Enhanced Magnetocaloric Effect and Single-Molecule Magnet Behavior in a Series of Sulfur-Containing Ligand-Based Ln₉ Clusters (Ln = Gd, Tb, and Dy)

Abstract

As an important branch of lanthanide-based complexes, clusters show unique properties in magnetocaloric effect (MCE) and single-molecule magnets (SMMs) using O/N ligands, while research on heavy p-block elements (e.g., S atom) with larger atomic radii and more diffuse p valence orbitals as coordinating atoms remains relatively scarce. Herein, using the sulfur-containing ligand of 2-pyridinethiol 1-oxide (HL), we successfully synthesized a series of hourglass-like Ln₉ clusters [Ln₉(L)₁₇(μ₃-OH)₉(μ₄-OH)]·nH₂O (1: Ln = Gd, n = 3; 2: Ln = Tb, n = 3; 3: Ln = Dy, n = 1). Magnetic data analysis reveals that cluster 1 shows a significant MCE, with the entropy change (−ΔS_m) reaching a maximum of 34.41 J kg⁻¹ K⁻¹ at 2 K under ΔH = 7 T. Cluster 3, meanwhile, exhibits distinct frequency- and temperature-dependent behavior, indicating its SMM characteristics. Interestingly, despite possessing the highest molar mass among reported Gd₉ clusters with MCE, 1 exhibits a competitive −ΔS_m value, highlighting the critical role of sulfur-containing ligand on the structure and even exchange interactions. This work offers new insights into synthesizing high-performance MCE materials and understanding magneto-structural relationships.

1. Introduction

From household refrigerators to space probes, refrigeration technology is deeply integrated into every facet of modern society [1]. While current ³He gas compression technology can meet ultra-low-temperature environmental demands, it faces two long-term challenges: scarcity of ³He resources [2] and the low efficiency of traditional vapor-compression refrigeration technology (5–10% of the theoretical Carnot cycle value) [3]. Therefore, developing alternatives to ³He has become an urgent need to support the development of future technologies. Magnetic refrigeration [4,5,6] has emerged as a research focus in the cooling field due to its dual advantages of high energy efficiency and environmental friendliness. The technology’s core principle relies on the magnetocaloric effect (MCE), a phenomenon where magnetic materials’ temperature changes with varying magnetic fields (H), enabling cooling with 30−60% Carnot cycle efficiency while eliminating ozone-damaging emissions [7].

To achieve high magnetic entropy changes (−ΔS_m), a central parameter in magnetocaloric performance, metal centers with negligible magnetic anisotropy, large spin ground state, and quenched orbital angular momentum are essential [4,8,9,10,11]. The Gd³⁺ ion, with its isotropic ⁸S_7/2 ground state, exemplifies these criteria and serves as a benchmark in molecular refrigerant design [4]. Efforts to enhance −ΔS_m have primarily focused on two strategies: increasing the magnetic density and engineering weak magnetic interactions [8,12]. On the one hand, the theoretical upper limit of −ΔS_m is Rln(2S + 1) (R is the gas constant and S is the spin state), typically expressed in molar units (J mol⁻¹ K⁻¹) [13]. However, experimental data are often normalized to mass units (J kg⁻¹ K⁻¹) or volume units (mJ cm⁻³ K⁻¹), where higher magnetic density directly correlates with larger −ΔS_m. Thus, most current high-performance molecular-based magnetic refrigerants employ light ligands such as inorganic anions [14] and carboxylate ligands [15,16]. On the other hand, when magnetic interactions between metal centers are weak, −ΔS_m is a linear superposition of each ion, giving −ΔS_m^max = nRln(2S + 1) (n is the number of paramagnetic centers). In contrast, strong antiferromagnetic coupling reduces −ΔS_m due to the cancellation of adjacent magnetic moments, unless spin frustration [17] exists in the system; meanwhile, strong ferromagnetic coupling leads to a large ground-state spin that decreases entropy change to Rln(2nS + 1) [12,13]. The MCE performance of Gd³⁺-based clusters depends on a delicate balance between magnetic ion density and exchange coupling. For example, Gd₁₄₀ (M_W = 46730.00 g mol⁻¹, magnetic density N_Gd/M_W = 0.00300, Curie−Weiss constant θ = −2.4 K) [15] shows −ΔS_m = 38.0 J kg⁻¹ K⁻¹ at 2 K for ΔH = 7 T, which is lower than Gd₆₀’s −ΔS_m of 48.0 J kg⁻¹ K⁻¹ (θ = −3.71 K, N_Gd/M_W = 0.00302, M_W = 19871.97 g mol⁻¹) despite weaker antiferromagnetic coupling [16]. Conversely, Gd₂₄ (M_W = 8169.48 g mol⁻¹, N_Gd/M_W = 0.00294, θ = −0.16 K) [18], with the lowest magnetic ion density and weakest coupling, delivers −ΔS_m of 46.12 J kg⁻¹ K⁻¹ at 2.5 K and ΔH = 7 T, outperforming Gd₁₄₀.

Given the oxophilicity of lanthanide ions [19], employing oxygen-containing bidentate or multidentate ligands with controlled hydrolysis to generate μ_2/3/4/5-O/OH groups promotes the aggregation of metal cores, which is one of the effective strategies for synthesizing structurally unique clusters [12,20,21]. However, synthesis involving heavier p-block elements, such as S atoms, is usually more challenging, primarily due to their reduced coordination affinity for lanthanide ions and the inherently less predictable/controllable nature of their coordination modes [22,23,24,25,26]. Notably, the larger atomic radii and diffuse p valence orbitals of these elements impart unique physicochemical properties to the resulting clusters [27,28], enabling structures ideal for studying magneto-structural relationships [29,30] and entropy change mechanisms. In complex cluster structures, when ligands containing heavy p-block elements coordinate in a terminal mode, they are likely to increase certain key parameters—such as intermetallic distances and metal–ligand bond lengths/angles—that directly influence magnetic coupling [31]. A substantial increase in the distance between Gd³⁺ ions, for example, may promote magnetic decoupling and reduce exchange pathways [32], ultimately leading to a significantly enhanced magnetic entropy change. Conversely, when ligands containing heavy p-block elements coordinate in a bridging mode, the diffuse p orbitals can facilitate stronger magnetic exchange coupling, thereby improving the relaxation dynamics in single-molecule magnets (SMMs) [33]. Additionally, strategic placement of soft S donors in the equatorial plane effectively weakens the transverse component of the crystal field, which contributes to enhanced SMM performance [27,28,29,30].

To this end, we employed 2-pyridinethiol 1-oxide (HL), a rarely explored ligand in lanthanide chemistry [34,35,36,37,38,39,40] that features both O and S donor sites, to construct lanthanide-based clusters. Using solvothermal methods, we successfully synthesized a new family of Ln₉ clusters [Ln₉(L)₁₇(μ₃-OH)₉(μ₄-OH)]·nH₂O (1: Ln = Gd, n = 3; 2: Ln = Tb, n = 3; 3: Ln = Dy, n = 1). Single-crystal X-ray diffraction analysis reveals that the nine metal centers adopt an hourglass geometric configuration in space. Magnetic studies of clusters 1–3 show distinct behaviors: cluster 1 features dominant antiferromagnetic interactions and a significant MCE with −ΔS_m = 34.41 J kg⁻¹ K⁻¹ at ΔH = 7 T and 2 K, while cluster 3 exhibits SMM behavior. This family enables comparison with previously reported MCE of Ln₉ clusters supported by O/N donor ligands [41,42,43] and helps to understand the influence of S coordination on cluster assembly and magnetic properties.

2. Materials and Methods

2.1. Materials and Characterization

All the starting materials were commercially available reagents of analytical grade and were used without further purification. 2-pyridinethiol 1-oxide was purchased from Aladdin, Shanghai, China; LnCl₃·6H₂O (Ln = Gd, Tb, Dy) were purchased from 3A Material, Anqing, Anhui, China; triethylamine, and all solvents were purchased from Energy Chemical, Shanghai, China. Elemental analyses (C, N, H, and S) were carried out on a EUROVECTOR EA3000 elemental analyzer (Euro Vector, Sesena Comasco, MI, Italy). The powder X-ray diffraction (PXRD) measurements were recorded on a Bruker D8 ADVANCE X-ray diffractometer (Bruker, Karlsruhe, BW, Germany). Direct-current (dc) magnetic susceptibilities were measured on a Quantum Design MPMS-squid VSM magnetometer (Quantum Design, San Diego, CA, USA). Diamagnetic corrections were made with Pascal’s constants for all the constituent atoms and the sample holder. Alternating-current (ac) magnetic susceptibility data were collected on the same instrument employing a 1.5 Oe oscillating field at frequencies up to 1000 Hz.

2.2. Syntheses of Complexes 1–3

[Gd₉(L)₁₇(μ₃-OH)₉(μ₄-OH)]·3H₂O (1): A mixture of GdCl₃·6H₂O (185.85 mg, 0.5 mmol), ligand HL (127.16 mg, 1.0 mmol; HL = 2-pyridinethiol 1-oxide), 278.0 μL of triethylamine (2.0 mmol), and 8 mL of CH₃OH was sealed in a Teflon-lined autoclave, which was heated at 130 °C for 24 h. After cooling to room temperature in 48 h, light-yellow block crystals of 1 suitable for single-crystal X-ray diffraction analysis were obtained. The crystals were washed with methanol (5 × 4.0 mL) and subsequently examined under an optical microscope to separate the white flocculent impurities from the target crystals. Drying the crystals under air at room temperature afforded a desolvated and hydrated species that was analyzed as 1. Yield: 49.6% (based on Gd). Elemental analysis calcd (%) for 1 (C₈₅H₈₄N₁₇S₁₇Gd₉O₃₀): C 26.98, N 6.29, H 2.24, S 14.41; found: C 26.69, N 6.30, H 2.36, S 13.92.

[Tb₉(L)₁₇(μ₃-OH)₉(μ₄-OH)]·3H₂O (2): This compound was synthesized by the same method as 1, except that GdCl₃·6H₂O was replaced with TbCl₃·6H₂O, affording light-yellow block crystals. The crystals were washed with methanol (5 × 4.0 mL) and subsequently examined under an optical microscope to separate the white flocculent impurities from the target crystals. Drying the crystals under air at room temperature afforded a desolvated and hydrated species that was analyzed as 2. Yield: 38.7% (based on Tb). Elemental analysis calcd (%) for 2 (C₈₅H₈₄N₁₇S₁₇Tb₉O₃₀): C 26.87, N 6.27, H 2.23, S 14.35; found: C 26.73, N 6.26, H 2.20, S 13.92.

[Dy₉(L)₁₇(μ₃-OH)₉(μ₄-OH)]·H₂O (3): This compound was synthesized by the same method as 1, except that GdCl₃·6H₂O was replaced with DyCl₃·6H₂O, affording light-yellow block crystals. The crystals were washed with methanol (5 × 4.0 mL) and subsequently examined under an optical microscope to separate the white flocculent impurities from the target crystals. Drying the crystals under air at room temperature afforded a desolvated species that was analyzed as 3. Yield: 42.8% (based on Dy). Elemental analysis calcd (%) for 3 (C₈₅H₈₀N₁₇S₁₇Dy₉O₂₈): C 26.90, N 6.27, H 2.12, S 14.36; found: C 26.54, N 6.76, H 2.24, S 14.22.

2.3. Single-Crystal Structure Determination

Single-crystal X-ray diffraction data were recorded on a Bruker D8 Venture diffractometer (Bruker, Karlsruhe, BW, Germany) with MoKα radiation. Diffraction data for crystals of 1, 2, and 3 were collected at 150 K using the APEX4 program. The structures were solved by the SHELXT-2024 software package and refined using a full-matrix least-squares method on F² with anisotropic thermal parameters for all nonhydrogen atoms. Hydrogen atoms were located geometrically and refined with a riding model with relative isotropic displacement parameters. Structural refinement revealed disorder and pronounced thermal motion in some lattice solvent molecules, triggering CheckCIF alerts (e.g., missing O–H acceptors). These effects are common in highly solvated crystals and do not compromise the integrity of the main framework. Details can be found in the Cambridge Crystallographic Data Centre using the CCDC numbers 2475935 (1), 2475936 (2), and 2475937 (3).

3. Results and Discussion

3.1. Crystal Structure

Single-crystal X-ray diffraction analyses reveal that complexes 1 and 2 are isostructural, both crystallizing in the triclinic P-1 space group, whereas complex 3 crystallizes in the monoclinic P2₁/c space group (Table S1). Thus, the structures of complexes 1 and 3 are described in detail.

The asymmetric units of both complexes 1 and 3 feature nine metal ions, seventeen L⁻ ligands, nine μ₃-OH and one μ₄-OH groups, and some free solvent molecules. The eight Ln³⁺ (Ln1–Ln4 and Ln6–Ln9, Ln = Gd, Dy) ions occupy the vertices of a square antiprism, and the ninth (Ln5) resides at its geometric center, forming a canonical hourglass geometric configuration. This configuration consists of two quadrilateral base planes and eight triangular planes, resulting in an [Ln₉(μ₃-OH)₉(μ₄-OH)]¹⁷⁺ core encapsulated by seventeen bidentate L⁻ ligands. To facilitate the description of ligand coordination modes, three types are identified: (1) μ₁-η¹:η¹: terminal bidentate coordination through both S and O donors to a single lanthanide center; (2) μ₂-η¹:η²: monodentate S-coordination to one lanthanide ion coupled with μ₂-O bridging to a neighboring metal center; and (3) μ₂-η¹:η²: monodentate O-coordination to one lanthanide ion accompanied by μ₂-S bridging to an adjacent metal ion (Figure 1).

In complex 1, a μ₄-OH group bridges the four Gd³⁺ ions (Gd1–Gd4) of the upper quadrilateral base plane (O atom 0.57 Å above the plane (Figure 2a); adjacent Gd···Gd distances in the range of 3.6107(6)–3.6700(6) Å). Adjacent Gd³⁺ ions in this plane are further interconnected by μ₂-η¹:η² bridges from ligand L⁻ (Mode II: μ₂-O and monodentate S), with the exception of the Gd1–Gd4 edge, where ligand disorder results in mixed μ₂-η¹:η² bridging (approximately 60% Mode II (μ₂-O) and 40% Mode III (μ₂-S)) (Figure 3a). Four μ₃-OH groups connect the upper quadrilateral plane to Gd5, forming four triangular planes. The Gd1–Gd4 ions are all eight-coordinate (Figure S1), adopting a triangular dodecahedron (D_2d) local geometric configuration as determined by the SHAPE 2.1 software [44] (Table S2), with each coordination sphere containing two μ₂-η¹:η² ligands, one μ₁-η¹:η¹ ligand, one μ₄-OH, and two μ₃-OH groups. The central Gd5 ion occupies the geometric center, coordinated to eight μ₃-OH groups that connect it to both the upper (Gd1–Gd4) and lower (Gd6–Gd9) quadrilateral planes, adopting a square antiprism (D_4d) local geometry. The centers of the two quadrilateral base planes are separated by 5.5476 (2) Å with an interplanar torsion angle of 47.318(105)°. The lower quadrilateral base plane (Gd6–Gd9) exhibits distinct structural features (Figure S1). A μ₃-OH group (O atom 0.53 Å below the plane) bridges Gd6, Gd7, and Gd9, while the plane displays significant distortion from ideal square geometry (adjacent Gd···Gd distances ranging from 3.5658(7) to 3.9598(7) Å and the bond lengths of Gd–μ₃-O varying between 2.413(4) and 2.540(1) Å; Tables S3 and S4). This geometric asymmetry results in varied coordination environments for Gd6–Gd9 compared to the more symmetric upper Gd1–Gd4 plane, highlighting the overall molecular asymmetry. While adjacent Gd³⁺ ions in the lower plane are similarly interconnected by μ₂-η¹:η² bridges from ligand L⁻ (Mode II: μ₂-O and monodentate S), their coordination environments diverge significantly. Gd6 and Gd7 maintain eight-coordinate triangular dodecahedron (D_2d) geometries, each binding to two μ₂-η¹:η² ligands (combing one S atom and two μ₂-O), one μ₁-η¹:η¹ L⁻ ligand, and three μ₃-OH groups. In contrast, Gd9 expands to nine-coordination through two μ₂-η¹:η² modes (two S atoms and two μ₂-O), one μ₁-η¹:η¹ L⁻ ligand, and three μ₃-OH groups, resulting in a spherical capped square antiprism (C_4v) local geometry. Gd8 remains eight-coordinate with a triangular dodecahedron (D_2d) local geometry but exhibits a distinct arrangement, coordinating to two μ₂-O donors (from two μ₂-η¹:η² L⁻), two μ₁-η¹:η¹ L⁻ ligands, and two μ₃-OH groups.

According to the packing diagram (Figure S2), the shortest intermolecular Gd···Gd distance is 9.0353(7) Å. The presence of hydroxyl groups and solvent molecules within the cluster forms intra- and intermolecular hydrogen bonds (Table S5). Further analysis reveals that the pyridine rings mediate intra- and intermolecular π···π stacking (dihedral angle < 20°) (Table S6) and intermolecular C–H···π interactions, with distances between the hydrogen atoms and the ring centroids ranging from 2.68 to 2.98 Å (Table S7). These noncovalent interactions notably enhance the thermal and structural stability of the air-stable metal clusters.

In complex 3, the spatial arrangement of metal ions (Dy1–Dy9) and their linkage pattern across the eight triangular planes are identical to those in complex 1, forming a [Dy₉(μ₃-OH)₉(μ₄-OH)]¹⁷⁺ core structure (Figure 2b and Figure 3b). Notably, all Dy³⁺ ions are eight-coordinate. Dy1−Dy5 display coordination geometries that closely resemble those of their Gd³⁺ analogs (Gd1–Gd5), with Dy1–Dy4 adopting D_2d local geometries and Dy5 exhibiting a D_4d geometry (Table S8). Dy9 shows identical coordination to Gd6 and Gd7 (Figure S3), also featuring a D_2d local geometry. However, Dy6 and Dy7 share a distinct coordination sphere comprising one μ₃-OH from the lower plane, two μ₃-OH bridges to central Dy5, one μ₂-O donor (from one μ₂-η¹:η² L⁻), and two μ₁-η¹:η¹ L⁻ ligands (Figure S4). Despite this similarity, their local geometries differ slightly, adopting D_4d and D_2d configurations, respectively. Dy8 adopts a unique environment, coordinated by two μ₃-OH groups, two μ₂-η¹:η² L⁻ ligands (containing two S and two μ₂-O), and one μ₁-η¹:η¹ L⁻ ligand, exhibiting a D_2d local geometry. The adjacent Dy···Dy distances for Dy6–Dy9 range from 3.5824(7) to 3.8408(7) Å, and the Dy−μ₃-O bond lengths display a wider variation (2.470(5)–2.715(5) Å) than those found in 1 (Tables S9 and S10). The packing analysis reveals that the shortest intermolecular Dy···Dy distance is 9.8618(6) Å (Figure S5), longer than that in 1. The structure also features an enhanced hydrogen bonding network (Table S5). Notably, the pyridine rings are only engaged in intramolecular π···π stacking (Table S6) and intermolecular C–H···π interactions, with distances between the hydrogen atom and the ring centroid ranging from 2.66 to 2.85 Å (Table S7).

Overall, in contrast to previously reported symmetric hourglass-like Ln₉ clusters [24,41,42,43,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69], the present Ln₉ family exhibits significant structural asymmetry: Ln1–Ln4 and Ln6–Ln9 differ entirely in coordination environments, while the upper and lower basal planes feature different bridging modes (μ₄-OH and μ₃-OH, respectively). To facilitate subsequent studies on magneto-structural relationships, we compared cluster 1 with four previously reported Gd₉ clusters that exhibit MCE [41,42,43]. Gd1–Gd5 share similar bridging modes: adjacent Gd1–Gd4 ions are connected by μ₂-O bridges (Gd···Gd distance ≈ 3.6 Å) with a central μ₄-OH group (diagonal Gd···Gd distance in the upper plane ≈ 5.2 Å), while Gd5 links to eight Gd³⁺ ions via eight μ₃-OH bridges (Gd_1–4···Gd₅ distance ≈ 3.8 Å). Despite these similarities in connectivity and distances, cluster 1 exhibits distinct bond angles compared to the four cases: its adjacent Gd–μ₂-O–Gd angles for Gd1–Gd4 (96.1–100.6°) are in a medium range (Table S11), its diagonal Gd–μ₄-O–Gd angles in the upper plane (155.2–156.2°) are smaller, and its Gd_1–4–μ₃-O–Gd₅ angles (107.0–108.1°) show a larger average (Table S11). These differences become even more pronounced in Gd6–Gd9, which display greater variation in adjacent Gd···Gd distances (3.6–4.0 Å) with Gd–μ₂-O–Gd angles (93.3–107.1°, Table S11). Here, the diagonal Gd6···Gd8 and Gd7···Gd9 distances are 5.7 Å and 4.8 Å, respectively, and the Gd_6–9–O–Gd₅ angles range from 102.4 to 109.9°. Considering that the key difference in cluster 1 lies in the partial replacement of conventional N/O donors by S atoms from the ligands, with a disordered segment containing μ₂-S bridging Gd1 and Gd4, we propose that the asymmetric structure and variations in bond angles and Gd···Gd distances likely arise from the coordination and bridging of sulfur-containing ligands.

The powder X-ray diffraction patterns of polycrystalline samples of 1 and 2 are distinctly different from that of 3, matching well with their respective single-crystal X-ray diffraction simulations (Figure S6). This agreement confirms the high phase purity of all samples.

3.2. Magnetic Properties

Variable-temperature magnetic susceptibility measurements of complexes 1–3 were performed on polycrystalline samples under a 1 kOe direct current (dc) magnetic field over the temperature range of 2–300 K. At 300 K, the χ_MT products for complexes 1–3 are 68.26, 104.02, and 125.64 cm³ K mol⁻¹, respectively (Figure 4a), in close agreement with the theoretical values calculated for non-interacting magnetic centers: 70.92 cm³·K·mol⁻¹ for nine independent Gd³⁺ ions (S = 7/2, g = 2.0), 106.38 cm³·K·mol⁻¹ for nine isolated Tb³⁺ ions (S = 3, g = 3/2), and 127.53 cm³ K mol⁻¹ for nine non-coupled Dy³⁺ ions (S = 5/2, g = 4/3). Upon cooling, complex 1 exhibits nearly constant χ_MT values above 80 K, reflecting the dominant paramagnetic behavior of non-interacting Gd³⁺ ions; below 80 K, χ_MT decreases gradually before undergoing a steep decline to 34.66 cm³ K mol⁻¹ at 2 K, indicating the onset of antiferromagnetic interactions. Curie–Weiss analysis (2–300 K) yields Curie constant C = 69.35 cm³ K mol⁻¹ and Curie temperature θ = −2.15 K, with the negative θ confirming antiferromagnetic interactions between metal ions (Figure 4b). Complex 2 exhibits a subtle decrease in χ_MT above 100 K, while complex 3 shows a more pronounced reduction in this regime. Both systems undergo progressive declines followed by steep reductions below 50 K, reaching minima of 39.12 and 76.30 cm³ K mol⁻¹ at 2 K for 2 and 3, respectively. This behavior originates from thermal depopulation of Stark sublevels, with potential contributions from weak antiferromagnetic exchange.

To further explore the magnetic interactions between Gd³⁺ ions in 1, we classify the exchange pathways into six distinct types (J₁–J₆) based on their bridging motifs (Figure 5a). The magnetic interaction denoted as J₁ stems from the coupling between Gd1 and Gd2, which are bridged by one μ₄-OH, one μ₃-OH, and a μ₂-O ligand. Notably, ligand disorder along the Gd1–Gd4 edge, which leads to a mixed μ₂-η¹:η² bridging mode, is not specifically considered in the magnetic model, similar to J₁. J₂ characterizes the diagonal magnetic interaction between Gd³⁺ ions in the upper Gd1–Gd4 quadrilateral base plane via a μ₄-OH bridge. J₃ describes the magnetic interaction between Gd5 and its adjacent Gd³⁺ ions through two μ₃-OH groups. J₄ accounts for the magnetic coupling between Gd³⁺ ions mediated by two μ₃-OH and one μ₂-O ligand. J₅ quantifies the interaction between adjacent Gd³⁺ ions bridged by one μ₃-OH and one μ₂-O ligand. Finally, J₆ defines the magnetic exchange interaction between Gd7 and Gd9, which are connected by a single μ₃-OH bridge. Thus, the spin Hamiltonian of the system is derived by integrating these exchange interactions.

$$\begin{gathered} \widehat{H}=-2J_1\left(S_1{S}_2+S_2{S}_3+S_3{S}_4+S_1{S}_4\right)-2J_2\left(S_1{S}_3+S_2{S}_4\right)-2J_3\left(S_1{S}_5+S_2{S}_5+S_3{S}_5+S_4{S}_5+ \\ {S}_6{S}_5+S_7{S}_5+S_8{S}_5+S_9{S}_5\right)-2J_4\left(S_6{S}_7+S_6{S}_9\right)-2J_5\left(S_7{S}_8+S_9{S}_8\right)-2J_6\left(S_7{S}_9\right) \end{gathered}$$

(1)

In this model, S₁–S₉ represent the spin of Gd1–Gd9, respectively, where positive values of J indicate ferromagnetic interactions, and negative values correspond to antiferromagnetic interactions.

To address computational challenges in modeling the magnetic properties of a nonanuclear cluster, we implement a reduced pentanuclear approximation. Given the prohibitively large exchange matrix for the full Gd₉ system, we strategically retain the core magnetic unit comprising the central Gd5 ion and four vertex ions (Gd₅: Gd1–Gd4 from the upper plane or Gd6–Gd9 from the lower plane) (Figure 5b,c). This simplification exploits the inherent S₄ symmetry of the cluster, where Gd5 occupies the inversion center and the upper/lower Gd₄ planes exhibit congruent coordination environments. The resultant Hamiltonian matrix enables computationally tractable fitting while preserving the dominant exchange pathways.

$$\widehat{H}=-2J_1\left(S_1{S}_2+S_2{S}_3+S_3{S}_4+S_1{S}_4\right)-2J_2\left(S_1{S}_3+S_2{S}_4\right)-2J_3\left(S_1{S}_5+S_2{S}_5+S_3{S}_5+S_4{S}_5\right)$$

(2)

$$\widehat{H}=-2J_3\left(S_6{S}_5+S_7{S}_5+S_8{S}_5+S_9{S}_5\right)-2J_4\left(S_6{S}_7+S_6{S}_9\right)-2J_5\left(S_7{S}_8+S_9{S}_8\right)-2J_6\left(S_7{S}_9\right)$$

(3)

Considering the approximate treatments applied during the fitting, the χ_MT data for both Gd₅ models were derived by converting the χ_MT values of 1 (M_W = 3784.03 g mol⁻¹): χ_MT (Gd₅) = χ_MT (1)/9 × 5 (Figure S7). The optimal fitting of the experimental χ_MT vs. T data yields the magnetic parameters J₁ = −0.055 cm⁻¹, J₂ = −0.114 cm⁻¹, J₃ = 0.019 cm⁻¹, and g = 1.979 using Equation (2), and J₃ = 0.015 cm⁻¹, J₄ = −0.097 cm⁻¹, J₅ = −0.082 cm⁻¹, J₆ = −0.072 cm⁻¹, and g = 1.980 using Equation (3) [70]. These results are consistent with established magneto-structural relationships [42,71,72]. The ferromagnetic J₃ coupling originates from μ₃-OH bridges, aligning with empirical models where the Gd–O–Gd bond angles between 105 and 135° favor ferromagnetic interactions in Gd1–Gd5 (Table S4, bold font) [42,71,72]. However, in Gd5–Gd9, only 62.5% of the Gd–O–Gd bond angles fall within the 105–135° range. This may account for the smaller magnitude of the J₃ in Equation (3) compared to that in Equation (2). In contrast, the antiferromagnetic J₁, J₂, J₄, and J₆ arise from μ₄-OH/μ₃-OH/μ₂-O bridges, which is consistent with the correlation that excessively large or small bond angles result in antiferromagnetic coupling (Table S4, underlined font and wavy font, respectively). Compared with other hourglass-like Ln₉ clusters [24,41,42,43,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69], the structural differences in compound 1—beyond variations in ligands and symmetry—are mostly reflected in bond angles and Gd···Gd distances. For the upper base, the presence of μ₄-OH bridging groups restricts the ability of sulfur-containing ligands to modify the distances between central metal ions during coordination. For the lower base, however, as only three Gd³⁺ ions are connected by one μ₃-OH bridging group, the influence of sulfur-containing ligands becomes more prominent. They widen the Gd···Gd distances (Gd7···Gd8 = 3.96 Å, Gd8···Gd9 = 3.87 Å), make contributions to reducing magnetic exchange pathways [32], and also affect the distribution of Gd–O–Gd bond angles (Table S11). All these factors directly influence the magnetic coupling between metal ions.

The field-dependent magnetization of complex 1 was measured at discrete temperatures (2–10 K) under applied magnetic fields up to 7 T (Figure 6a). The magnetization (M) versus field curves exhibit a nearly linear increase at low fields (< 2 T), followed by a gradual approach to saturation, reaching a value of 62.13 Nβ at 2 K and 7 T, which is in close agreement with the theoretical saturation magnetization of 63 Nβ for nine non-interacting Gd³⁺ ions. Given the weak magnetic interactions observed in 1 and the well-known MCE in Gd³⁺-based clusters, the −ΔS_m values were calculated by the magnetic data using the Maxwell equation:

$$\mathsf{\Delta }S\mathrm{m}\left(T\right) =\int [\partial M(T, H)/\partial T{]}_H\mathrm{d}H$$

(4)

where T is the testing temperature, H is the applied magnetic field, and M is magnetization.

As shown in Figure 6b, the −ΔS_m values demonstrate a monotonic increase with decreasing temperature and increasing magnetic field change (ΔH), reaching a maximum value of −ΔS_m = 34.41 J kg⁻¹ K⁻¹ at 2 K under ΔH = 7 T (Figure 6b). This value is approximately 84% of the theoretical limit of 41.2 J kg⁻¹ K⁻¹ calculated by −ΔS_m^max = nRln(2S + 1)/M_W, with the reduction primarily attributed to the presence of weak interactions between adjacent metal ions. Notably, while moderate among molecular magnetic coolers generally [4,8,9,10,11], this −ΔS_m value ranks as the second highest reported for Gd₉ clusters (Table S12). When the number of central metal ions is the same, magnetic density—a key parameter that determines entropy change—can be readily inferred from the molecular weight. For instance, 1 has the largest molar mass (M_W = 3784.03 g mol⁻¹), corresponding to the lowest value of N_Gd/M_W among these Gd₉ clusters [41,42]. In MCE materials research, a larger molar mass and lower magnetic density are generally considered unfavorable for achieving high −ΔS_m values, as a lower concentration of magnetic ions per unit mass tends to limit the degree of magnetic ordering that contributes to entropy change under an external magnetic field [4]. Despite this, 1 exhibits a −ΔS_m value comparable to that of Gd₉(L¹)₄(μ₄-OH)₂(μ₃-OH)₈(μ₂-OCH₃)₄(NO₃)₈(H₂O)₈}(OH)·2H₂O (HL¹ = 2,6-dimethoxyphenol, M_W = 3015.28 g mol⁻¹). This compound, although not the lightest, displays weak antiferromagnetic and ferromagnetic interactions and holds the highest −ΔS_m value (40.60 J kg⁻¹ K⁻¹ at 2 K under ΔH = 7 T) reported for Gd₉ clusters to date (Table S12) [41,42,43]. Meanwhile, 1 has a −ΔS_m slightly larger than that of the third-ranked cluster, [Gd₉(L²)₄(NO₃)₁₂(μ₃-OH)₈(μ₄-OH)₂(CH₃CH₂OH)₄]·4.5CH₃CH₂OH·3Et₃NH (H₂L² = N-methyldiethanolamine, M_W = 3288.90 g mol⁻¹, −ΔS_m = 33.65 J kg⁻¹ K⁻¹ at 3 K under ΔH = 7 T) [41], and much larger than that of the fourth-ranked cluster, [Gd₉(L³)₈(NO₃)₈(μ₃-OH)₈(μ₄-OH)₂]·NO₃ (HL³ = 2-(2-aminoethoxy)ethanol; acac = acetylacetonate; M_W = 2976.45 g mol⁻¹, −ΔS_m = 25.22 J kg⁻¹ K⁻¹ at 3 K under ΔH = 7 T) [41] with the highest magnetic density and lowest molecular weight in Gd₉ clusters with MCE (Table S12).

Research findings reveal that both magnetic density and magnetic interactions affect the −ΔS_m value. For complex 1, magnetic density seems to play a minor role in determining the large −ΔS_m. We thus propose three potential factors contributing to its enhanced magnetocaloric performance. First, the incorporation of the heavy p-block S atoms from the HL ligands alters the cluster architecture, particularly affecting the Gd³⁺ ions at the vertices of the upper and lower basal planes, which are bridged by a μ₄-OH and μ₃-OH, respectively. Next, these sulfur-containing ligands in terminal coordination mode modulate key structural parameters—specifically Gd–μ₂/μ₃/μ₄-O–Gd bond angles and Gd···Gd distances—rendering the structure distinct from previously reported Gd₉ clusters ligated solely by N/O donors. Last, these geometric perturbations are expected to influence the nature and strength of magnetic exchange pathways, including both ferromagnetic and antiferromagnetic interactions. Collectively, these effects enhance the magnetic entropy change, despite the higher atomic mass of sulfur compared to conventional N/O-coordinating atoms.

Magnetization versus field measurements for complex 2 at 2 K reveal a gradual increase to a maximum moment of 46.31 Nβ at 7 T without a saturation plateau (Figure S8). Alternating-current (ac) magnetic susceptibility measurements under zero dc field with an oscillating field of 1.5 Oe show no detectable out-of-phase magnetic susceptibility (χ″) signal down to 2 K, suggesting the absence of magnetic relaxation (Figure S9). Consistently, hysteresis measurements at 2 K at a sweep rate of 200 Oe s⁻¹ exhibit vanishingly small coercivity (Figure S10). This collective behavior precludes SMM behavior under these conditions.

Magnetization versus field measurements for complex 3 at 2 K show a gradual approach to 50.91 Nβ at 7 T (Figure S11). The absence of distinct saturation and temperature-dependent non-superposition of M(H) curves possibly originates from strong intrinsic magnetic anisotropy. Frequency dependence of χ″ under 12 K confirms the slow magnetic relaxation characteristic of SMM behavior (Figure 7 and Figure S12). However, the absence of a discernible peak in the χ″ signal prevents the determination of relaxation time and thus the relaxation energy barrier. This behavior is similar to most reported nonanuclear Dy³⁺-based compounds [48,50,56,63]—except for one Dy₉ compound with an energy barrier of U_eff = 9.24 K [47]. Zero-field-cooled and field-cooled (ZFC–FC) susceptibility measurements at H = 50 Oe show no divergence, ruling out long-range magnetic ordering or superparamagnetic transitions (Figure S13). Additionally, hysteresis measurements at 2 K at a sweep rate of 200 Oe s⁻¹ exhibit minimal coercivity (Figure S14).

4. Conclusions

In summary, three nonanuclear lanthanide-based clusters [Ln₉(L)₁₇(μ₃-OH)₉(μ₄-OH)]·nH₂O (1: Ln = Gd, n = 3; 2: Ln = Tb, n = 3; 3: Ln = Dy, n = 1) were synthesized under hydrothermal conditions with sulfur-containing bidentate ligand 2-pyridinethiol 1-oxide. Remarkably, all three clusters exhibit a unique asymmetric architecture in which the upper and lower Ln₉ cores are bridged by μ₄-OH and μ₃-OH groups, respectively. Of these three clusters, 1 exhibits an excellent cryogenic MCE with −ΔS_m = 34.41 J kg⁻¹ K⁻¹ at 2 K under ΔH = 7 T, and 3 shows the SMM behavior. It is worth noting that, compared with the other four reported Gd₉ clusters with MCE, 1 exhibits a magnetic entropy change value that is second only to the highest among Gd₉ systems, despite having the largest molar mass and the lowest magnetic density, indicating the dominant role of magnetic coupling in determining the magnetocaloric performance. Specifically, the sulfur-containing bidentate ligands, coordinated in a terminal mode, influence key structural parameters of the nonanuclear cluster, including increasing the distances between Gd³⁺ ions, modifying the Gd–O–Gd bond angles, and reducing the number of bridging groups. This work not only expands research on the MCE of Gd₉ clusters but also provides a new synthetic strategy for constructing high-performance molecular-based magnetic cooling materials using ligands containing heavy p-block elements.