Recent years have witnessed a terrific increase in the number of molecule-based materials proposed as magnetic refrigerants for liquid-helium temperatures.1–15 Refrigeration proceeds adiabatically via the magnetocaloric effect (MCE), which describes the changes of magnetic entropy (ΔSm) and adiabatic temperature (ΔTad), following a change in the applied magnetic field (ΔB). As in the first paramagnetic salt that permitted sub-Kelvin temperatures to be reached in 1933,16 gadolinium is often present because its orbital angular momentum is zero and it has the largest entropy per single ion.1 The controlled spatial assembly of the Gd3+ spin centers is vital for designing the ideal magnetic refrigerant. On the one hand, the magnetic density should be maximized by, for example, limiting the amount of non-magnetic elements which act passively in the physical process. On the other hand, magnetic ordering for B = 0 should be avoided, since this results in the decrease of MCE above the target working temperature of the refrigerant. Therefore a compromise becomes necessary, especially for reaching low temperatures.
Metal–organic framework (MOF) materials have recently attracted interest for their cooling properties, combined with their synthetic variety and intrinsic robustness.11–15 Indeed, the dimensionality of Gd-MOFs has no effect in itself on the MCE, bar its intrinsic density. Light and short bridging ligands, such as the formate ion, are clearly advantageous in this regard. We therefore focus here on gadolinium formate, Gd(HCOO)3, a dense MOF material, characterized by a relatively high packing density of Gd3+ ions, linked only through lightweight formate ligands, whose structure was originally determined on powder specimens.17, 18 Surprisingly, no previous magnetic measurements on Gd(HCOO)3 are reported in the literature, except for initial Mössbauer experiments.19 The single-crystal structure determination of Gd(HCOO)3 is reported here, completing the original powder diffraction study. Our detailed magnetic and thermal studies allow direct and indirect estimation of its MCE and show that, while presenting a sub-Kelvin ordering temperature, Gd(HCOO)3 indeed possesses a huge MCE, positioning this material in an enviable position within this research area.
Single crystals of Gd(HCOO)3 were grown by allowing a solution of Gd(NO3)3·5H2O (0.5 g, 1 mmol), formic acid (15 mL), and H2O (10 mL) to evaporate slowly over several days. The product was collected as a crystalline solid and dried under vacuum (> 90% yield) and analyzed satisfactorily (Anal. calcd for GdC3H3O6: Gd 53.80, C 12.33, H 1.03; found: Gd 53.57, C 12.32, H 1.07). The large colorless blocks allowed re-determination of the crystal structure from single-crystal diffraction, and in particular confirmed the crystal system to be hexagonal and in the space group R3m, with a = 10.4583(4) Å and c = 3.9869(3) Å. The structure of Gd(HCOO)3 describes chains of Gd3+ ions propagating along the c axis, each bridged to its neighbors through three μ-formate O-atoms (see Figure 1a). These chains are connected in the bc plane through the formate ions bridging in μ-O,O' anti –anti mode, resulting in the dense hexagonal framework (calculated density is 3.856 g cm−3) shown in Figure 1b. The Gd3+ ion is nine-coordinate in an almost perfect tricapped trigonal prismatic environment, with Gd–O distances of 2.496(4) and 2.527(4) Å for the prismatic oxygen O1 and 2.403(4) Å for the capping oxygen O2. The nearest and next-nearest neighbor Gd···Gd separations are 3.9869(3) Å within the chains, coinciding with the cell parameter c, and 6.183(1) and 6.597(1) Å between chains, respectively.
The molar magnetization (M) was collected for temperatures between 2 and 10 K (Figure S1, Supporting Information). The magnetization saturates to the expected value of 7 μB for a Gd3+ spin moment, according to which s = 7/2 and g = 2. The M(B) curves can be described well by a Brillouin function – see the dashed line in Figure S1 for an ideal paramagnet at T = 2 K. Deviations of the experimental data from the paramagnetic behavior are barely noticeable, and only for the lowest temperatures, and can be ascribed to the presence of a weak antiferromagnetic interaction. This is corroborated by the temperature dependence of the magnetic susceptibility (χ). As shown by the solid line in the inset of Figure S1, the susceptibility data can be fitted above 2 K to a Curie–Weiss law χ = g2 μB2s(s + 1)/[3kB (T − θ)], obtaining a negative, although small, θ = −0.3 K, which suggests that the Gd3+ moments are weakly antiferromagnetically correlated in the paramagnetic phase.
The top panel of Figure 2 shows the measured low-temperature heat capacity (C) as a function of temperature for several applied fields. A sharp lambda-like peak can be observed in the zero-field data for TC1 ≈ 0.8 K, denoting the presence of a phase transition, which is accompanied by a smooth, tiny feature at TC2 ≈ 0.4 K. The magnetic origin of both anomalies is proved by the fact that external applied fields fully suppress them.20 In agreement with M(T,B), the analysis of the field-dependent C reveals that magnetic interactions between the Gd3+ spin centers are relatively weak, since an applied field B = 1 T is sufficient for fully decoupling all spins. As shown in Figure 2, the calculated Schottky contributions (solid lines) for the field-split levels of the non-interacting s = 7/2 multiplet nicely account for the magnetic contribution to the experimental heat capacity (Cm). For T ≥ 7 K, the large field-independent contribution can be attributed to the lattice phonon modes of the crystal. The dashed line in the top panel of Figure 2 represents a fit to this contribution, with the well-known Debye function yielding a value of ΘD = 168 K for the Debye temperature, which is remarkably large for molecular21 and MOF15 materials, denoting a relatively rigid lattice. A larger ΘD implies a correspondingly lower lattice entropy in the low-temperature region, ultimately favoring the MCE. From the experimental heat capacity the temperature dependence of the magnetic entropy Sm(T) is derived by integration, i.e.,
where Cm is obtained by subtracting the lattice contribution to the total C measured. The so-obtained Sm(T) is shown in the bottom panel of Figure 2 for the corresponding applied fields. For B = 0, the lack of experimental Cm for T ≤ 0.3 K has been taken into account by matching the limiting Sm at high temperature with the value obtained from the in-field data. One can notice that there is a full entropy content of Rln(8) = 17.3 J mol−1 K−1 = 59.0 J kg−1 K−1 per mole Gd3+ involved, as expected from Rln(2s + 1) and s = 7/2, where R is the gas constant and the molecular mass is m = 292.30 g mol−1.
Next, we indirectly evaluate the MCE of Gd(HCOO)3 from the experimental data presented so far. From the bottom panel of Figure 2, we obtain the magnetic entropy changes ΔSm(T,ΔB) for different applied field changes ΔB = Bf − Bi. The so-obtained results are depicted in Figure 3. A similar set of data can also be derived from an isothermal process of magnetization by employing the Maxwell relation, i.e., ΔSm(T, ΔB) = [∂M(T, B)/∂T]B dB. From the experimental M(T,B) data in Figure S1, we then obtain curves that rather beautifully agree with the corresponding results previously derived from the heat capacity – see the top panel of Figure 3. Furthermore, to a cooling process under adiabatic conditions, one naturally associates a temperature change whose estimate is made feasible by knowing C and thus Sm. The bottom panel of Figure 3 shows ΔTad(T,ΔB), where T denotes the final temperature of the adiabatic cooling, e.g., going from C(T = 3.4 K, B = 1 T) to A(T = 0.95 K, B = 0) in Figure 2. A far more elegant and reliable method for determining the MCE is by directly measuring ΔTad(T,ΔB) under quasi-adiabatic conditions.22 Following the procedure described in the Supporting Information, we have performed measurements for the experimental conditions corresponding to the magnetization (A → C) and demagnetization (D → B) processes highlighted in Figure 2. Starting from Ti = 0.98 K, the result, depicted in Figure S2, Supporting Information, yields Ti → T → 3.45 K for 0 → B → 1 T and Ti → T → 0.47 K for 1 T → B → 0, thus corresponding to ΔTad = 2.47 and 0.51 K for magnetization and demagnetization, respectively, in good agreement with what is obtained from the entropy data (see Figure 2).
The MCE of Gd(HCOO)3 is exceptionally large, especially in comparison with other molecule-based magnetic refrigerants, as summarized in Table 1 for three representative examples from the recent literature. All of them are characterized by a pronounced maximum of the MCE at T max ≈ 1 K for ΔB = 2 T, as for Gd(HCOO)3. The choice of ΔB = 2 T is dictated by the fact that, for widespread applications, the interest is chiefly restricted to applied fields which can be produced with permanent magnets. In Table 1, the maximum entropy changes −ΔSmmax are reported per unit volume. Although these units are not often used, they are better suited for assessing the implementation of the refrigerant material in a designed apparatus.23 On this point, one could correctly argue that the MCE of molecule-based refrigerant materials is disfavored by their typically low mass density, ρ. However, Gd3+ centers in Gd(HCOO)3 are interconnected only by short and extremely lightweight HCOO− ligands, resulting in a relatively large ρ of 3.86 g cm−3. Ultimately, this enhances the MCE, favored by a larger weight of magnetic elements with respect to non-magnetic ones, which act passively. To the best of our knowledge, no other molecule-based refrigerant material has a MCE as large as in Gd(HCOO)3: −ΔSmmax ≈ 168.5 and 215.7 mJ cm−3 K−1 for ΔB = (2 − 0) T and (7 − 0) T, respectively, as shown in Figure 3. This comparison would not be complete without assessing the efficiency of refrigeration for every selected material. This is accomplished by estimating the relative cooling power (RCP),23 defined as the product of −ΔSmmax and the full width at half maximum (FWHM) of the corresponding −ΔSm(T) curve, i.e., δTFWHM. Among the other molecule-based refrigerants in Table 1, Gd(HCOO)3 shows the largest relative cooling power with an RCP of 522.4 mJ cm−3. Lastly, we extend this comparison to also include gadolinium gallium garnet (GGG), which is the reference magnetic refrigerant material for the 1 K < T < 5 K range.24, 25 Indeed, its functionality is commercially exploited, also owing to its large ρ of 7.08 g cm−3, which contributes to provide record values for −ΔSmmax of 145 mJ cm−3 K−1 and an RCP of 478.5 mJ cm−3 for the same applied field change of 2 T. As can be seen in Table 1, these values are close to, but still lower than, the reported ones for Gd(HCOO)3.
|ρ [g cm−3]||−ΔSmmax [mJ K−1 cm−3]||Tmax [K]||δTFWHM [K]||RCP [mJ cm−3]||Ref.|
In conclusion, we experimentally determine the MCE of the Gd(HCOO)3 MOF material. Under quasi-adiabatic conditions, sub-Kelvin direct measurements of the temperature change corroborate the results inferred from indirect methods. The comparison of gadolinium formate with other excellent magnetic refrigerants for liquid-helium temperatures, such as the benchmark GGG, reveals that Gd(HCOO)3 has an unprecedentedly large MCE. Our observations are interpreted as the result of a light and compact structural framework promoting very weak magnetic correlations between the Gd3+ spin centers.
Finally, we foresee that synthetic and technological strategies, already developed for the surface deposition of MOF materials, could ultimately facilitate the integration and exploitation of Gd(HCOO)3 within molecule-based microdevices for on-chip local refrigeration.26