Introduction

The magnetocaloric effect (MCE) is known as the thermal response of a magnetic material to changes in external magnetic fields. In the vicinity of a magnetic phase transition, external magnetic fields can effectively tune the entropy of the magnetic sublattice. When the magnetized material is demagnetized, a temperature drop is obtained. Such an effect was observed more than one hundred years ago. In 1926, Debye and Giauque theoretically deduced the possibility of adiabatic demagnetization refrigeration based on the MCE1. Subsequently, Giauque and MacDougall first used Gd2(SO4)3·8H2O as a magnetic coolant in adiabatic demagnetization refrigeration technology to achieve ultralow temperatures down to 0.25 K2. Since then, magnetic refrigeration technology based on the MCE has received extensive attention, and thus far, it has been widely used in many fields, such as cooling bolometers for astrophysical measurements in space, providing a cryogenic environment for quantum computing and the production of superfluid liquid helium3,4,5,6,7,8,9,10,11,12. Due to the solid nature of the working materials, in particular, it is more appealing for space applications without the influences of gravity over fluid-based technology options such as 3He/4He dilution refrigeration.

The critical issue of the development of magnetic refrigeration technology is the identification of more efficient magnetocaloric materials with a larger isothermal magnetic entropy change (ΔSm), larger adiabatic temperature change (ΔTad), and smaller driving magnetic field (ΔH). Therefore, extensive efforts have been devoted to tackling this challenge. In 1973, Fisher et al. systematically studied the thermomagnetic properties of gallium gadolinium garnet (GGG) single crystals along the [001], [110], and [111] directions, and the maximum ΔSm reached 38 J kg−1 K−1 under a magnetic field change of 70 kOe13,14,15. Since then, GGG has become the primary choice for commercial adiabatic demagnetization refrigerators around the liquid-helium temperature as well as a benchmark for magnetocaloric materials exploration16,17. Although an increasing number of low-temperature magnetocaloric materials with large ΔSm values have been reported18,19,20,21,22 to satisfy the growing demands for space exploration and quantum computation, strong magnetic fields are usually needed, which are currently only provided by heavy and large superconducting magnets. Furthermore, as commercial adiabatic demagnetization refrigerators are usually applied for precision detection in low-temperature environments, magnetic shielding must be considered. Both of the above aspects increase the cost and complicate the design of refrigeration systems. In addition, the low volume ratio of the magnetocaloric material to the magnetic refrigeration device results in bulky systems. These disadvantages have hindered practical application of magnetic refrigeration technology. Therefore, a material possessing excellent magnetocaloric performance under a magnetic field lower than 10 kOe provided by permanent magnets can significantly improve the efficiency of magnetic refrigeration equipment and facilitate the manufacture of more compact equipment.

Compounds consisting of rare earth (RE) elements usually exhibit excellent magnetocaloric properties due to their large intrinsic magnetic moments. Among them, lithium rare earth fluorides with the chemical formula LiREF4 have a tetragonal scheelite structure (space group I41/a), where RE can comprise rare earth elements including gadolinium (Gd), terbium (Tb), dysprosium (Dy), holmium (Ho), erbium (Er), thulium (Tm), and ytterbium (Yb). The unit cell of LiREF4 contains two magnetically equivalent trivalent lanthanide ions at sites with S4 point symmetry. They exhibit exotic physical properties at low temperatures23,24,25,26,27,28,29,30,31,32,33,34, such as quantum criticality. In regard to their basic magnetism, they can be categorized into three groups, namely, LiTmF4, which is Van-Vleck paramagnetic31; LiTbF4 and LiHoF4, which are ferromagnetic (FM) with Curie temperature (TC) values of 2.87 and 1.53 K, respectively24,25,26,28,29; and LiDyF4, LiErF4, and LiYbF4, which are antiferromagnetic (AFM) with Néel temperature (TN) values of 0.62, 0.38 and 0.128 K, respectively27,30,31,32. Currently, the magnetic ground state of LiGdF423 is still unknown. LiREF4 single crystals exhibit extremely high magnetocrystalline anisotropy due to crystal electric field effects33. The magnetic easy axes of LiGdF4, LiTbF4, and LiHoF4 are parallel to the c axis, while those of LiDyF4, LiErF4, LiYbF4, and LiTmF4 are perpendicular to the c axis. The high magnetocrystalline anisotropy underlies the rotating MCEs, where MCE materials are rotated in the static magnetic fields between the easy and hard axes, corresponding to magnetization and demagnetization. A summary of the basic crystal structure and magnetism is shown in Fig. 1.

Fig. 1: Basic magnetism of LiREF4.
figure 1

a The crystal structure and magnetic structures of LiREF4. The table shows their magnetic ground state, phase transition temperatures and magnetocrystalline anisotropies. b The temperature dependencies of ZFC-FC magnetization of LiREF4 single crystals with magnetic fields along the easy axes.

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In this work, the magnetocaloric properties of LiREF4 single crystals were systematically studied. These compounds exhibit extraordinary performance levels, much higher than that of the prototype GGG. Under a magnetic field as low as 5 kOe, the largest ΔSm values was obtained in LiHoF4, at approximately 16.7 J kg−1 K−1. The largest entropy changes (ΔSr) of rotating MCEs were also achieved in LiHoF4, at approximately 16.5 J kg−1 K−1 under 5 kOe, 21.1 J kg−1 K−1 under 10 kOe and 22.6 J kg−1 K−1 under 20 kOe. More importantly, the direct ΔTad value of FM LiHoF4 is approximately 2.38 K under 5 kOe using the pulsed magnetic field method. This remarkable performance renders LiREF4 a promising next-generation working material for magnetic refrigerators around the liquid-helium temperature.

Results

Magnetic properties of LiREF4 single crystals

Zero-field cooled (ZFC) and field-cooled (FC) magnetization curves were collected as a function of the temperature in the temperature range from 2 to 50 K for the above seven compounds. A magnetic field of 100 Oe was applied to the crystals along their magnetic easy axes except for LiTmF4. Due to the weak magnetism of LiTmF4, the applied magnetic field was 1000 Oe. LiTbF4 experienced a FM transition at approximately 2.85 K, which is consistent with previous reports24,25,26. The magnetization for all compounds increased upon cooling, but no long-range magnetic order was found for the other fluorides above 1.8 K. Among these seven fluorides, LiTmF4 exhibited a different tendency, and the ZFC and FC curves of LiTmF4 showed that magnetization is a temperature-independent phenomenon below 8 K, which is a sign of Van-Vleck paramagnetism31. Notably, the ZFC and FC curves of all compounds overlapped, indicating high thermal reversibility.

Magnetic isotherms were measured in the temperature region from 1.8 to 24 K in very fine steps up to 20 kOe along both the easy and hard axes for the seven fluorides. The isothermal magnetization curves of LiGdF4, LiTbF4, and LiHoF4 are shown in Supplementary Figs. 1–3, while those of LiDyF4, LiErF4, LiYbF4 and LiTmF4 are shown in Supplementary Figs. 4–7. Based on the single-crystal alignment (refer to the Methods section below) and magnetization curves, we determined that the magnetic easy axes of the former three fluorides are parallel to the c axis, whereas those of the latter four fluorides are perpendicular to the c axis. Their magnetocrystalline anisotropic properties are consistent with previously reported g-values of the system33. Along the easy axis, the magnetization of LiTbF4 and LiHoF4 at the lowest temperature increased so rapidly with increasing magnetic field that they were almost saturated at approximately 10 kOe. This feature suggests that they are FM in nature. The saturation magnetization approached 8.7 and 7.2 μB/RE3+ for LiTbF4 and LiHoF4, respectively. In this temperature region, LiGdF4, LiDyF4 and LiErF4 exhibit PM properties, but with notable magnetic fluctuations so that the magnetization also rapidly increased under low fields. This is similar to PM LiYbF4. However, the magnetic isotherms of LiTmF4 were almost linear, which is consistent with the nature of Van-Vleck paramagnetism.

It is clear that the magnetization along the easy axes is much higher than that along the hard axes under small fields, indicating the high magnetocrystalline anisotropy of LiREF4. LiDyF4 exhibited the largest difference. At 1.8 K, the magnetization reached approximately 6.9 μB/RE3+ along the easy axis and below 0.84 μB/RE3+ along the hard axis, which suggests a remarkable rotating MCE. In addition, the magnetization along the hard axis did not decrease continuously with increasing temperature. Supplementary Fig. 8 shows M–T curves under increasing magnetic fields. With decreasing temperature, the magnetization of the LiDyF4 single-crystal sample first increased, then decreased, and finally increased again due to the crystal electric field effects27.

Conventional MCEs of LiREF4

The temperature dependency of the isothermal entropy change ΔSm for LiREF4 under magnetic field variations of 5, 10, and 20 kOe along the easy and hard axes is shown in Fig. 2, where the data for the GGG single crystal are also included for comparison. Along the easy axes, the maxima of -ΔSm for LiGdF4, LiTbF4, LiHoF4, LiDyF4, LiErF4, LiYbF4, and LiTmF4 single crystals were 6.6, 10.1, 16.7, 7.8, 6.7, 1.7, and 0.04 J kg−1 K−1, respectively, when the magnetic field was changed from 0 to 5 kOe, 22.5, 17.9, 21.7, 18.9, 16.1, 6, and 0.16 J kg−1 K−1, respectively, when the magnetic field was changed from 0 to 10 kOe, and 46.7, 21.2, 25.5, 24.4, 21.9, 14.7, and 0.7 J kg−1 K−1, respectively, when the magnetic field was changed from 0 to 20 kOe. Under a magnetic field of 5 kOe, LiHoF4 yielded the largest -ΔSm value among all fluorides, larger than that of polycrystalline LiHoF421. With increasing magnetic field, LiGdF4 performed the best under 10 and 20 kOe. The corresponding values for GGG are 1.0, 3.9, and 14.4 J kg−1 K−1, respectively, which are remarkably smaller, and the data are consistent with the results of Brodale et al. 15. The profiles of the -ΔSm–T curves are very consistent with their magnetic natures. As LiTbF4 is FM in nature, its -ΔSm–T curve peaked at a TC value of 2.85 K. LiHoF4 exhibited a TC value of approximately 1.53 K, which is just beyond the current measurement interval, but there is a saturation tendency as the temperature is lowered to 1.8 K. Regarding the other compounds, which either have much lower magnetic ordering temperatures (LiDyF4, LiErF4, and LiYbF4) or are PM in nature (LiGdF4), their -ΔSm–T curves exhibited a monotonous increasing tendency. -ΔSm of LiTmF4 was marginal due to its Van-Vleck paramagnetism. Regarding all the LiREF4 crystals, the magnetization and demagnetization curves greatly overlapped, which indicates the excellent magnetic reversibility of the MCE (Supplementary Fig. 9).

Fig. 2: Conventional MCEs of LiREF4 single crystals with magnetic fields along the magnetic easy and hard axes.
figure 2

a, d 5 kOe, b, e 10 kOe and c, f 20 kOe.

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Just as the magnetic isotherms indicate remarkable magnetocrystalline anisotropy, as shown in Supplementary Figs. 1–7, -ΔSm greatly differs between the easy and hard axes. Choosing LiTbF4 as an example, the maximum -ΔSm values along the magnetic hard axis were 1.2, 4, and 10.7 J kg−1 K−1 under 5, 10, and 20 kOe, respectively, which are much smaller than the values of 10.1, 17.9, and 21.2 J kg−1K−1, respectively, along the easy axis. In addition, -ΔSm along the hard axis of LiDyF4 was negative, which might be attributed to the unique crystal electric field effects. From the temperature dependence of magnetization under the different magnetic fields (Supplementary Fig. 8), the magnetization was suppressed under magnetic fields below 5 K, and the minimum value slightly shifted to higher temperatures. In terms of the magnetic Maxwell relation, this negative -ΔSm value is understandable.

Rotating MCEs of LiREF4

As reflected by the observed magnetizations and conventional MCEs above, the LiREF4 single crystals exhibited very high magnetocrystalline anisotropy. Consequently, large rotating MCEs are highly anticipated. Under the conventional magnetic refrigeration scenario, magnetization and demagnetization processes are realized by moving the magnetocaloric materials in and out of the magnetic field zone, respectively. However, effective magnetic fields can be tuned by rotating the magnetocaloric single crystals (the rotating MCE). The magnetization process is actualized when the magnetic easy axis of the single crystals is oriented along the direction of the external magnetic fields, after which the single crystals are rotated by 90 degrees to achieve demagnetization. Thus, the entropy changes of the rotating MCE, ΔSr, can be defined as the difference in ΔSm between the magnetic easy and hard axes. This system indeed exhibits considerable rotating MCEs, as shown by the temperature dependency of ΔSr under 5, 10, and 20 kOe in Fig. 3. Except for LiTmF4 (not shown here), the maxima of ΔSr for the other fluorides are all higher than 10 J kg−1 K−1 under 20 kOe. Since the magnetic entropy change of LiREF4 along the hard axis is very small, its rotating magnetic entropy change is almost the same as that along the easy axis. The largest value is obtained for LiHoF4, at 22.6 J kg−1 K−1. In fact, the maximum ΔSr value exceeds 21.1 J kg−1 K−1 even under 10 kOe for LiHoF4.

Fig. 3: Rotating MCEs of LiREF4 single crystals.
figure 3

a LiGdF4, b LiDyF4, c LiTbF4, d LiErF4, e LiHoF4, and f LiYbF4.

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ΔT ad of LiREF4

In addition to the isothermal magnetic entropy change, the adiabatic temperature change (ΔTad) is another critical parameter characterizing magnetocaloric materials, which is defined as the temperature change of a magnetocaloric material in response to varying magnetic fields under adiabatic conditions. ΔTad can be adopted to evaluate the real performance in magnetic refrigeration applications more easily. A larger ΔTad value underlies a sharper temperature gradient between the magnetic refrigeration working material and thermal loading, which facilitates heat exchange.

The direct ΔTad value can be measured using pulsed magnetic fields under nearly adiabatic conditions, which was achieved in magnetocaloric Gd and GGG35,36. In regard to FM LiTbF4 and LiHoF4 as well as AFM LiDyF4 single crystals, pulsed magnetic fields were applied along their easy axes, as shown in Fig. 4a–c. At a given initial base temperature (Tb), the temperature of the sample (Ts) was recorded as the pulsed magnetic fields increased to 250 kOe and decreased to 0. The direct ΔTad value can be defined as the difference between Ts and Tb. Due to the short pulse structure and thus nearly ideal thermal insulation, this temperature increase is quite close to the theoretical ΔTad value. The ΔTad values at magnetization and demagnetization nearly coincide, which indicates the cycling ability. The largest ΔTad value of LiTbF4 was obtained at 4.2 K, which is as high as 30 K, consistent with a previous study37. It is reasonable that LiTbF4 is FM in nature below 2.85 K, and the largest magnetic fluctuations are expected at a temperature slightly higher than TC. The FM nature was also manifested in the saturation tendency of ΔTad under higher magnetic fields. FM LiHoF4 also exhibited the same properties. As a benchmark, AFM LiDyF4 was also considered under similar conditions. Notably, the profiles of ΔTad did not show saturation behavior, conforming with its AFM nature. In Fig. 4d, ΔTad of LiHoF4 in the region below 5 kOe is highlighted. At the base temperature of 1.6 K, the highest value was obtained, reaching as high as 2.38 K. In other words, adiabatic removal of the magnetic field of 5 kOe at approximately 4 K leads to cooling to 1.6 K.

Fig. 4: Adiabatic temperature changes of LiREF4.
figure 4

The temperature change Ts – Tb of LiTbF4 (a), LiHoF4 (b), and LiDyF4 (c) measured with pulsed magnetic fields applied along easy axes. d The temperature change Ts – Tb of LiHoF4 when magnetic fields ramped from 5 kOe down to 0.

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Discussion

LiREF4 has shown great potential as a magnetocaloric material since Numazawa et al. investigated the magnetocaloric effects of polycrystalline LiGdF4 in 200623. Very recently, polycrystalline LiGdF4, LiHoF4, and LiErF4 have also been reported with entropy changes of 44, 25.9, and 17.5 J kg−1 K−1, respectively, under 20 kOe21,23,38. Due to the high magnetocrystalline anisotropy, the polycrystalline samples exhibited a limited performance under a small magnetic field. Here, by using a single crystal, the magnetocaloric performance under small magnetic fields was significantly improved. Under magnetic fields of 5 kOe, LiHoF4 yielded the largest -ΔSm value among all fluorides. As listed in Table 1, LiHoF4 holds the record of -ΔSm among these known magnetocaloric compounds.

Table 1 Comparison of magnetic entropy change (-ΔSm) of leading magnetocaloric materials under a magnetic field changing from 0 to 5 kOe.
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The encouraging results here for LiREF4 single crystals open an emergent route to compact magnetic refrigerators around liquid-helium temperature intervals or even lower. First, -ΔSm and ΔTad, as two critical factors for magnetic refrigeration, are significantly larger than those of the prototype GGG. This feature ensures that fewer working materials are necessary for a given refrigeration loading, which reduces the volume of the whole refrigerator. Second, under a small magnetic field, such as 10 kOe or even 5 kOe, which can be easily generated by a permanent magnet, the magnetocaloric performance of these single crystals is almost saturated. In contrast, current magnetic refrigerators can only be operated under large magnetic fields, and superconducting magnets are mandatory. For example, Kwon et al. designed a refrigerator consisting of a sorption cooler and an adiabatic demagnetization refrigerator, in which the magnetic working medium was GGG under a magnetic field of 40 kOe17. It has been recognized that the volume or weight of the superconducting magnets accounts for approximately one-third of the whole system39. Thus, the replacement of a superconducting magnet with a permanent magnet is anticipated to greatly reduce the cost and volume of the whole system. Third, the significant reduction in the working magnetic fields greatly simplifies the magnetic shielding system necessary for high-precision detection. Without a complicated magnetic shielding system, the volume of the system can be further reduced. Fourth, the superior rotating MCEs discovered in LiREF4 single crystals provide a chance to achieve much smaller devices than the conventional reciprocating configuration, as schematically shown in Supplementary Fig. 10. Finally, the magnetic ordering temperatures of this family cover a very wide temperature region, where TN of LiYbF4 is as low as 0.128 K, enabling ultralow-temperature applications.

In summary, we systematically investigated the magnetocaloric properties of single crystals of the LiREF4 family, including LiGdF4, LiTbF4, LiHoF4, LiDyF4, LiErF4, LiYbF4, and LiTmF4. Their magnetic entropy changes were determined based on magnetization data, while the direct adiabatic temperature changes were obtained using pulsed magnetic fields. The entropy changes were significantly larger than those of the reference GGG single crystals. The very high magnetocrystalline anisotropy also resulted in notable rotating MCEs. In LiHoF4, specifically, the magnetic entropy change and the direct adiabatic temperature change reached 16.73 J kg−1 K−1 and 2.38 K under 5 kOe, respectively. This superior magnetocaloric performance renders this system promising in terms of replacing GGG as a next-generation working material for compact magnetic refrigeration around liquid-helium temperatures.

Methods

Sample preparation and structural characterizations

LiREF4 single crystals were grown by the Czochralski technique using a resistive or an RF-heating furnace. Powders (<99.99%) were loaded into a Pt crucible, where they were subjected to a fluorination process. Then, crystal growth was achieved in a high-purity CF4 (99.99%) atmosphere to effectively eliminate oxygen traces from the chamber. Single crystals were grown using a-oriented LiYF4 seeds. The details on crystal growth have been published elsewhere40. The single crystals were structurally characterized using powder X-ray diffraction (Supplementary Fig. 11) as well as the Laue back-reflection method (Supplementary Fig. 12). The alignments of the single crystals for magnetic measurements were also determined using the Laue back-reflection method. GGG single crystals were purchased from Hefei Kejing Materials Technology Co., Ltd.

Magnetic experiments

The magnetic properties of the LiREF4 single-crystal samples as well as the reference GGG single crystals were measured using a superconductor quantum interference device magnetometer (MPMS-XL, Quantum Design). Magnetic fields were applied along the magnetic easy and hard axes. The magnetic entropy changes ΔSm were calculated based on magnetic isotherms according to the Maxwell relationship41:

$$\triangle {S}_{m}\left(T,H\right)={\int }_{0}^{H}{\left(\frac{\partial M}{\partial T}\right)}_{H}{dH}=\,\frac{1}{{T}_{1}-{T}_{2}}\left[{\int }_{0}^{H}M\left({T}_{1},H\right){dH}-{\int }_{0}^{H}M\left({T}_{2},H\right){dH}\right]$$
(1)

Regarding the rotating MCE, the magnetic entropy change was defined as the difference in ΔSm when the magnetic fields are oriented along the hard and easy axes, as follows:

$$\triangle {S}_{r}=\triangle {S}_{H\parallel {{\mathrm{easy}}}}-\triangle {S}_{H\parallel {{\mathrm{hard}}}}$$
(2)

In this rotating process, the effective magnetic fields were increased, so \(\triangle {S}_{r} < 0\).

Direct measurement of the adiabatic temperature change

ΔTad of the LiREF4 single crystals were measured at the Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology. Pulsed high fields up to 250 kOe were generated by a long-pulse magnet with a duration of 80 ms, and the exact temperature was detected by a thin film RuO2 thermometer on the surface of the sample. At various base temperatures, Ts versus H curves of the LiREF4 single crystals were obtained under pulsed magnetic fields applied along the easy axis. ΔTad was calculated from Ts–H data by subtracting the corresponding initial base temperature35,36,41.