Pressure Tunable Electronic Bistability in Fe(II) Hofmann-like Two-Dimensional Coordination Polymer [Fe(Fpz)2Pt(CN)4]: A Comprehensive Experimental and Theoretical Study

A comprehensive experimental and theoretical study of both thermal-induced spin transition (TIST) as a function of pressure and pressure-induced spin transition (PIST) at room temperature for the two-dimensional Hofmann-like SCO polymer [Fe(Fpz)2Pt(CN)4] is reported. The TIST studies at different fixed pressures have been carried out by magnetic susceptibility measurements, while PIST studies have been performed by means of powder X-ray diffraction, Raman, and visible spectroscopies. A combination of the theory of elastic interactions and numerical Monte Carlo simulations has been used for the analysis of the cooperative interactions in TIST and PIST studies. A complete (T, P) phase diagram for the compound [Fe(Fpz)2Pt(CN)4] has been constructed. The critical temperature of the spin transition follows a lineal dependence with pressure, meanwhile the hysteresis width shows a nonmonotonic behavior contrary to theoretical predictions. The analysis shows the exceptional role of the total entropy and phonon contribution in setting the temperature of the spin transition and the width of the hysteresis. The anomalous behavior of the thermal hysteresis width under pressure in [Fe(Fpz)2Pt(CN)4] is a direct consequence of a local distortion of the octahedral geometry of the Fe(II) centers for pressures higher than 0.4 GPa. Interestingly, there is not a coexistence of the high- and low-spin (HS and LS, respectively) phases in TIST experiments, while in PIST experiments, the coexistence of the HS and LS phases in the metastable region of the phase transition induced by pressure is observed for a first time in a first-order gradual spin transition with hysteresis.

The measured spectrum consists of two bands: one at central wavelength of 415 nm (red color) and a second at 450 nm (green color). With pressure increase the first band decreases and the second one increases (see Figure S1 at P = 2.01 GPa). At higher pressure the first band vanishes, the second increases and appears a third band (blue color) with a central wavelength of 493 nm (see P = 3.78 GPa). Based on the previous analyzes of optical absorption spectra in Hoffman-like complexes we assign the first band to the metal -ligand chard transfers (MLCT) in the HS state, and the second and third bands to the 1 A 1g → 1 T 2g and 1 A 1g → 1 T 1g transitions, respectively, belonging to low spin state. So, at ambient pressure we see that the compound under studying is in the HS state. The observed small amount of LS state (the band centered at λ = 450 nm) is caused by the difficulties to receive ambient pressure in anvil pressure cells, because even a very small moving of the anvils increases the pressure. Under pressure increase the decrease of the HS state and increase the LS state is observed. The received γ HS -P diagram is presented in Figure 5.

S7
The third-order Birch-Murnaghan equation: where P is the pressure, V 0 is the reference volume, V is the deformed volume, B 0 is the bulk modulus, and B 0 ' is the derivative of the bulk modulus with respect to pressure.   Table S2: Thermodynamic parameters of TIST under pressure obtained using the elastic model.

P (Gpa)
T 1/2 ↓ (K) T 1/2 ↑ (K) T 1/2 (K) ΔT 1/2 (K)  Figure S8. Pressure dependence of the ratio of the interaction parameter between molecules to the splitting energy Γ/(ΔH + Δ elast -Γ+ PΔV HL ). This ratio determines the width of the hysteresis in all theoretical approximations and, as can be seen from its behavior and the experimental change in the width of the hysteresis (Figure 3), it qualitatively reflects the experimental behavior of the hysteresis width, when the change of entropy at ST is a constant value.

The Monte Carlo model
Theoretical study was conducted in framework of microscopic Ising-like model with the help of Monte Carlo technique based on the Heatbath algorithm. Given model considers intermolecular interaction in the nearest neighbor's approach according to the following Hamiltonian: here si is the fictitious spin for each site (i = 1, 2, . . ., N) which takes two values ±1 and corresponds to HS and LS states, respectively. The first term in the Hamiltonian describes the intermolecular interactions through a parameter which accounts the ferromagnetic coupling (J > 0) between neighboring spins i and j.
-sum over all nearest-< i, j > neighboring spins (sites). The second term characterizes the occurrence of intramolecular processes and describes the action of the crystal field together with the influence of temperature and external pressure on the spin-crossover site: where Δ is the energy gap between HS and LS states; T is the absolute temperature (in Kelvin degree); k B is the Boltzmann constant; g = g HS /g LS is degeneracy ratio of spin crossover states; p is the external pressure, ΔV HL is the molecular volume change during transition between the states. The second term of the ligand field (2) is the heat energy k B T and it account is justified by the internal entropy effects. Since the applied pressure simultaneously changes the molecular volume, the pressure action in given model is considered by the product -PΔV HL .
Simulation technique was conducted on a two-dimensional square lattice with periodical boundary conditions and the size of N = L × L = 70 × 70 (L -the side length) which is enough to eliminate the size effect. The system was initialized with all spins down at a low temperature. Then we increase the temperature and put the system in contact with heat bath at every considered temperature T. When the temperature increases, the spins randomly flip. The transition probability of each spin according to Heatbath algorithm is defined as: here ΔH{si} is the energy difference when a spin changes between spin states. For modeling we used 5000 Monte Carlo steps per Kelvin degree. Besides, the first 1000 of which were discarded to eliminate the effect of the Monte Carlo steps length and to balance the system before averaging its parameters. One Monte Carlo step is considered completed when all molecules are swept. In given approach we took k B = 1 and g=150 for reasons of obtaining entropy close to the generally accepted value.
The resulted system magnetization was calculated as average on Monte Carlo steps (N MC ): S11 where m = 〈 〉 #( 6)# 〈 〉 = 1 ∑ #( 7)### The relation between this magnetization and system's order parameter is the following: In the case of gradual spin transition with hysteresis it is not possible to fit the all curve γ HS (P). It possible to fit the curve at only at γ HS =1/2 and at P 1/2 . This fitting allows receiving the change of enthalpy ΔH HL and interaction parameter Γ at PIST.