the ligand-to-metal charge transfer phenomenon in these molecules. The high-spin fraction versus temperature plots reveal that the surface of each of the molecules studied herein is found to be in the high-spin state at temperatures both in the vicinity of room temperature and below their respective transition temperature alike, with the stability of the high-spin state of these molecules varying with the choice of ligand.

The Valence and Spin State Tuning of Iron(II/III) Porphyrazines with Bulky Pyrrolyl Periphery in Solution and Solid State.

Iron(III) porphyrazines containing peripheral 2,5-dimethyl-, 2-methyl-5-phenyl-, and 2,3,5-triphenyl-1H-pyrrol-1-yl substituents were synthesized and subjected to physicochemical characterization. This was accomplished by high-resolution mass spectrometry, nuclear magnetic resonance (as diamagnetic Fe(II) derivatives), HPLC purity analysis, and UV-Vis spectroscopy, accompanied by the solvation study in dichloromethane and pyridine. X-ray structure analysis was performed for a single crystal of the previously obtained 2,5-diphenyl-substituted derivative of porphyrazine complex (5d). The octahedral geometries of iron cation, present in the porphyrazine core, influenced the packing mode of molecules in the crystals. Mössbauer studies, performed for solid samples of iron porphyrazines, indicated that low-spin reduced iron states might occupy low- or high-symmetry binding sites. It was found that the hyperfine parameters and the subsequent contribution of the iron cations depend on the number of phenyl groups surrounding the pyrrolyl moiety. For iron(II) porphyrazine 2,3,5-triphenylpyrrol-1-yl substituents (5b), a high-spin ferrous state fraction was observed. Temperature-dependent measurements showed that the freed rotation of the peripheral porphyrazine ligands and the increased flexibility of the macrocycle ring result in the Fe2+ ion being stabilized in a diamagnetic state at a binding site of high symmetry at room temperature in the solid state. This process is most probably stimulated by the range of collective motions of the polymeric ribbons consisting of iron(II) porphyrazines observed in the X-ray.

Static and dynamic properties of two-sublattice spin-crossover systems

We investigate the static and dynamic properties of spin-crossover systems in the presence of an external magnetic field using two-sublattice Ising-like Hamiltonian. At low temperatures both sublattices are in the LS state, and in the HS state at high temperatures. The new feature of spin-crossover is depicted for our model when we take the non-equivalent sublattices JA≠JB, the two-step spin-crossover phase transition is obtained with the presence of the hysteresis loop. In order to study the properties of two-step spin-crossover, we use the lowest approximation of the cluster variation method for static properties. The dynamic properties of the system with bilinear interactions are studied by the path probability method. We present high-spin state fraction nHS vs temperature and magnetic field variations for constant values of the degeneracy ratio between high-spin and low-spin states. In the present model, we obtained the relaxation curves of the order parameters SA and SB using different temperature values. Finally, the flow diagram of the order parameters is depicted for different values of rate constant k1 and temperature, which displays the stable, metastable, and unstable properties. Static and dynamic self-consistent equations of the system were performed by using Newton-Raphson and Runge-Kutta methods.

A Smart Molecule Showing Spin Crossover Responsive Aggregation-Induced Emission

A Smart Molecule Showing Spin Crossover Responsive Aggregation-Induced Emission

Slow Phase Transition-Induced Scan Rate Dependence of Spin Crossover in a Two-Dimensional Supramolecular Fe(III) Complex

Slow Phase Transition-Induced Scan Rate Dependence of Spin Crossover in a Two-Dimensional Supramolecular Fe(III) Complex

New Spin-Crossover Compounds Containing the [Ni(mnt)] Anion (mnt = Maleonitriledithiolate)

Two novel salts containing the anion [Ni(mnt)2]− (mnt = maleonitriledithiolate) have been synthesized. The counter-ions, [Fe(II)(L1 or L2)2], are cationic complexes where L1 and L2 are methylated derivatives of 2,6-bis(pyazolyl)pyridine or pyrazine, which are similar to ligands found in a series of spin-crossover (SCO) complexes. Both salts are characterized by variable temperature single crystal X-ray diffraction and bulk magnetization measurements. Compound 1, [Fe(II)(L1)2][Ni(mnt)2]2 displays an incomplete and gradual SCO up to 300 K, followed by a more rapid increase in the high-spin fraction between 300 and 350 K. Compound 2, [Fe(II)(L2)2][Ni(mnt)2]2.MeNO2, shows a gradual, but more complete SCO response centered at 250 K. For compound 2, the SCO is confirmed by variable temperature Mössbauer spectroscopy. In both cases, the anionic moieties are isolated from each other and so no electrical conductivity is observed.

Coupling and decoupling of spin crossover and ferroelastic distortion: Unsymmetric hysteresis loop, phase diagram, and sequence of phases

Spin-transition materials can exhibit thermal hysteresis due to cooperative elastic interactions in between active molecular sites. It results from the coupling of the nonsymmetry-breaking high spin fraction order parameter to the lattice volume strain. However, a symmetry-breaking order parameter responsible for crystallographic phase transition, like a ferroelastic distortion, can also couple to the volume strain. Here, we use the Landau theory to study the elastic coupling between a spin-crossover instability and a discontinuous ferroelastic distortion and the different phase transition lines. Below the triple point, the first-order line involves simultaneous ferroelastic distortion and spin transition. Above, the purely first-order ferroelastic distortion and the spin crossover occur sequentially. Our model, related to the coupling and decoupling of the ferroelastic phase transition and spin crossover, explains exotic behaviors reported experimentally in the literature for diverse spin-crossover systems, plastic crystals, or Prussian blue analogues. The unsymmetric hysteresis loops and the stepwise evolution of the spin conversion or volume strain under pressure result from different sequences of phase transitions. The model shows that the ferroelastic phase transition is the driving force of the cooperative spin transition hysteresis in this case.

Magnetic-field induced multi-step transitions in ferromagnetic spin-crossover solids within the BEG model

We study by means of the 2D Blume–Emery–Griffiths (BEG) spin-1 model, spin-crossover (SCO) and prussian blue analogs (PBAs) solids. In this model, the spin states, which can be high-spin (HS) or low-spin (LS), interact magnetically and elastically with their nearest neighbors. To account for the volume change, accompanying the spin transition phenomenon, all interactions through the lattice are assumed as temperature-dependent. In addition, the system is subject to a variable magnetic field lifting the degeneracy in the HS state. A stochastic cooperative dynamics of this BEG-like Hamiltonian, describing the equilibrium and nonequilibrium properties of ferromagnetic spin-crossover solids, is derived from the Glauber approach, with appropriate Arrhenius microscopic transition rates. The model generates under the magnetic field, sigmoidal relaxation and a hysteresis phenomenon of the HS fraction, as well as multistep behavior of the magnetization. These behaviors open the way to new route of multi-stable systems, desired in multi-byte electronics.

Crystal Size Effect on the Spin-Crossover Behavior of {Fe(py)2[Pt(CN)4]} (py = Pyridine) Monitored by Raman Spectroscopy.

The spin-crossover phenomenon in nanomaterials has been the subject of exploratory investigations for stimuli-responsive switching properties at nanoscale. Using variable-temperature Raman spectroscopy, we investigated changes in the temperature-driven spin-transition property of {Fe(py)2[Pt(CN)4]} (py = pyridine) induced by a size reduction from a bulk polycrystalline powder to an ultrathin film (crystallite size, 15 nm). When the crystallite size was reduced, the spin-transition temperature shifted lower and the spin-transition curves became less steep. In the thin-film form, the residual high-spin fraction was found to be about 20%.

Theoretical investigations on the pressure effects in spin-crossover materials: Reentrant phase transitions and other behavior

Pressure effects have been widely studied in spin-crossover (SCO) solids due to their immediate influence on the thermal dependence of the high-spin (HS) fraction. In most of the cooperative SCO materials, the applied pressure shifts the transition temperatures upward and decreases the thermal hysteresis widths to such an extent that it vanishes at some critical pressure. However, several other unexpected experimental features were found in the literature, showing that the applied pressure may (i) induce an increase of the thermal hysteresis width or even (ii) lead to a reentrant behavior on the thermal hysteresis whose width first increases for low applied pressures and then decreases at high-pressure values. These nonstandard behaviors have been classified as anomalous, even though the transition temperature always increases under pressure. In this theoretical contribution, we rationalize all these behaviors by describing the spin-crossover system under pressure with an elastic description accounting for the difference of lattice parameters between the low-spin (LS) and HS phases including the pressure effects. The analytical study of this elastic model in the homogeneous mechanical system demonstrated its isomorphism with an Ising-like model with infinitely long-range interactions, in which the pressure acts linearly on the ligand field and nonlinearly on the strength of the interactions. The resolution of this model brings to light the existence of a pressure-induced interplay between these two contributions allowing one to recover a wide range of normal and abnormal observed experimental thermal dependences of the spin transition under pressure.

Extension of Azine-Triazole Synthesis to Azole-Triazoles Reduces Ligand Field, Leading to Spin Crossover in Tris-L Fe(II).

The first examples of azole-triazole Rat ligands, bidentate L4NMeIm(3-(1-methyl-1H-imidazol-4-yl)-5-phenyl-4-(p-tolyl)-4H-1,2,4-triazole) and L4SIm (4-(5-phenyl-4-(p-tolyl)-4H-1,2,4-triazol-3-yl)thiazole), have been prepared, by extension of the general synthesis used to access many examples of azine-triazoles. The tris-L FeII complexes of the azine-triazoles are consistently low spin (LS). As intended, these new azole-triazole ligands provide lower field strengths, resulting in high-spin (HS) [FeII(L4NMeIm)3](BF4)2 (1·4H2O) and spin crossover (SCO) active [FeII(L4SIm)3](BF4)2 (2·0.5H2O). Single-crystal structure determinations revealed that at 100 K 1·solvents is HS whereas 2·solvents is LS. Solid-state variable temperature magnetic studies of air-dried crystals showed that the methylimidazole-triazole complex 1·4H2O remains HS while the thiazole-triazole complex 2·0.5H2O undergoes a two-step gradual SCO (T1/2 approximately 275 and 350 K). Variable-temperature Evans method NMR studies of 2, in five different solvents (CD3NO2, CD3CN, CD3COCD3, CD2Cl2, and CDCl3) gave T1/2 values in a relatively narrow range, 214-259 K. These T1/2 values did not correlate with the solvent polarity index P' (R2 = 0.25) but did correlate with the solvent basicity parameter SB (R2 = 0.90). Variable-temperature UV-vis studies on a golden yellow CH3CN solution of 2, with monitoring of the d-d transition at 530 nm (ε = 39 L mol-1 cm-1 at 293 K) while the solution was heated from 253 to 303 K, showed that the high-spin fraction increased from 0.51 to 0.77. Cyclic voltammetry studies in CH3CN revealed a Fe(III)/Fe(II) redox process that was reversible for 1 and irreversible for 2, with significant tuning of the Epa value: the methylimidazole-triazole complex 1 is significantly easier to oxidize (0.46 V) than the thiazole-triazole complex 2 (0.68 V; both vs 0.01 M Ag/AgNO3).

Light-induced spin transition in the spin-crossover complex FePt2 detected by optical pump -coherent resonant nuclear elastic scattering

We report the results of optical pump-nuclear resonance probe experiments on the SCO complex [FeII(L-PtII(t-but-tpy))2](BF4)2 with L being 2,6-di(pyrazol-1-yl)-4-(trimethylsilylethynyl)pyridine) and t-but-tpy being 4,4′,4″-Tri-tert-Butyl-2,2′:6′,2″-terpyridine using a novel experimental set-up at the beamline P01, Petra III, DESY Hamburg. We investigate the changes in the spin state of the complex when it is excited by laser pulses of 766 nm wavelength and pulse width < 100 ps. Our simulations of the nuclear forward scattering data indicate a dominant low spin state along with some high spin fraction in the absence of laser pulses. We observe clear changes in the time-spectrum following the instant at which the laser pulse hits the sample. Furthermore, these alterations are recorded as the relative timing of the laser pulses with respect to the synchrotron pulses is varied.

Evidence of Photo-Thermal Effects on the First-Order Thermo-Induced Spin Transition of [{Fe(NCSe)(py)2}2(m-bpypz)] Spin-Crossover Material

We have investigated by means of optical microscopy and magnetic measurements the first-order thermal spin transition of the [{Fe(NCSe)(py)2}2(m-bpypz)] spin-crossover compound under various shining intensities, far from the light-induced spin-state trapping region. We found evidence of photo-heating effects on the thermally-induced hysteretic response of this spin-crossover material, thus causing the shift of the thermal hysteresis to lower temperature regions. The experimental results are discussed in terms of the apparent crystal temperature and are analyzed theoretically using two evolution equations of motion, written on the high-spin (HS) fraction and heat balance between the crystal and the thermal bath. A very good qualitative agreement was found between experiment and theory in the stationary regime, explaining the experimental observations well and identifying the key factors governing these photo-thermal effects.

Ising-like model applied to a triangular lattice of 2D spin-crossover nanoparticles: evidence of a re-entrant phase transition

We consider a 2D spin crossover (SCO) nanoparticles configuration under the influence of an external environment. Each nanoparticle is at the vertex of a triangular lattice leading to hexagonal-shaped systems. Each molecule located in the bulk is then connected to six nearest-neighbours (nn) while those situated at the surface have three or four nn.Adapting the entropic sampling Monte Carlo method, using three parameters: nHS (the total high spin fraction), s (the correlation: the sum of nn interactions the molecules) and nsHS (the high-spin fraction at the surface), we determined the density of macrostates D(nHS, nsHS,s) by scanning the full spin configurations. This information is then used to analyse the thermal behaviour of the system taking into account for the short- (J) and long-range (G) interactions as well for the interactions (L) between the molecules at the surface and the matrix (environment). The present contribution is devoted to the investigations of the required physical conditions which allow this triangular 2D lattice to exhibit a re-entrant phase transition, in particular when the size of the nanoparticles is reduced.