Single-crystal X-ray diffraction analysis revealed that (Yb_1-xGd_x)₂SO₄(OH)₂F₂ crystallizes in the monoclinic space group (Supporting Information (SI), Table S1). The powder X-ray diffraction patterns of 1—3 are in good agreement with the simulated pattern, confirming the phase purity of the samples (SI, Figure S1). The ratio of Gd to Yb in 2 and 3 were determined by inductively coupled plasma mass spectrometry (ICP-MS) (SI, Table S2). In addition, elemental mapping of 2 and 3 (SI, Figure S2) demonstrates the homogeneous distribution of Gd and Yb throughout the samples. Given their structural similarities, the structure of Yb₂SO₄(OH)₂F₂ is discussed in detail below. The asymmetric unit in 1 contains two crystallographically independent Yb³⁺ ions, one SO₄²⁻ group, two OH⁻ ligands, and two F⁻ ligands (Figure 1a). One Yb³⁺ center is eight-coordinated by two F⁻, three OH⁻, and three O atoms from two SO₄²⁻ groups, giving a slightly distorted triangular dodecahedron (SI, Figure S3a) with continuous shape measure (CShM) values of 1.018—1.098 (SI, Table S3). In contrast, the other Yb³⁺ center is eight-coordinated by three F⁻, three OH⁻, and two O atoms from two SO₄²⁻ groups, giving a slightly distorted square antiprism (Figure S3b) with CShM values of 0.953—1.016. Three neighboring Yb³⁺ ions are interconnected by three OH⁻ ligands and one F⁻ ligand to form a triangular trinuclear motif, with Yb…Yb separations ranging from 0.3623 to 0.3720 nm (Figure 1b). Two such triangular units are related by a horizontal flip (Figure 1c) and are further connected to generate a hexanuclear {Yb₆} unit. These {Yb₆} units are subsequently linked in a zigzag, or “Z”-shaped, manner along the a axis through shared OH⁻ ligands, forming an infinite one-dimensional chain structure (Figure 1d). Furthermore, neighboring zigzag chains are interconnected by F⁻ and SO₄²⁻ groups, which act as interchain bridges and extend the structure into a three-dimensional framework (Figure 1e). The Yb—F and Yb—O bond lengths are 0.2121(3)—0.2465(7) and 0.2242(7)—0.2687(7) nm, respectively, while the Yb—F—Yb and Yb—O—Yb bond angles range from 99.4(3)° to 151.1(3)° and 90.0(3)° to 108.0(3)°, respectively. These parameters remain essentially unchanged upon Gd³⁺ doping, with corresponding bond lengths of 0.2121(5)—0.2479(7) and 0.2253(8)—0.2683(8) nm and bond angles of 100.1(3)°—150.7(3)° and 90.3(3)°—108.0(4)°, respectively.

Temperature-dependent magnetic susceptibility measurements were performed on polycrystalline samples of 1—3 under an applied DC field of 0.1 T (SI, Figure S4). At 300 K, the χ_mT values are consistent with those expected for the corresponding concentrations of magnetically isolated Yb³⁺ and Gd³⁺ ions (SI, Table S4). Upon cooling, χ_mT decreases gradually for all three compounds. Although this behavior may suggest antiferro- magnetic interactions, the magnetic properties of Yb³⁺- based systems are often strongly influenced by crystal-field splitting, which can also contribute significantly to the temperature dependence of χ_mT. To minimize the influence of thermally populated crystal electric field excited states and thereby better reflect the intrinsic low-temperature magnetic interactions, Curie-Weiss fitting was performed over the 2—10 K range, following common practice for rare-earth magnetic systems. This analysis yielded Weiss constants (θ) of -0.57, -0.52, and -0.74 K for 1—3, respectively (Figure 2). These small negative θ values indicate the presence of weak antiferromagnetic interactions in all three compounds. Although Gd substitution slightly increases the magnitude of θ at higher doping levels, the magnetic interactions remain weak across the series. Notably, Gd incorporation increases the spin density without introducing significant magnetic exchange, thereby achieving a favorable balance between large magnetic entropy and suppressed magnetic ordering, both of which are desirable characteristics for efficient adiabatic demagnetization refrigeration at sub-kelvin temperatures.^[21]

Considering the preference for low magnetic fields in practical applications, heat-capacity measurements were performed for 1—3 between 0.1 and 20 K under zero field and an applied magnetic field of 2 T to evaluate their low-temperature magnetocaloric effects (Figures 3a and S5). At higher temperatures, the heat capacity is dominated by lattice contributions, whereas magnetic contributions become increasingly significant upon cooling. To isolate the magnetic contribution from the total heat capacity, the lattice contribution (C_lattice) was estimated using the Debye model, and the magnetic heat capacity (C_m) was then obtained by subtracting C_lattice from the total heat capacity according to C_m=C_p-C_lattice. As shown in Figure 3b, the magnetic heat capacities exhibit pronounced λ-type anomalies characteristic of long-range magnetic ordering. The corresponding T₀ values are 0.65, 0.60, and 0.55 K for 1—3, respectively, revealing a gradual suppression of magnetic ordering upon Gd substitution. Notably, although Gd incorporation slightly strengthens the overall magnetic interactions, as indicated by the increased θ values, the ordering temperature is continuously reduced. This apparent contrast highlights the difference between local magnetic exchange interactions and the development of long-range magnetic order. In this system, Gd-induced exchange randomness, together with competing ferro- and antiferromagnetic interactions, likely frustrates long-range magnetic ordering and thus lowers T₀.^[18-20] While increasing the Gd³⁺ content can enhance the magnetic entropy, it also strengthens exchange and dipolar interactions, which tend to raise T₀. In principle, dilution of a pure Gd³⁺ lattice with diamagnetic Y³⁺ can also suppress magnetic interactions and reduce the magnetic ordering temperature. However, due to the strong dipolar interactions associated with the large magnetic moment of Gd³⁺, achieving sufficiently low ordering temperatures generally requires extensive dilution, which inevitably reduces the magnetic ion density and thus significantly limits the achievable magnetic entropy change. This highlights the intrinsic trade-off between suppressing magnetic ordering and maintaining high magnetic density in designing efficient sub-Kelvin magnetocaloric materials. Herein, the combination of enhanced magnetic entropy (SI, Figure S6) and suppressed magnetic ordering is highly desirable for sub-kelvin magnetic refrigeration.

To further evaluate the effect of Gd substitution on the thermodynamic properties, the magnetic entropy (S_m) was calculated by integrating the magnetic heat capacity according to S_m(T)=∫(C_m/T)dT. As shown in Figure S7 (SI), the magnetic entropy increases systematically with increasing Gd content over the entire temperature range. Given its highest magnetic entropy and lowest ordering temperature among the three compounds (Figure S6b), 3 was selected as a representative system for detailed magnetocaloric investigation. As shown in Figures 3c and 3d, compound 3 exhibits a maximum magnetic entropy change of approximately 100 mJ•cm^-3•K^-1 under ΔH=2 T, which is substantially higher than those of hydrated paramagnetic salts such as CPA and FAA (Table 1). Although the magnetocaloric performance of 3 does not exceed that of the best-performing Yb-based fluoride refrigerants, which benefit from high magnetic-ion densities and minimal nonmagnetic components, its maximum entropy change remains highly competitive among reported Yb-based refrigerants. In particular, the -ΔS_m values of 3 surpass those of most pure Yb-based framework materials reported to date, demonstrating the effectiveness of the present fluorohydroxysulfate framework in preserving large magnetic entropy at sub-kelvin temperatures. More importantly, the enhanced magnetocaloric performance is achieved without compromising either structural stability or magnetic-ion density. In contrast to many Yb-based fluoride refrigerants, in which increasing Gd content typically strengthens magnetic correlations and raises the magnetic ordering temperature, Gd incorporation in the present fluorohydroxysulfate framework does not induce stronger magnetic ordering. Instead, T₀ is slightly suppressed with increasing Gd content. Consequently, the introduction of Gd³⁺ simultaneously increases the magnetic-ion density and preserves, or even enhances, the accessibility of magnetic entropy in the sub-kelvin regime. This unusual combination effectively mitigates the conventional trade-off between magnetic entropy density and magnetic ordering, leading to a substantially enhanced magnetocaloric response.

A mixture of Yb₂O₃ (1 mmol), concentrated H₂SO₄ (98%, 1 mmol) and hydrofluoric acid (≈40%, 2 mmol) was dissolved in 5 mL of H₂O and stirred for 20 min at room temperature. The resulting solution was transferred into a 23 mL Teflon-lined stainless-steel autoclave and heated at 230 ℃ for 3 d under autogenous pressure. After cooling to room temperature naturally, yellow block-shaped crystals were collected, washed with deionized water and dried in air. Caution! Hydrofluoric acid is highly toxic and corrosive and should be handled with extreme caution using appropriate protective equipment and safety procedures.

The preparation of (Yb_0.9Gd_0.1)₂SO₄(OH)₂F₂ is quite similar to 1 except that the dosage of rare earth oxides was adjusted as Yb₂O₃ (0.9 mmol) and Gd₂O₃ (0.1 mmol).

The preparation of (Yb_0.7Gd_0.3)₂SO₄(OH)₂F₂ is quite similar to 1 except that the dosage of rare earth oxides was adjusted as Yb₂O₃ (0.7 mmol) and Gd₂O₃ (0.3 mmol).

(Cheng, B.)