Observation of Haldane magnetism in organically templated vanadium phosphate (enH₂)_0.5VPO₄OH

Abstract

We prepared an organically templated magnet, (enH₂)_0.5VPO₄OH (enH₂ = diprotonated ethylenediamine), hydrothermally and characterized its crystal structure by powder X-ray diffraction and Fourier-transform infrared spectroscopy, and its physical properties by magnetization, specific heat and nuclear magnetic resonance measurements and density functional theory calculations. (enH₂)_0.5VPO₄OH consists of uniform chains of V³⁺ (d², S = 1) ions and exhibits Haldane magnetism with spin gap Δ = 59.3 K from the magnetic susceptibility χ(T) at μ₀H = 0.1 T, which is reduced to 48.4 K at μ₀H = 9 T according to the ³¹P shift. The NMR data evidence the formation of a spin-glass state of unpaired S = 1/2 spins at T_S–G ≈ 3 K and indicate that the Haldane S = 1 spin chain segments are much longer in the organically templated magnet (enH₂)_0.5VPO₄OH than in the ammonium counterpart NH₄VPO₄OH. The single-ion anisotropy D and the interchain exchange J′ in (enH₂)_0.5VPO₄OH and NH₄VPO₄OH were estimated in density functional calculations to find them very weak compared to the intrachain exchange J.

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Introduction

Haldane's prediction¹ of a singlet ground state in quasi-one-dimensional integer-spin antiferromagnets with low single-ion anisotropy D has stimulated an intensive search for compounds satisfying the strict criteria for its existence based on the D/J and J′/J ratios, where J′ and J are the interchain and the intrachain exchange interactions, respectively.² In chain compounds of S = 1 ions, the Haldane phase competes with the long-range ordered, dimerized and large-D phases. So far, ten metal–organic and three inorganic magnets based on Ni²⁺ (d⁸, S = 1) (i.e., Y₂BaNiO₅, SrNi₂V₂O₈ and PbNi₂V₂O₈) have been found to be Haldane magnets and hence have a spin gap between the continuum of excited states and the ground state.^3,4 Three more inorganic compounds, Ba₂V(VO₄)₂OH, AgVP₂S₆ and NH₄VPO₄OH, based on V³⁺ (d², S = 1) ions are also found to be Haldane magnets.^4,5 Here, we report synthesis and characterization of the first organically templated Haldane magnet based on V³⁺ ions, (enH₂)_0.5VPO₄OH, where enH₂ refers to the diprotonated ethylenediamine, H₃NCH₂CH₂NH₃²⁺. On the basis of density functional calculations, we establish the location of (enH₂)_0.5VPO₄OH on the D/J vs. J′/J phase diagram.

Synthesis and X-ray diffraction

(enH₂)_0.5VPO₄OH was synthesized hydrothermally in one step by mixing 0.0008 mol of V₂O₃, 0.0016 mol of H₃PO₄ and 0.005 mol of H₂N(CH₂)₂NH₂ in 0.44 mol of deionized H₂O at 100 rpm stirring at room temperature in a 30 ml Teflon vessel. The information on chemicals used for the synthesis is given in Table S1 of ESI.† The vessel then was sealed in steel autoclave and the mixture was hydrothermally treated at 205 °C for 7 days under constant stirring (750 rpm). After that, the autoclave was naturally cooled down to room temperature, to obtain a pale-sandy fine powder sample. The latter was carefully filtrated and washed with deionized water 5 times by centrifugation. Then it was dried overnight at 75 °C in a vacuum oven and kept under inert (Ar) atmosphere until further use.

Powder X-ray diffraction (PXRD) patterns were collected with a Bruker D8 ADVANCE powder diffractometer (λ_CuKα1 = 1.54051 Å, λ_CuKα2 = 1.54433 Å) equipped with an energy dispersive detector LYNXEYE XE in Bragg–Brentano reflection geometry (5–130° 2θ°, 0.02° scan step). The crystal structure was refined from the PXRD data with the TOPAS-Academic software package using the Rietveld method.⁶ Isostructural (enH₂)_0.5FePO₄OH was used as a starting structural model.⁷ The background was estimated by a set of polynomials, the calculation of the unit cell parameters and the refinement of the atomic coordinates were performed. According to the phase analysis no traceable impurities were observed, as shown in Fig. 1. Broad peak at about 70° is due to the sample holder. The inset to Fig. 1 represents the scanning electron microscopy (SEM) image of the sample showing its needle-like morphology. The calculated unit cell parameters are given in Table 1. Atomic fractional coordinates for (enH₂)_0.5VPO₄OH according to the Rietveld refinement are given in Table S2 of ESI.†

Fig. 1 Experimental, calculated and difference diffraction profiles of (enH₂)_0.5VPO₄OH. Inset: The SEM image of the sample.

Table 1 Rietveld refinement of cell parameters of (enH₂)_0.5VPO₄OH

Formula	(enH2)0.5VPO4OH
S.G.	P21/c
a, Å	4.5282(6)
b, Å	6.1098(12)
c, Å	18.5879(17)
β, °	94.781(3)
V, Å^3	512.48(13)
Z	4
GOF	2.43
R exp, %	3.17
R p, Rwp, %	5.62, 7.73

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As shown in Fig. 2a, (enH₂)_0.5VPO₄OH possesses a layered structure, in which the VPO₄OH⁻ layers alternate with ribbons of enH₂²⁺ cations running along the a axis. In each VPO₄OH⁻ layer, the chains of edge-sharing VO₅OH octahedra are interconnected by PO₄ groups (Fig. 2b). (enH₂)_0.5VPO₄OH belongs to the structural type of (enH₂)_0.5MPO₄OH (M = Fe, Ga)^7,8 and closely related to NH₄MPO₄OH (M = V, Ga)^5,9 (see ESI and Fig. S1†).

Fig. 2 (a) A perspective view of the crystal structure of (enH₂)_0.5VPO₄OH showing that the VPO₄OH layers are separated by the layers of the enH₂²⁺ cations. (b) A single VPO₄OH layer showing how the edge-sharing ribbon chains are interconnected by the PO₄ groups to form a VPO₄OH layer. Colors: vanadium atoms – light green, phosphorus atoms – yellow, oxygen atoms – red, nitrogen atoms – light blue, carbon atoms – intense blue, hydrogen atoms – pale pink.

Fourier-transform infrared spectroscopy

The presence of the ethylenediamine and hydroxyl groups in (enH₂)_0.5VPO₄OH was confirmed by infrared spectroscopy, as shown in Fig. 3. Fourier-transform infrared (FTIR) spectra were collected with an ALPHA II compact FTIR spectrometer (Bruker). The spectra were recorded in the 4000–400 cm⁻¹ range with 2 cm⁻¹ resolution. The reproducibility was checked by probing three different spots of the same powder sample. The presence of the hydroxyl group is manifested by a sharp maximum located at 3492 cm⁻¹ (ν(OH)).¹⁰ The group between 3300 and 2400 cm⁻¹ corresponds to the N–H and C–H vibrations in the enH₂²⁺ moiety. The most intense maximum (∼3166 cm⁻¹) is associated with N–H (stretch), which is involved in hydrogen bonding. At lower wavenumbers (1750–1250 cm⁻¹), three groups of peaks are observed, which reflect presence of enH₂²⁺ in the interlayer space. The complex shape of the spectra in this range is defined by a joint C–H and N–H vibrations.¹¹ Taking into account few previous reports about ethylenediamine-containing metal–organic compounds, we can assume that the first and second couples of maxima fall into the range of bending N–H modes and may also contain some contribution of C–H vibrations (most likely bending ones). The third couple of peaks corresponds to the C–H (bending and/or twisting) modes.^12–14 The maxima located in the 1100–500 cm⁻¹ range (except the one at 810 cm⁻¹ – δ(V–OH)) are related to the bending and stretching vibrations of the O–P–O bonds. The peak at 1100 cm⁻¹ corresponds to the δ(P–OH).⁹

Fig. 3 FTIR spectrum of (enH₂)_0.5VPO₄OH.

Thermodynamics

Thermodynamic properties of (enH₂)_0.5VPO₄OH, i.e., the magnetization M and the specific heat C_p were measured using relevant options of “Quantum Design” Physical Properties Measurements System PPMS-9T in the temperature range 2–300 K in a magnetic field μ₀H up to 9 T. The temperature dependence of the magnetic susceptibility, χ = M/H, taken at μ₀H = 0.1 T in the field-cooled mode is shown in Fig. 4a. It shows a broad correlation hump centred at about 150 K, which is followed by a rapid increase on lowering the temperature. This upturn at low temperatures can be ascribed to a trace amount, n_imp, of impurities in the chain, which produce dangling bonds of spin S = 1/2 at the ends of the spin-chain segments.

Fig. 4 (a) Temperature dependence of the magnetic susceptibility measured for (enH₂)_0.5VPO₄OH using the field-cooled protocol at μ₀H = 0.1 T. The experimental data (blue symbols) are fitted by the sum of the impurity contribution (red solid line) and the defect-free chain contribution (green solid line). The latter was obtained by removing the impurity contribution. (b) Field dependence of the magnetization at 2 K. The red dash line is the tangent at high field. (c) Temperature dependence of specific heat (symbols) fitted by the sum of Debye (green line) and Einstein (blue line) modes.

The χ(T) curve can be fitted by the sum of Curie law

χ = χ₀ + C/(T − Θ) (1)

responsible for the impurities, and the susceptibility of the defect-free chain as given by the Padé expansion¹⁵where N_A, μ_B and k_B are the Avogadro number, Bohr magneton and Boltzmann constant, respectively. Under the assumption of Δ = 0.41J and g-factor g = 2, the best fit shown in Fig. 4a was obtained using the temperature-independent term χ₀ = −6.88 × 10⁻⁵ emu mol⁻¹, the Curie constant C = 0.045 emu K mol⁻¹, the Weiss temperature Θ = −2.1 K and the intrachain exchange parameter J = 144.7 K (hence, Δ = 59.3 K). The value of C corresponds to n_imp = 0.75%. Each impurity brings two S = 1/2 dangling spins at the ends of the Haldane chain segments. The value of χ₀ is in agreement with the sum of the Pascal constants of the individual ions in (enH₂)_0.5VPO₄OH, which equals to −7.72 × 10⁻⁵ emu mol⁻¹.¹⁶ The negative sign of the Weiss temperature points to the weak antiferromagnetic coupling between the dangling bonds of spin S = 1/2.

The field dependence of magnetization in (enH₂)_0.5VPO₄OH taken at 2 K is shown in Fig. 4b. The tangent to this curve shown by the dash line extrapolates to 2.7 × 10⁻²μ_B per f.u., which corresponds to 1.35% of impurities. This estimation, which is higher than estimation obtained from the Curie–Weiss fitting reflects the field-induced polarization of spin S = 1/2 at the ends of the spin-chain segments forming the spin-glass state (see NMR section).

The temperature dependence of the specific heat in (enH₂)_0.5VPO₄OH is shown in Fig. 4c. No anomalies were observed down to 2 K, which excludes the transition into a long-range ordered state. At room temperature, the value of C_p is still far from the Dulong-Petit limit 3RN = 374 J mol⁻¹ K, where the number of atoms per formula unit N = 15 and the universal gas constant R = 8.314 J mol⁻¹ K. The experimental data can be fitted by the sum of Debye (temperature Θ_D = 282.5 K and weight a_D = 3.66) and Einstein (temperature Θ_E = 734.5 K and weight a_E = 6.07) modes, as shown by green and blue solid lines in Fig. 4c. These two modes reflect the presence of heavy (V, P) and light (H, C, N, O) atoms in the structure of (enH₂)_0.5VPO₄OH.

Nuclear magnetic resonance

NMR spectra of ³¹P nuclei as well as their spin–lattice relaxation were measured using a custom designed phase coherent pulsed NMR spectrometer with direct quadrature signal detection at the carrier frequency at a constant magnetic field of 9 T in the temperature range of 2.5–310 K. For spectra accumulation, we used the Hahn spin echo pulse sequence augmented by the fast Fourier-transform summation method.^17–19 The nuclear spin–lattice relaxation rate was measured by means of the saturation recovery method.

The set of ³¹P NMR spectra of (enH₂)_0.5VPO₄OH is shown in Fig. S2 of the ESI† with four selected spectra measured at 4.5, 9, 150 and 310 K presented in the upper inset of Fig. 5. Similar to NH₄VPO₄OH,⁵ the spectra consist of a single and almost symmetric line, which progressively broadens with decreasing temperature. The temperature dependence of the ³¹P NMR linewidth estimated as a full width at half maximum (FWHM) is shown in the lower inset to Fig. 5. It is well described by the power law ∼Tⁿ with n = −0.40 ± 0.01 in the entire temperature range investigated in contrast to NH₄VPO₄OH. Below 20 K, the latter shows the Curie–Weiss-like FWHM behavior, which was observed due to the magnetic contribution from the unpaired edge spins S = 1/2.⁵

Fig. 5 Temperature dependence of the ³¹P NMR shift measured for (enH₂)_0.5VPO₄OH. The thick gray line is the best fit to eqn (2). The upper inset: ³¹P NMR spectra taken at 4.5, 9, 150 and 310 K. The position of the Larmor frequency in 85% H₃PO₄ aqueous solution at μ₀H = 9 T is indicated by the dashed line. The lower inset: The FWHM of ³¹P NMR spectra as a function of temperature in (enH₂)_0.5VPO₄OH and NH₄VPO₄OH (adopted from ref. 5).

The temperature dependence of the shift K(T) taken as a position of the line maximum in relation to the Larmor frequency at μ₀H = 9 T in 85% phosphoric acid aqueous solution is shown in Fig. 5, which exhibits a broad maximum at around 140 K similar to that observed in the χ(T) curve obtained at μ₀H = 0.1 T at around 150 K. In the entire temperature range, the temperature dependence of the experimental K(T) was successfully approximated by the Padé equation for Haldane chains (eqn (2)) with J = 118(2) K providing the gap value Δ = 48.4 K. This gap is smaller than that obtained from the χ(T) curve since it was obtained at a much higher field (i.e., 9 T). Note, the determination of the gap from the ³¹P shift is independent from the impurity contribution. In contrast to NH₄VPO₄OH,⁵ (enH₂)_0.5VPO₄OH does not show a pronounced low temperature Curie–Weiss-like behavior of the ³¹P shift, which originates from unpaired S = 1/2 spins at the edges of finite length Haldane S = 1 spin chains. This observation is in line with the magnetic susceptibility data, which show that (enH₂)_0.5VPO₄OH has much less paramagnetic centers than does NH₄VPO₄OH (i.e., 0.75% vs. 3% (ref. 5)), indicating that the Haldane S = 1 spin chain segments of (enH₂)_0.5VPO₄OH are much longer than those of NH₄VPO₄OH.

The ³¹P nuclear magnetization recovery curves exhibit a double exponential behavior with the fast and slow components approximated by a simple and a stretched exponential function, exp[−(τ/T_1fast)] and exp[−(τ/T_1slow)^β] (0 ≤ β ≤ 1), respectively. The fast component is dominated (one order of magnitude) above 40 K and is therefore attributed to the relaxation channel via the S = 1 electronic spins of the Haldane chains. Apparently, the slow relaxation term is caused by unpaired edge S = 1/2 spins. Below 30 K, the Haldane chain approaches its spin singlet ground state and the relative weights of two relaxation components become almost equal. With decreasing temperature below 10 K, both 1/T_1fast and 1/T_1slow start to increase reaching a maximum at around 3 K. Such a behavior is characteristic for the formation of a disordered spin-glass of unpaired S = 1/2 spins at T_S–G ≈ 3 K. The latter originates from a critical slowing down of the spin fluctuations when approaching the freezing temperature,^20,21 as observed in NH₄VPO₄OH⁵ as well. Temperature dependences of the fast and slow ³¹P spin–lattice relaxation rates in (enH₂)_0.5VPO₄OH measured at 9 T are shown in Fig. S3 of ESI.†

Density functional analysis

We now determine the intrachain spin exchange J, the interchain spin exchange J′ and the single-ion anisotropy D of (enH₂)_0.5VPO₄OH based on density functional theory (DFT) calculations, to establish its position on the Sakai–Takahashi phase diagram² described in terms of the D/J and 2J′/J ratios. The parameters J and J′ are obtained by the energy-mapping analysis^22–24 based on DFT calculations.^25–27 Since (enH₂)_0.5VPO₄OH is a magnetic insulator, our energy-mapping analysis was carried in DFT+U calculations²⁸ (with U_eff = 2 and 3 eV on V) using the spin Hamiltonianwhere J_ij = J or J′, so that antiferromagnetic (ferromagnetic) spin exchanges were represented by positive (negative) J_ij values, while the parameter D was calculated by DFT+U+SOC calculations²⁹ (see the ESI† for details). With U_eff = 2 eV, the calculated J value is quite close to the experimental one, namely, 146.8 K for (enH₂)_0.5VPO₄OH. For NH₄VPO₄OH, the best agreement, namely 92.8 K, with experimental data⁵ is achieved also at U_eff = 2 eV. Relative energies of the ordered spin states obtained from DFT+U calculations are given in Table S3 of ESI,† while the relative energies ΔE of the ∥z and ⊥z spin orientations of (enH₂)_0.5VPO₄OH and NH₄VPO₄OH obtained from DFT+U+SOC calculations as well as the spin and orbital moments μ_S and μ_L are given in Table S4.† The calculated J, J′ and D values for (enH₂)_0.5VPO₄OH are summarized in Table 2, where the corresponding values calculated for NH₄VPO₄OH are listed for comparison.

Table 2 Values of J, J′, D and Δ = 0.41 J values (in K) calculated for (enH₂)_0.5VPO₄OH and NH₄VPO₄OH

Magnet	U eff	J	J′	D	2J′/J	D/J	Δ
(enH2)0.5VPO4OH	2	146.8	−0.38	0.23	−5.2 × 10^−3	1.57 × 10^−3	60.2
	3	121.3	0.38	0.12	3.1 × 10^−3	9.89 × 10^−4	49.7
NH4VPO4OH	2	92.8	3.28	0.12	7.1 × 10^−2	1.29 × 10^−3	38.0
	3	73.0	3.02	0.12	3.3 × 10^−2	1.64 × 10^−3	29.9

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To fall into the Haldane sector of the Sakai–Takahashi phase diagram, the system should satisfy the limiting value of 2J′/J < 0.0648.³⁰ When D/J > 0, the Haldane phase persists up to the ratio D/J = 1.033.³¹ Beyond this point, the quantum paramagnet phase appears. When D/J < 0, the Haldane phase persists down to the ratio D/J = −0.316,³² below which the Néel phase appears. (enH₂)_0.5VPO₄OH falls into the middle of Haldane sector of Sakai–Takahashi phase diagram, while NH₄VPO₄OH falls closer to the verge of this sector.²

Discussion

It is noted that the intrachain exchange J is stronger for (enH₂)_0.5VPO₄OH than for NH₄VPO₄OH by a factor of about 1.6, while the interchain exchange J′ is much weaker than the intrachain exchange J in both (enH₂)_0.5VPO₄OH and NH₄VPO₄OH. These observations originate from the fact that each V³⁺⋯V³⁺ chain along the b-axis is a consequence of the edge-sharing between adjacent VO₅(OH) octahedra, with the shared edges forming a ribbon chain along the b-axis (Fig. 1b, S4 and S5†). It is convenient to distinguish two different kinds of O atoms in each ribbon chain; the O atoms involved in the edge-sharing will be referred to as the equatorial O atoms, O_eq, while the O atoms above and below each ribbon plane as the axial O atoms, O_ax. Each ribbon chain exhibits a slight twisting and zigzag bending in (enH₂)_0.5VPO₄OH, but it does not in NH₄VPO₄OH. If we take the local x-axis along the V³⁺⋯V³⁺ direction (Fig. S6 of ESI†), and the xy plane parallel to the ribbon plane (disregarding the slight zigzag bending), then the t_2g set of each V³⁺ ion has the x² − y², xz and yz states. (If the local x-axis is chosen along a V–O_eq bond, the t_2g set would be described by the xy, xz and yz states.) The direct V³⁺⋯V³⁺ interaction is strong between the x² − y² states (Fig. 6a) and also between the xz states (Fig. 6b), so the t_2g set splits into the (x² − y², xz) set lying below the yz state (Fig. 6c). This point was verified by calculating the partial density of states (PDOS) for (enH₂)_0.5VPO₄OH and NH₄VPO₄OH (see the PDOS plots in Fig. S7 and S8 of ESI†). Thus, the x² − y² and xz states act as the magnetic orbitals of each V³⁺ ion. The V³⁺⋯V³⁺ distance is slightly shorter for (enH₂)_0.5VPO₄OH than for NH₄VPO₄OH⁵ (3.058 vs. 3.082 Å), so the direct V³⁺⋯V³⁺ interaction is stronger and hence the intrachain exchange J becomes greater for (enH₂)_0.5VPO₄OH.

Fig. 6 (a) Direct V³⁺⋯V³⁺ interaction between the x² − y² orbitals across the shared edge. (b) Direct V³⁺⋯V³⁺ interaction between the xz orbitals across the shared edge. (c) Split of the t_2g set by the direct V³⁺⋯V³⁺ interaction.

The reason why the interchain J′ is very weak in (enH₂)_0.5VPO₄OH and NH₄VPO₄OH is explained by analyzing how the two adjacent ribbon chains are interconnected by the PO₄ groups. As shown in Fig. 2b, the interchain spin exchange occurs through the V–O⋯P⁵⁺⋯O–V paths. Note that each PO₄ group corner-shares with one O_eq of one ribbon chain and with two O_ax atoms of the other ribbon chain such that the V–O⋯P⁵⁺⋯O–V paths are of the V–O_eq⋯P⁵⁺⋯O_ax–V type. (The fourth O atom of PO₄ makes hydrogen bonds with two different enH₂²⁺ cations, Fig. 2a.) The latter practically vanishes because the x² − y² and xz magnetic orbitals do not have their p-orbital tails on both V–O_eq and V–O_ax bonds (Fig. S9 of ESI†).

We now discuss why the V³⁺ ions in the ribbon chains of (enH₂)_0.5VPO₄OH and NH₄VPO₄OH exhibit a very weak single-ion anisotropy. The d-states of the V³⁺ ion in each VO₆ octahedron in these magnets are split as shown in Fig. 6c. The preferred spin orientation of a magnetic ion is predicted by the selection rule^22,33 based on the interaction of the highest-occupied state with the lowest-unoccupied state, which is induced by spin–orbit coupling (SOC). This selection rule predicts that the interaction of the occupied xz state with the unoccupied yz state favours the spin orientation along the local c-axis, but that of the occupied x² − y² state with the unoccupied yz state favours the spin orientation perpendicular to the local c-axis. The presence of the two opposing trends leads to a very weak magnetic anisotropy.

Conclusion

To summarize, we observed a Haldane magnetic behaviour in the first V-based organically templated magnet (enH₂)_0.5VPO₄OH from magnetic susceptibility and NMR measurements. The energy gap Δ = 59.3 K between the spin-singlet ground state and the triplet excited states is observed from the χ(T) curve taken at μ₀H = 0.1 T, and this gap is reduced to 48.4 K at μ₀H = 9 T as observed from the ³¹P shift. The NMR results indicate that the Haldane S = 1 spin chain segments are much longer in (enH₂)_0.5VPO₄OH than in its ammonium counterpart NH₄VPO₄OH, and that a spin-glass ground state of unpaired S = 1/2 spins forms at T_S–G ≈ 3 K as observed in NH₄VPO₄OH. The parameters J, J′ and D describing this magnet were evaluated and compared with those in NH₄VPO₄OH. The reasons for the weaker interchain exchange interaction J′ and single-ion anisotropy D compared to the intrachain exchange interaction J are two-fold: one is that the t_2g state of each V³⁺ ions split into the (x² − y², xz) state below the yz state (with the x-axis taken along the V³⁺⋯V³⁺ direction), and the other is that the PO₄ groups interconnecting adjacent ribbon chains lead to the V–O_eq⋯P⁵⁺⋯O_ax–V type spin exchanges.

Data availability

ESI,† including details on synthesis, crystal structure, nuclear magnetic resonance are theoretical DFT calculations for (enH₂)_0.5VPO₄OH, are available at https://doi.org/DOI. Crystallographic data for (enH₂)_0.5VPO₄OH has been deposited at the CCDC under CCDC 2356612.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The research was carried out within the framework of the scientific program of the National Centre of Physics and Mathematics under the project “Research in strong and superstrong magnetic fields”. This work was supported by the Ministry of Science and Higher Education of the Russian Federation within the framework of the Priority-2030 strategic academic leadership program at NUST MISIS. SSF acknowledge funding from RSF grant 23-73-10125 for the synthesis and structural/chemical characterization. LVS acknowledge the support through RSF grant 22-42-08002 for the measurements of thermodynamic properties. The work at KHU was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2020R1A6A1A03048004).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4dt01675k

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