Magnetocaloric Effect of Two Gd-Based Frameworks

: Magnetic refrigeration material is the key to adiabatic demagnetization refrigeration technology. In this work, two magnetic refrigerants, Gd 5 (C 4 O 4 )(HCOO) 3 (CO 3 ) 2 (OH) 6 · 2.5H 2 O ( 1 ) and Gd 2 (OH) 4 SO 4 ( 2 ), were prepared through hydrothermal reaction. Magnetic study reveals that their magnetic entropy changes are 24.8 J kg − 1 K − 1 for 1 and 15.1 J kg − 1 K − 1 for 2 at 2 K and 2 T, respectively. The magnetic entropy changes of 1 and 2 at T = 2 K and ∆ H = 2 T exceed most gadolinium hydroxyl compounds, indicating that magnetic refrigerants with large magnetic entropy changes at low magnetic ﬁelds can be obtained by introducing more weak magnetic exchange ligands to replace hydroxyl groups in gadolinium hydroxyl compounds.


Introduction
Since the magnetocaloric effect (MCE) of Fe and Ni was observed by Warburg and Weiss in 1881 [1] and 1917 [2], respectively, the adiabatic demagnetization refrigeration (ADR), which is based on the MCE, has gained extensive attention over the century, not only because it has the advantages of environmental friendliness and energy efficiency [3][4][5] but it is also a promising method to reach the subkelvin temperature region (below 1 K) without the use of rare 3 He gas [6,7]. Owing to the magnetic entropy changes (−∆S m ) of magnetic refrigerants being the driving force of ADR, a great many efforts have been made in the preparation of large MCE magnetic refrigerants in the past decades. Although some large MCE magnetic refrigerants, such as Gd(HCOO) 3 [8], Gd(OH) 3 [9], Gd(OH)CO 3 [10], GdPO 4 [11] and GdF 3 [12], have been successfully obtained so far, on one hand, these compounds are already known and thus it is necessary to find new magnetic refrigerants with large MCE. On the other hand, although various Gd-based materials, such as inorganic salts [11][12][13], molecule-based clusters [14][15][16][17][18][19][20], inorganic metallic oxides [21][22][23] and coordination polymers [24][25][26], were selected as magnetic refrigerants in the past decades, few of them contain four different inorganic ligands and thus how the collaboration among these ligands affects their MCE remains unclear. Here we report syntheses and MCE of two magnetic refrigeration materials, namely, Gd 5 (C 4 O 4 )(HCOO) 3 (CO 3 ) 2 (OH) 6 ·2.5H 2 O (1) and Gd 2 (OH) 4 SO 4 (2), of which compound 1 represents the very rare example of inorganic Gd-based compound formed by four different inorganic anions.

Results and Discussion
Compound 1 was synthesized through the hydrothermal reaction of gadolinium chloride hexahydrate with squaric acid in the mixed solvent of N,N-dimethylformamide (DMF) and water. Compound 2 was synthesized by the hydrothermal reaction of gadolinium nitrate hexahydrate with ammonium carbonate and sulfuric acid in aqueous solution. Powder X-ray diffraction (PXRD) patterns of the bulk sample 1 and 2 reveal that the experimental diffraction patterns are consistent with those simulated by the single crystal Inorganics 2022, 10, 91 2 of 8 data ( Figure S1, see the Supplementary Materials), demonstrating the purity of the bulk sample 1 and 2. Thermogravimetric analysis (TGA) under nitrogen atmosphere indicates the weight loss at 265 • C is 3.89% for 1, attributed to the loss of two and a half H 2 O. The total weight loss of 29.78% corresponds well to the theoretical value of 30.31% when the residue is Gd 2 O 3 . Sample 2 has good thermal stability and can remain stable up to 350 • C. The weight loss of 7.29% matches well with that of 7.52% calculated by two H 2 O at the temperature of 430 • C ( Figure S2). Both the experimental PXRD patterns and TGA further confirm the purity of the bulk sample 1 and 2. The O atoms in the main structure are assigned to hydroxyl groups based on bond valence sum (BVS) calculations [27] and charge balance requirements (Tables S1 and S2).
Single crystal X-ray diffraction analysis shows that 1 and 2 crystallize in the monoclinic system with space groups P2 1 /c and C2/m, respectively ( Figures S3 and S4). Crystal data and structural refinement details are shown in Table S3. The asymmetric unit of 1 consists of five Gd 3+ ions, six OH − anions, two CO 3 2− anions, three HCOO − anions, one C 4 O 4 2− anion and two and a half H 2 O. Gd1 to Gd4 are all coordinated with four OH − , one HCOO − , two CO 3 2− and one C 4 O 4 2− in monodentate mode. Gd5 is coordinated with two OH − , two monodentate HCOO − and two CO 3 2− in chelated mode. Gd1 and Gd2 are in triangular dodecahedron geometry calculated by continuous shape measurements [28] (CShM). Gd3 and Gd4 are in square antiprism, while Gd5 is in biaugmented trigonal prism (Table S4). Figure 1a shows that four Gd 3+ ions are linked by four OH − , generating a [Gd 4 (OH) 4 ] n 8n+ cubane. Four [Gd 4 (OH) 4 ] n 8n+ cubanes centered by a Gd 3+ ion through the connection of HCOO − , CO 3 2− and OH − form a butterfly-shaped unit of [Gd 17 (OH) 20 (HCOO) 3 (CO 3 ) 2 ] n 24n+ , as shown in Figure 1b. It is worth noting that the two cubanes on the left side of the butterfly-shaped unit are connected to the central Gd 3+ through two HCOO − and one CO 3 2− , while these on the right side of the butterfly-shaped unit are connected to the central Gd 3+ through one HCOO − and one CO 3 2− . Based on previous work, the ligands of CO 3 2− and HCOO − were generated from the decomposition of squaric acid in situ under hydrothermal conditions [29,30]. Adjacent butterfly-shaped units expand into a 2D layer of [Gd 5 (OH) 6 (HCOO) 3 (CO 3 ) 2 ] n 2n+ through sharing edges, as shown in Figure 1c. The adjacent layers are pillared by squarate in a µ 4 −η 1 :η 1 :η 1 :η 1 coordination mode, forming into a 3D framework of 1 (Figure 1d).
Inorganics 2022, 10, 91 2 of 8 experimental diffraction patterns are consistent with those simulated by the single crystal data ( Figure S1, see the Supplementary Materials), demonstrating the purity of the bulk sample 1 and 2. Thermogravimetric analysis (TGA) under nitrogen atmosphere indicates the weight loss at 265 °C is 3.89% for 1, attributed to the loss of two and a half H2O. The total weight loss of 29.78% corresponds well to the theoretical value of 30.31% when the residue is Gd2O3. Sample 2 has good thermal stability and can remain stable up to 350 °C. The weight loss of 7.29% matches well with that of 7.52% calculated by two H2O at the temperature of 430 °C ( Figure S2). Both the experimental PXRD patterns and TGA further confirm the purity of the bulk sample 1 and 2. The O atoms in the main structure are assigned to hydroxyl groups based on bond valence sum (BVS) calculations [27] and charge balance requirements (Tables S1 and S2).
Single crystal X-ray diffraction analysis shows that 1 and 2 crystallize in the monoclinic system with space groups P21/c and C2/m, respectively ( Figures S3 and S4). Crystal data and structural refinement details are shown in Table S3. The asymmetric unit of 1 consists of five Gd 3+ ions, six OH − anions, two CO3 2− anions, three HCOO − anions, one C4O4 2− anion and two and a half H2O. Gd1 to Gd4 are all coordinated with four OH − , one HCOO − , two CO3 2− and one C4O4 2− in monodentate mode. Gd5 is coordinated with two OH − , two monodentate HCOO − and two CO3 2− in chelated mode. Gd1 and Gd2 are in triangular dodecahedron geometry calculated by continuous shape measurements [28] (CShM). Gd3 and Gd4 are in square antiprism, while Gd5 is in biaugmented trigonal prism (Table S4). Figure 1a shows that four Gd 3+ ions are linked by four OH − , generating a [Gd4(OH)4]n 8n+ cubane. Four [Gd4(OH)4]n 8n+ cubanes centered by a Gd 3+ ion through the connection of HCOO − , CO3 2− and OH − form a butterfly-shaped unit of [Gd17(OH)20(HCOO)3(CO3)2]n 24n+ , as shown in Figure 1b. It is worth noting that the two cubanes on the left side of the butterfly-shaped unit are connected to the central Gd 3+ through two HCOO − and one CO3 2− , while these on the right side of the butterfly-shaped unit are connected to the central Gd 3+ through one HCOO − and one CO3 2− . Based on previous work, the ligands of CO3 2− and HCOO − were generated from the decomposition of squaric acid in situ under hydrothermal conditions [29,30]. Adjacent butterfly-shaped units expand into a 2D layer of [Gd5(OH)6(HCOO)3(CO3)2]n 2n+ through sharing edges, as shown in Figure 1c. The adjacent layers are pillared by squarate in a μ4−η 1 :η 1 :η 1 :η 1 coordination mode, forming into a 3D framework of 1 (Figure 1d).  Compound 2 is a known compound [31,32], but its single crystal structure has not yet been obtained. The asymmetric unit of 2 contains half of one Gd 3+ ion, one OH − anion and a quarter of one SO 4 2− anion. The central Gd 3+ is coordinated by six OH − anions and two SO 4 2− anions in chelated mode in metabidiminished icosahedron geometry (Table S5). Figure 2a reveals that the Gd 3+ ions are bridged by µ 3 −OH − , forming a classic 2D layer of [Gd 2 (OH) 4 ] n 2n+ as observed in Gd(OH) 2 Cl [33]. The 3D framework can be viewed as the adjacent layers connected by sulfates in a µ 4 −η 1 :η 1 :η 2 :η 2 coordination mode, as shown in Figure 2b. It was mentioned that although the 2D layer structure in 1 is very similar to that in Gd(OH) 2 Cl, the latter is in fact a 3D supramolecular network viewed as a connection of adjacent 2D layer structures through electrostatic interactions between Cl − anions and [Gd(OH) 2 ] n n+ layers.
Compound 2 is a known compound [31,32], but its single crystal structure has not yet been obtained. The asymmetric unit of 2 contains half of one Gd 3+ ion, one OH − anion and a quarter of one SO4 2− anion. The central Gd 3+ is coordinated by six OH − anions and two SO4 2− anions in chelated mode in metabidiminished icosahedron geometry (Table S5). Figure 2a reveals that the Gd 3+ ions are bridged by μ3−OH − , forming a classic 2D layer of [Gd2(OH)4]n 2n+ as observed in Gd(OH)2Cl [33]. The 3D framework can be viewed as the adjacent layers connected by sulfates in a μ4−η 1 :η 1 :η 2 :η 2 coordination mode, as shown in Figure 2b. It was mentioned that although the 2D layer structure in 1 is very similar to that in Gd(OH)2Cl, the latter is in fact a 3D supramolecular network viewed as a connection of adjacent 2D layer structures through electrostatic interactions between Cl − anions and [Gd(OH)2]n n+ layers.  (Tables S6 and S7). The bond lengths and angles are comparable to those reported in Gd(OH)2Cl [33]. Figure 3a illustrates the temperature-dependent magnetic susceptibility of 1 and 2 measured in a temperature range of 2 to 300 K under a direct current (dc) magnetic field of 1000 Oe. At room temperature, the values of χMT of 1 and 2 are 39.21 cm 3 K mol −1 and 15.48 cm 3 K mol −1 , respectively, corresponding to the calculated theoretical values of 39.40 cm 3 K mol −1 for five spin−only Gd 3+ ions ( 8 S7/2, S = 7/2, g = 2) and 15.48 cm 3 K mol −1 for two Gd 3+ ions. From 300 K to 100 K, the χMT values of the two compounds remain unchanged. Then, the χMT values decrease slowly till temperature continues to cool down to 25 K. Further decreasing the temperature, the χMT values start to decrease rapidly and reach 20.78 cm 3 K mol −1 for 1 and 5.49 cm 3 K mol −1 for 2 at 2 K. The rapid decreasing χMT vs. T curves indicate the existence of antiferromagnetic (AFM) interactions between adjacent Gd 3+ ions in both 1 and 2. Consistently, fitting the χM −1 vs. T data of 1 and 2 with the Curie−Weiss law gives C = 39.57 cm 3 K mol −1 and θ = −2.25 K for 1 and C = 15.71 cm 3 K mol −1 , θ = −2.78 K for 2. The negative Weiss constants further manifest the presence of antiferromagnetic coupling between Gd 3+ ions of 1 and 2. Figure S5 shows the isothermal magnetization data in applied magnetic field from 0 to 7 T in the temperature range from 2 to 10 K for 1 and 2. The magnetization increases with the decrease of temperature at a given applied magnetic field and decreases with the decrease of magnetic field at a given temperature. At 2 K and 7 T, the magnetizations of the two samples approach the saturation values and reach 34.78 NμB for 1 and 13.93 NμB for 2, which are consistent with the  (Tables S6 and S7). The bond lengths and angles are comparable to those reported in Gd(OH) 2 Cl [33]. Figure 3a illustrates the temperature-dependent magnetic susceptibility of 1 and 2 measured in a temperature range of 2 to 300 K under a direct current (dc) magnetic field of 1000 Oe. At room temperature, the values of χ M T of 1 and 2 are 39.21 cm 3 K mol −1 and 15.48 cm 3 K mol −1 , respectively, corresponding to the calculated theoretical values of 39.40 cm 3 K mol −1 for five spin−only Gd 3+ ions ( 8 S 7/2 , S = 7/2, g = 2) and 15.48 cm 3 K mol −1 for two Gd 3+ ions. From 300 K to 100 K, the χ M T values of the two compounds remain unchanged. Then, the χ M T values decrease slowly till temperature continues to cool down to 25 K. Further decreasing the temperature, the χ M T values start to decrease rapidly and reach 20.78 cm 3 K mol −1 for 1 and 5.49 cm 3 K mol −1 for 2 at 2 K. The rapid decreasing χ M T vs. T curves indicate the existence of antiferromagnetic (AFM) interactions between adjacent Gd 3+ ions in both 1 and 2. Consistently, fitting the χ M −1 vs. T data of 1 and 2 with the Curie-Weiss law gives C = 39.57 cm 3 K mol −1 and θ = −2.25 K for 1 and C = 15.71 cm 3 K mol −1 , θ = −2.78 K for 2. The negative Weiss constants further manifest the presence of antiferromagnetic coupling between Gd 3+ ions of 1 and 2. Figure  S5 shows the isothermal magnetization data in applied magnetic field from 0 to 7 T in the temperature range from 2 to 10 K for 1 and 2. The magnetization increases with the decrease of temperature at a given applied magnetic field and decreases with the decrease of magnetic field at a given temperature.  Since 1 and 2 both have large mass ratio of metal to ligand, the experimental MCE of 1 and 2 was investigated by using multiple temperature data of magnetization to fit the Maxwell equation [34] below: As shown in Figure 3b,c, the magnetic entropy changes (−ΔSm) of 1 and 2 increase monotonically with the decrease of temperature and the increase of magnetic field, reaching the maximum value of 59.8 J kg −1 K −1 (221 mJ cm −3 K −1 ) and 57.6 J kg −1 K −1 (293 mJ cm −3 K −1 ), respectively, at 2 K and 7 T.
For comparison, the theoretical −ΔSm for 1 and 2 was also calculated by the equation −ΔSm = nRln(2S + 1)/Mw [35,36], which shows that the −ΔSm is 66.5 J kg −1 K −1 for 1 and 72.2 J kg −1 K −1 for 2. Both the experimental MCE of 1 and 2 were obviously smaller than theoretical MCE of 1 and 2; this is attributed to the existence of relatively strong antiferromagnetic interactions in 1 and 2, which degrade the spin degeneracy causing the inability to obtain large magnetic entropy changes under limited magnetic field [37]. Table 1 lists the magnetic interactions and the magnetic entropy changes of some excellent magnetic refrigerants reported to date under the applied magnetic field of 2 T and 7 T. For comparison, the magnetic interactions and the magnetic entropy changes of some magnetic refrigerants containing OH − group are also listed. Although the MCE of 1 and 2 at 7 T is significantly smaller than that of GdF3 and Gd(OH)CO3, it is comparable to that of [Gd3(CO3)(OH)6]OH, Gd(OH)3 and Gd(OH)2Cl. It was mentioned that although the MCE of Gd(HCOO)3 at 7 T is obviously smaller than that of 1 and 2, its MCE at 2 T is significantly larger than that of 1 and 2. This result distinctly indicates that weak magnetic interaction favors to obtain large MCE magnetic refrigerants at low applied magnetic field. Because of the limitation of weight and high magnetic field interference in space missions, the magnetic field above 4 T cannot be generated properly [38], and commercial magnets such as NbTi [39] and NdFeB [40,41], can easily provide a magnetic field of 2 T. Except for Gd(OH)CO3, Gd(OH)3 and Gd4(OH)4(SO4)4(H2O)4, the magnetic entropy changes of other gadolinium hydroxyl compounds listed in Table 1 are all lower than that of 1 in low magnetic field. In combination with the composition of these compounds, this result indicates that magnetic refrigerants with large MCE at low fields can be obtained by introducing more weak magnetic exchange ligands to replace hydroxyl groups in gadolinium hydroxyl compounds, consistent with the fact that the MCE of Gd(OH)CO3 is significantly larger than that of Gd(OH)3. Based on the Table 1, the MCE of Gd(OH)3 larger than that of 1 is obviously related to the fact that its magnetic density is higher than that of 1. Since 1 and 2 both have large mass ratio of metal to ligand, the experimental MCE of 1 and 2 was investigated by using multiple temperature data of magnetization to fit the Maxwell equation [34] below: As shown in Figure 3b,c, the magnetic entropy changes (−∆S m ) of 1 and 2 increase monotonically with the decrease of temperature and the increase of magnetic field, reaching the maximum value of 59.8 J kg −1 K −1 (221 mJ cm −3 K −1 ) and 57.6 J kg −1 K −1 (293 mJ cm −3 K −1 ), respectively, at 2 K and 7 T.
For comparison, the theoretical −∆S m for 1 and 2 was also calculated by the equation −∆S m = nRln(2S + 1)/M w [35,36], which shows that the −∆S m is 66.5 J kg −1 K −1 for 1 and 72.2 J kg −1 K −1 for 2. Both the experimental MCE of 1 and 2 were obviously smaller than theoretical MCE of 1 and 2; this is attributed to the existence of relatively strong antiferromagnetic interactions in 1 and 2, which degrade the spin degeneracy causing the inability to obtain large magnetic entropy changes under limited magnetic field [37]. Table 1 lists the magnetic interactions and the magnetic entropy changes of some excellent magnetic refrigerants reported to date under the applied magnetic field of 2 T and 7 T. For comparison, the magnetic interactions and the magnetic entropy changes of some magnetic refrigerants containing OH − group are also listed. Although the MCE of 1 and 2 at 7 T is significantly smaller than that of GdF 3 and Gd(OH)CO 3 , it is comparable to that of [Gd 3 (CO 3 )(OH) 6 ]OH, Gd(OH) 3 and Gd(OH) 2 Cl. It was mentioned that although the MCE of Gd(HCOO) 3 at 7 T is obviously smaller than that of 1 and 2, its MCE at 2 T is significantly larger than that of 1 and 2. This result distinctly indicates that weak magnetic interaction favors to obtain large MCE magnetic refrigerants at low applied magnetic field. Because of the limitation of weight and high magnetic field interference in space missions, the magnetic field above 4 T cannot be generated properly [38], and commercial magnets such as NbTi [39] and NdFeB [40,41], can easily provide a magnetic field of 2 T. Except for Gd(OH)CO 3 , Gd(OH) 3 and Gd 4 (OH) 4 (SO 4 ) 4 (H 2 O) 4 , the magnetic entropy changes of other gadolinium hydroxyl compounds listed in Table 1 are all lower than that of 1 in low magnetic field. In combination with the composition of these compounds, this result indicates that magnetic refrigerants with large MCE at low fields can be obtained by introducing more weak magnetic exchange ligands to replace hydroxyl groups in gadolinium hydroxyl compounds, consistent with the fact that the MCE of Gd(OH)CO 3 is significantly larger than that of Gd(OH) 3 . Based on the Table 1, the MCE of Gd(OH) 3 larger than that of 1 is obviously related to the fact that its magnetic density is higher than that of 1. Therefore, in order to obtain gadolinium hydroxyl compounds with large magnetic entropy changes, it is necessary to maintain high magnetic density of the gadolinium hydroxyl compounds, in addition to introducing more weak magnetic exchange ligands to replace hydroxyl groups in gadolinium hydroxyl compounds. It was noted that although the mass magnetic entropy change of 1 (24.8 J kg −1 K −1 ) at 2 T is obviously larger than that of Gd(OH) 2 Cl (17.6 J kg −1 K −1 ) at 2 T, the volumetric magnetic entropy change of 1 (92 mJ cm −3 K −1 ) at 2 T is close to that of Gd(OH) 2 Cl (91 mJ cm −3 K −1 ) at 2 T. No obvious difference in the volumetric magnetic entropy change between them is attributed to that the crystal density of 1 is significantly smaller than that of Gd(OH) 2 Cl. In this sense, the introduction of heavy atoms into gadolinium hydroxyl compounds is beneficial to improving their volumetric magnetic entropy change when their magnetic density and magnetic interaction are close. Ref.

Conclusions
In summary, we reported on the crystal structures and MCE of the two magnetic refrigeration reagents 1 and 2. Magnetic study reveals that 1 and 2, respectively, exhibit magnetic entropy changes of 59.8 J kg −1 K −1 and 57.6 J kg −1 K −1 at T = 2 K and ∆H = 7 T. Significantly, the magnetic entropy changes of 24.8 J kg −1 K −1 for 1 and 15.1 J kg −1 K −1 for 2 at T = 2 K and ∆H = 2 T exceed most gadolinium hydroxyl compounds, indicating that magnetic refrigerants with large MCE at low fields can be obtained by introducing more weak magnetic exchange ligands to replace hydroxyl groups in gadolinium hydroxyl compounds when the magnetic density remains unchanged.

General Information
All materials and reagents were commercially available and used without further purification.
Powder X-ray diffraction data (PXRD) was collected on a Rigaku Ultima IV powder X-ray diffractometer (Cu Kα, λ = 1.54184 Å) in the 2θ range of 5-60 • at room temperature. Thermogravimetric analysis (TGA) curve was conducted on an SDT_Q600 thermal analyzer at a rate of 10 • C per minute up to 800 • C under a constant nitrogen gas. Elemental analyses were carried out using a CE Instruments EA 1110 elemental analyzer. Magnetic measurement was carried out using a Quantum Design MPMS−XL5 superconducting quantum interference device (SQUID).    (2) Compound 2 was synthesized by a mixture of Gd(NO 3 ) 3 ·6H 2 O (0.226 g, 0.5 mmol) and ammonium carbonate (0.144 g, 1.5 mmol) dissolved in 5 mL deionized water. An amount of 10 µL concentrated sulfuric acid was introduced into the solution while stirring. The resulting solution was stirred for another 30 min before being transferred into a Teflon-lined autoclave at 250 • C for 3 days and cooled down to room temperature at a rate of 3 • C h −1 . Colorless crystals were obtained in 72% yield based on Gd 3+ . Elem. anal. Calculated (found): H, 0.84% (0.59%).

X-ray Crystallographic Analysis of 1 and 2
Single crystal data of 1 and 2 were collected by a Rigaku XtaLAB Synergy diffractometer with monochromatic Cu Kα radiation (λ = 1.54184 Å). Data reduction and absorption correction were applied by using the multi-scan program. The structures were determined and refined using full matrix least squares based on F 2 with SHELXS and SHELXL [45] within Olex2 [46]. All non-hydrogen atoms were refined anisotropically. CCDC numbers 2164597 and 2164596 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via http://www.ccdc.cam.ac.uk/conts/retrieving.html. (Accessed on 24 June 2022)

The Bond Valence Sum (BVS) Analysis of 1 and 2
The bond valence sum (BVS) analysis was used to determine the oxidation states of oxygen atoms in compound 1 and 2. The calculation formula is S ij = exp[(R 0 − R ij )/b], in which S ij is the valence of the individual bond, R ij is the observed bond length, R 0 is a constant depended upon the bonded elements, and b is a constant of 0.37. As shown in Tables S1 and S2, the total BVS values of O atoms are very close to the state of +1, for which we identify the states of all O atoms assigned to hydroxyl groups.

Conflicts of Interest:
The authors declare no conflict of interest.