Giant magnetocaloric effect of the K₃Gd₅(PO₄)₆ compound at ultra-low temperature

Haojie Wang† ^ab, Junsen Xiang†^c, Zhaojun Mo^ab, Lei Zhang*^a, Heng Tu*^d, Guochun Zhang^d and Jun Shen^ae
aKey Laboratory of Rare Earths, Ganjiang Innovation Academy, Chinese Academy of Sciences, Ganzhou 341000, People's Republic of China. E-mail: lzhang@gia.cas.cn
^bSchool of Rare earths, University of Science and Technology of China, Hefei 230026, People's Republic of China
^cBeijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
^dCenter for Crystal Research and Development, Key Laboratory of Functional Crystals and Laser Technology, Center of Materials Science and Optoelectronics Engineering, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, People's Republic of China. E-mail: tuheng@mail.ipc.ac.cn
^eDepartment of Energy and Power Engineering, School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, People's Republic of China

First published on 6th August 2025

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1. Introduction

Cryogenic refrigeration has garnered significant interest owing to the increasing demand for cryogenic environments in fields such as frontier scientific research, quantum computing, and space applications.^1–4 Although dilution refrigeration (DR) is widely utilized to achieve very low temperatures, it relies heavily on the scarce resource ³He.⁵ Thus, the development of alternative low-temperature refrigeration technologies offers a potential solution to alleviate the ³He crisis.⁶ Adiabatic conditions allow for the manipulation of the temperature of magnetic materials through external magnetic fields, which is referred to as the magnetocaloric effect (MCE). Based on this effect, Giauque successfully established adiabatic demagnetization refrigeration (ADR) in the 1930s, achieving 0.25 K by the demagnetization of Gd₂(SO₄)₃·8H₂O.^7–9 Although the development of magnetic cooling in the sub-Kelvin range has been slow because of the wide application of DR, it has recently received considerable attention.^10–21 The magnetic entropy changes (−ΔS_M) of magnetic refrigerants, considered as the driving force of ADR, are the most critical parameter for evaluating the MCE of magnetic refrigerants. However, it is difficult to achieve high-performance magnetic refrigerants in the sub-Kelvin temperature region for practical applications. On the one hand, achieving the high performance of magnetic refrigerants often requires large magnetic ions per unit volume (n) to gain −ΔS_M. On the other hand, the magnetic ordering temperature (T_ord), below which the −ΔS_M rapidly diminishes as the temperature drops, should be sufficiently low to maintain MCE at sub-Kelvin temperatures, often resulting in low n. In addition, magnetic refrigerants possessing large −ΔS_M under low fields (generally below μ₀H = 4 T, considering the cost and the space of the magnetic refrigerator) are required for practical applications. Thus, it is necessary to explore the development of magnetocaloric materials with lower magnetic ordering temperatures and higher cooling power per unit mass or volume.^13,14,17,22

In fact, the Gd-based compounds, which show weak anisotropy and have a large theoretical magnetic entropy (Rln8), are ideal as magnetic cooling materials in the sub-Kelvin region, making them relatively easy to saturate at low magnetic fields compared to other rare earth elements.^23–31 Two well-known gadolinium-based magnetic coolants, GdLiF₄ (GLF) and Gd₃Ga₅O₁₂ (GGG), have been successfully employed in ADRs.^10,32 In the search for efficient magnetic refrigeration at sub-Kelvin temperatures, many Gd-based compounds with large MCE have been reported. Among them, Gd(HCOO)₃, GdF₃, Gd(OH)CO₃, Gd(OH)₃, Gd(OH)F₂, KBaGd(BO₃)₂ and GdPO₄ have been found to exhibit large MCE at low magnetic changes in the sub-Kelvin region.^{11,13,16–19,33} Recently, investigations have suggested that materials with weak ferromagnetic interactions have the potential to enhance low-field MCE.^17,21,33 To obtain magnetic refrigerants with large MCE, materials possessing both appropriate magnetic density and ferromagnetic interactions seem to be a promising candidate of magnetic refrigeration.

K₃Gd₅(PO₄)₆ is a monoclinic structure with space group C2/c. The framework of K₃Gd₅(PO₄)₆ is constructed from Gd polyhedra separated by PO₄ tetrahedra.³⁴ As a result, K₃Gd₅(PO₄)₆ has a medium n. Furthermore, it has been reported that K₃Gd₅(PO₄)₆ exhibits weak ferromagnetic interactions and no magnetic order above 2 K.³⁵ These findings indicate that it could be a promising material for sub-Kelvin magnetic refrigeration.

In this study, we have investigated the magnetic properties and MCE of the polycrystalline K₃Gd₅(PO₄)₆ compound below 2 K. The excellent low-field MCE of K₃Gd₅(PO₄)₆ even below its order temperature makes it a potential candidate as a magnetic refrigerant at the sub-Kelvin temperature region.

2. Experimental

2.1. Sample preparation

The polycrystalline compound K₃Gd₅(PO₄)₆ was synthesized by solid-state reaction. The starting materials for the analytical reagents, K₂CO₃, NH₄H₂PO₄ and Gd₂O₃, were weighed in a molar ratio of 3:12:5. These reactants were mixed and sufficiently ground in an agate mortar to ensure uniform mixing and reactivity. To thoroughly decompose K₂CO₃ and NH₄H₂PO₄, the pulverized mixture was placed in a platinum crucible and heated at 573 K and 5 h. The reactants were then thoroughly ground and heated at 1273 K and 10 h with several intermediate grinding steps.

2.2. X-ray crystallography

Powder X-ray diffraction analyses of the polycrystalline sample were performed at room temperature using an automated Bruker D8 X-ray diffractometer (Cu-Kα radiation, λ = 1.5418 Å). The XRD patterns were recorded in the two-theta region from 10° to 80° in steps of 0.2°. The K₃Gd₅(PO₄)₆ (space group C2/c) structural model was used as the initial structural model for Rietveld refinement.

2.3. Magnetic measurements

Above 2 K, magnetic measurements were carried out on a quantum design magnetic property measurement system (MPMS) using a superconducting quantum interference device (SQUID) magnetometer. Below 2 K, the magnetic measurement was performed by a ³He refrigerator affiliate of MPMS. A quasi-adiabatic demagnetization device, which is described elsewhere,³⁶ was used to evaluate the MCE performance of K₃Gd₅(PO₄)₆. To enhance the thermal conductivity of the sample used in quasi-adiabatic demagnetization measurement, it was compressed into a 1.46 g tablet with a 1:1 mass ratio of well-mixed silver powder and K₃Gd₅(PO₄)₆. The sample was placed in the quasi-adiabatic demagnetization device with a thermometer attached to the tablet. The device was then inserted into the quantum design physics property measurement system (PPMS), and the sample's temperature was recorded as the field was changed.

3. Results and discussion

3.1. Crystal structure

The crystal structure of K₃Gd₅(PO₄)₆ is presented in Fig. 1(a); the structure belongs to the monoclinic system with the space group C2/c. The GdO₈, GdO₉ polyhedra and isolated PO₄ tetrahedra are the basic structural units. The PO₄ tetrahedron is independent and only connected to the Gd polyhedron through shared O atoms, while all the Gd polyhedra are connected to the isolated PO₄ tetrahedra through shared O atoms. The interaction forms a three-dimensional [Gd₅(PO₄)₆]³⁻ anionic framework containing infinite channels along the c axis, which are occupied by K⁺ ions.³⁴ A room temperature powder XRD measurement was performed on the synthesized sample. The resulting XRD pattern, along with the Rietveld refinement to the experimental data of K₃Gd₅(PO₄)₆, are presented in Fig. 1(b). The XRD pattern exhibits a high degree of agreement with that reported by Zhu et al.³⁴ By using the GSAS program,³⁷ the refined unit cell parameters of K₃Gd₅(PO₄)₆ are: a = 17.456 Å, b = 6.9299 Å, c = 18.092 Å, β = 114.41°, and V = 1992.985 ų with R_p = 2.22%, R_wp = 2.87%, which are similar to the reported data.³⁵ The above results have confirmed that the obtained K₃Gd₅(PO₄)₆ sample is of high quality.

3.2. Magnetic properties

Fig. 2(a) shows the zero-field cooling (ZFC) and field cooling (FC) curves, in addition to the inverse magnetic susceptibility χ⁻¹(T) curve under a magnetic field of μ₀H = 0.01 T for the K₃Gd₅(PO₄)₆ material over a temperature range of 2 K to 300 K. The plot indicates that the ZFC and FC curves are coincident, and there is no long-range magnetic ordering above 2 K. The inverse magnetic susceptibility of the K₃Gd₅(PO₄)₆ shows linear behavior in the 2–300 K region, indicating that K₃Gd₅(PO₄)₆ obeys the Curie–Weiss law χ⁻¹(T) = (T − θ_CW)/C, where θ_CW represents the Curie–Weiss temperature and C is the Curie constant. The effective magnetic moment (μ_eff) value is evaluated as 7.60μ_B, which is close to the theoretical magnetic moment of Gd³⁺ (7.94μ_B). The compound exhibits weak ferromagnetic interactions, as indicated by its positive θ_CW value (0.74 K). This value is slightly larger than the previously reported θ_CW value of 0.38 K.³⁵ To examine the magnetic properties of K₃Gd₅(PO₄)₆ at temperatures below 2 K, we plot the FC curve of K₃Gd₅(PO₄)₆ in Fig. 2(b) for a magnetic field of μ₀H = 0.01 T and a temperature range of 0.4 K to 2 K. The FC reveal anomaly at approximately 0.64 K, which is close to θ_CW, as temperature decreases, the susceptibility decreases rapidly, indicating the presence of antiferromagnetic transition at this temperature.

Magnetization isotherm (M–H) curves were obtained for the K₃Gd₅(PO₄)₆ compound, which were measured at different temperatures and magnetic fields ranging up to 5 T at a temperature range of 2 K to 20 K, as indicated in Fig. 3(a). The M(H) curves depict a remarkable increase at considerably low fields and tend towards saturation at magnetic fields below 2 T. The Brillouin function, given by , where y = g·μ_B·J·B/k_BT, which describes the field dependence of magnetization without magnetic interaction, can be used to examine whether the dominant magnetic interaction of the compound is ferromagnetic. Thus, the Brillouin function is calculated by assuming that M is saturated in the applied field of 5 T of K₃Gd₅(PO₄)₆ at 2 K, as shown in the solid red line of Fig. 3(a). At 2 K, the field-dependent magnetization of K₃Gd₅(PO₄)₆ is larger than the curve derived from the Brillouin function calculation, suggesting that the predominant magnetic interaction is ferromagnetic in K₃Gd₅(PO₄)₆. The presence of both low T_ord and ferromagnetic interaction renders K₃Gd₅(PO₄)₆ a promising candidate for magnetic refrigerant at the sub-Kelvin region. Fig. 3(b) shows the isothermal magnetization curves (M–H) measured under magnetic fields of up to 5 T from 0.4 K to 1.8 K. The isothermal magnetization curve of 0.4 K quickly increases with the increase of the magnetic fields and saturates at 1 T. The magnetic moment is 6.96μ_B at 5 T, which is close to the free Gd³⁺ ion saturation moment (7μ_B). It may be attributed to the negligible anisotropy of Gd³⁺ ion, which can easily saturate the magnetization in all directions.

To evaluate the MCE performance of K₃Gd₅(PO₄)₆, the −ΔS_M is calculated from isotherm magnetization data by integrating the Maxwell relation, as shown in eqn (1).³⁸

	(1)

Fig. 4(a) illustrates the temperature-dependent −ΔS_M for K₃Gd₅(PO₄)₆ at magnetic fields changes of up to 5 T above 2 K. It can be observed that the −ΔS_M curves of K₃Gd₅(PO₄)₆ decrease monotonically with the temperature above 2.5 K. At 2.5 K, the −ΔS^max_M are 16.2 J kg⁻¹ K⁻¹, 29.1 J kg⁻¹ K⁻¹ and 43.7 J kg⁻¹ K⁻¹ for field changes of 0–1 T, 0–2 T and 0–5 T, respectively. The temperature-dependent plot of -ΔS_M for K₃Gd₅(PO₄)₆, ranging from 0.4 K to 2 K, is illustrated in Fig. 4 (b). The −ΔS^max_M of K₃Gd₅(PO₄)₆ corresponding to magnetic field changes of 1 T, 2 T and 3 T, are 25.4 J kg⁻¹ K⁻¹, 38.4 J kg⁻¹ K⁻¹ and 44.4 J kg⁻¹ K⁻¹, respectively. At 0.45 K, the -ΔS_M remains nearly constant for field changes above 3 T, with a value of approximately 20 J kg⁻¹ K⁻¹. Furthermore, the -ΔS_M with the field changes of 1 T at 0.45 K is still 13.4 J kg⁻¹ K⁻¹.

Some excellent magnetic coolants with large -ΔS_M at field changes of 1 T in 0.5 K - 3 K are shown in Table 1. The −ΔS^max_M of K₃Gd₅(PO₄)₆ was determined to be 24.2 J kg⁻¹ K⁻¹, which is larger than most of the compounds listed in Table 1. Compared with the refrigerants GGG,³⁹ the magnetocaloric effect of K₃Gd₅(PO₄)₆ is more than twice that of GGG at the magnetic field of 1 T.

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To gain more insight into the MCE of K₃Gd₅(PO₄)₆ at ultra-low temperatures, we proceeded to perform quasi-adiabatic demagnetization measurements. The inset of Fig. 5(a) presents a schematic illustration of the quasi-adiabatic demagnetization device,³⁶ which is similar to the one previously reported by other research groups.^15,22,41 Fig. 5(a) displays the quasi-adiabatic demagnetization curves with a field decrease of 0.01 T s⁻¹ of the sample under different initial conditions, along with that of GGG reported from previous published works.⁴² For the quasi-adiabatic demagnetization curve with the initial conditions T = 2 K and μ₀H = 4 T, the temperature initially drops as the magnetic field decreases; when the field decreases to 0.3 T, the sample reaches a minimum temperature of 310 mK. However, as the magnetic field decreases further, the sample temperature rises to 370 mK when the applied field reaches 0 T. In contrast, under the same initial condition, the quasi-demagnetization curves of GGG can only reach about 410 mK, with the temperature remaining almost unchanged as the applied field is further decreased.⁴² Under quasi-adiabatic conditions, the quasi-adiabatic demagnetization curves can be regarded as isentropic curves, which follow the equation given by ,⁴³ where C is the heat capacity. The existing dips of the isentropic curves indicated , suggesting that an antiferromagnetic-to-paramagnetic phase transition occurred at these inflection points. The presence of quantum fluctuations tend to increase the disorder of the spins near the quantum critical point. This phenomenon may also result in the formation of dips in isentropic curves, as evidenced in the case of KBaGd(BO₃)₂.¹⁹ Thus, to clarify the origin of the dip in K₃Gd₅(PO₄)₆, a more detailed investigation on single-crystalline samples is needed. For practical application, with the initial condition of 4 K and 4 T, the lowest obtainable temperature of K₃Gd₅(PO₄)₆ is 510 mK, while GGG can only reach about 880 mK under the same conditions.⁴² In addition, for the isentropic curve with an initial condition of 2 K and 4 T, the temperature decreases to 580 mK, and −ΔS_M is still as large as 17.5 J kg⁻¹ K⁻¹ according to Fig. 4(b). Based on the quasi-demagnetization curves of K₃Gd₅(PO₄)₆, T_ad, defined as the difference between the initial temperature (T_initial) and the temperature corresponding to the isentropic curve with zero magnetic field (T₀), is also calculated. As shown in Fig. 5(b), T_ad shows an almost linear trend with the initial temperature. It is important to note that T_ad is underestimated since the lowest temperature of K₃Gd₅(PO₄)₆ is not T₀. The isentropic curve with initial condition of 2 K and 4 T, the temperature decrease to 580 mK, the −ΔS_M is still as large as 17.5 J kg⁻¹ K⁻¹ according to Fig. 4(b). These results suggest that K₃Gd₅(PO₄)₆ is a promising candidate for sub-Kelvin magnetic refrigeration.

4. Conclusion

In summary, a detailed investigation was conducted on the magnetic and MCE properties of polycrystalline K₃Gd₅(PO₄)₆ at ultra-low temperatures. The findings indicate that K₃Gd₅(PO₄)₆ undergoes an antiferromagnetic transition at a Néel temperature of 0.64 K, while the dominant magnetic interaction is ferromagnetic. A −ΔS^max_M value of up to 25.4 J kg⁻¹ K⁻¹ is observed below 2 K when the field is changed by 1 T. The quasi-adiabatic demagnetization curves directly show the cooling effect of the K₃Gd₅(PO₄)₆ polycrystalline samples. At an initial temperature of 2 K and initial field of 4 T, temperatures as low as 310 mK can be achieved with μ₀H = 0.3 T. Furthermore, for practical application, at an initial temperature of 4 K and initial field of 4 T, temperatures as low as 510 mK can be achieved by demagnetization of K₃Gd₅(PO₄)₆. This is much lower than the temperature that GGG can reach under the same initial conditions (about 880 mK), surpassing the performance of GGG, which make K₃Gd₅(PO₄)₆ a competitive candidate of low-field magnetic refrigeration at very low temperatures.

Note added. Upon completing the present work, we note a recent study⁴⁴ that examines the MCE study of K₃Gd₅(PO₄)₆ through heat capacity measurements, revealing a large low-field magnetocaloric response above 2 K.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.

Data availability

The data supporting the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgements

The authors would like to express their gratitude to Prof. Shouguo Wang of Anhui University for his invaluable assistance in conducting the cryogenic magnetic property measurements, and to Prof. Peijie Sun of the Institute of Physics, Chinese Academy of Sciences for his support in the quasi-adiabatic demagnetization measurements. Additionally, the authors would like to acknowledge Prof. Wei Li from Institute of Physics, Chinese Academy of Sciences, for his insightful discussions. This work was supported by the National Key Research and Development Program of China (Grant 2022YFB3505101); the National Science Foundation for Distinguished Young Scholars (Grant No. 51925605); and the Research Projects of Ganjiang Innovation Academy, Chinese Academy of Sciences (Grant No. E355F001).

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Footnote

† These authors contributed equally to this work.

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