Excellent cryogenic magnetocaloric properties in heavy rare-earth based HRENiGa2 (HRE = Dy, Ho, or Er) compounds

RENiX2 compounds, where RE = rare-earth element and X = p-block element, have been highly regarded for cryogenic magnetocaloric applications. Depending on the elements, they can crystallize in CeNiSi2-type, NdNiGa2-type, or MgCuAl2-type crystal structures, showing different types of magnetic ordering and thus affect their magnetic properties. Regarding the magnetocaloric effect, MgCuAl2-type aluminides show larger values than those of the CeNiSi2-type silicides and the NdNiGa2-type gallides due to the favored ferromagnetic ground state. However, RENiGa2 gallides can crystallize in either NdNiGa2- or MgCuAl2-type structures depending on the RE element. In this work, we select heavy RE (HRE) elements for exploring the microstructure, magnetic ordering and magnetocaloric performance of HRENiGa2 (HRE = Dy, Ho or Er) gallides. They all crystallize in the desired MgCuAl2-type crystal structure which undergoes a second-order transition from ferro- to para-magnetic state with increasing temperature. The maximum isothermal entropy change (∣∆Sisomax∣) values are 6.2, 10.4, and 11.4 J kg−1 K−1 (0–5 T) for DyNiGa2, HoNiGa2, and ErNiGa2, respectively, which are comparable to many recently reported cryogenic magnetocaloric materials. Particularly, the excellent magnetocaloric properties of HoNiGa2 and ErNiGa2 compounds, including their composite, fall in the temperature range that enables them for the in-demand hydrogen liquefaction systems.


INTRODUCTION
Cooling technology has become an indispensable application in our modern society, in which the choice of optimal refrigeration technologies needs to be driven by environmental compatibility and energy efficiency. Regarding these aspects, the magnetic refrigeration (MR) technology based on the magnetocaloric effect (MCE), is expected to become a highly competitive cooling method due to its high-energy efficiency and the absence of hazardous and ozone-depleting gases in comparison to the conventional vapor-compression refrigeration [1][2][3][4][5][6]. The MCE is an inherent magneto-thermodynamic phenomenon that occurs in magnetic materials upon changing the external magnetic field, which is significant at temperatures close to the thermomagnetic phase transitions. It is characterized by an isothermal magnetic entropy change (ΔS iso ) and an adiabatic temperature change (ΔT ad ). By using a large variety of magnetic materials and different thermodynamic cycles, MR can operate in a very wide temperature range (from extremely low temperatures up to room temperature) [7][8][9][10][11][12][13][14][15][16][17]. In recent years, lowtemperature MR has received extensive attention due to its important applications, such as industrial gas liquefaction and storage, cryogenic space technology, and laboratory cryogenic basic research [18][19][20][21][22][23][24][25]. Liquid H 2 is a clean fuel that is widely used in the aerospace field and is expected to extend its use towards conventional applications. Moreover, for H 2 storage and transportation, the liquid state is more advantageous than the gaseous H 2 . Regarding the liquefaction processes, the efficiency of magnetic systems could reach 60% of the theoretical Carnot cycle, which is 50% higher than the actual ones of gas compression systems [26].
For these reasons, exploring MCE materials with excellent performance in the low-temperature range is of great interest. Specifically, it has been reported that several heavy rare-earth (HRE)-transition metal (TM) intermetallic compounds can be considered potential candidates for cryogenic MR materials for H 2 liquefaction [27][28][29][30][31][32][33]. This is due to the large total orbital quantum numbers (J) of HRE elements, which lead to large magnetic moments that are beneficial to the magnetocaloric properties. Recently, ternary intermetallic compounds, HRE-TM-X (X = p-block elements) with the stoichiometric ratio of 1:1:2, have received extensive attention for their diverse crystal structure and unique magnetic properties [34][35][36][37][38][39][40][41][42][43][44][45][46][47]. Their magnetic phase transition and magnetocaloric properties can be varied depending on the TM and p-block elements. For TM = Ni and X = Al, the samples crystallize in the orthorhombic MgCuAl 2 -type structure, presenting ferromagnetic (FM) order at low temperatures (Curie temperature (T C ) ranges around 2.4-28.0 K) [39][40][41]. For X = Si, the compounds crystallize in the CeNiSi 2 -type structure, revealing antiferromagnetic order at low temperatures (Néel temperature ranges around 3.0-25.0 K) [44]. When X = Ga, depending on the RE element, two different types of crystal structures have been reported [46]: NdNiGa 2 -type for RE = La-Nd, Sm or Gd and MgCuAl 2 -type for RE = Y or Tb-Lu.
For the former structure, CeNiGa 2 and GdNiGa 2 were reported to show antiferromagnetic ordering at 4 and 22 K, respectively, and both direct and inverse MCE were observed in these two samples [48,49]. On the other hand, for MgCuAl 2 -type gallides, although their MCE properties have not been reported, the isostructural aluminides exhibit excellent direct MCE in low temperature range, making it of interest to investigate the magnetocaloric behavior and properties of MgCuAl 2 -type gallides. Hence, in this work, with the aim of obtaining suitable materials for cryogenic applications, we vary the type of HRE elements in the HRENiGa 2 system (HRE = Dy, Ho, or Er) and investigate their influence on the structural, thermomagnetic, and magnetocaloric behavior.

EXPERIMENTAL SECTION
A series of polycrystalline samples were fabricated by arc-melting from high-purity (at least 99.9%) elements in an Ar atmosphere with a nominal composition of HRENiGa 2 (HRE = Dy, Ho, or Er). An excess of 2 wt% of HRE elements was used to compensate for the losses caused by volatilization during the arc-melting process. The obtained ingots were wrapped in the Ta foil and sealed in a quartz tube for annealing. The annealing process was performed in a muffle furnace at 1073 K for one week, and then quenched in ice water. The phase and crystal structure analysis of the HRENiGa 2 was performed by X-ray diffraction (XRD) using a Bruker D8 diffractometer (Cu-Kα radiation). The magnetization data of the HRENiGa 2 were collected using the Vibrating Sample Magnetometer (VSM) option of the physical properties measurement system (PPMS-9). Fig. 1a displays the powder XRD as well as the Rietveld refinement results for DyNiGa 2 , HoNiGa 2 , and ErNiGa 2 compounds. Both DyNiGa 2 and HoNiGa 2 samples are single-phase crystallizing in the orthorhombic MgCuAl 2 -type structure (Cmcm space group). While for ErNiGa 2 , extra diffraction peaks corre-sponding to the Er 2 O 3 phase (~1.0 wt%) are detected. The refined factors (included in Fig. 1a) reveal a good agreement between the structural model and the experimental data, being the weighted profile R factor (R wp ) of~10% and a goodness of fit (GoF) of 1.5-1.9 [50]. The refined lattice parameters a and c are shown in Fig. 1b. It is worth noting that the lattice parameters decrease monotonically with the decrease of RE ion radius. A schematic of the crystal structure for HRENiGa 2 is included in Fig. 1c. HRE and Ni atoms occupy the same Wyckoff sites of 4c with the m2m point symmetry, whereas Ga occupies the 8f sites with the m.. point symmetry.

RESULTS AND DISCUSSION
The temperature dependence of magnetization (M) and reciprocal susceptibility (1/χ) at μ 0 H = 1 T for HRENiGa 2 are shown in Fig. 2a. From the M-T curves, all samples undergo a gradual magnetic transition from FM to paramagnetic (PM) states. The T C can be estimated by the derivative of M-T curves (dM/dT-T curves) under the field of 0.01 T, which are also shown in Fig. 2b. The corresponding temperatures of the inflection points are 46.0, 26.0, and 11.0 K for DyNiGa 2 , HoNiGa 2 , and ErNiGa 2 compounds, respectively. According to the Ruderman-Kittel-Kasuya-Yosida (RKKY) indirect interaction theory [51], the T C for RE-based compounds will be expected to be proportional to the de Gennes factor (dG). This factor is determined by the Lande factor (g) and the total orbital quantum number (J): The relationship between T C and dG for the samples is shown in the inset of Fig. 2b. As expected, a positive linear trend is observed, revealing the dominant role of RE-RE long-range interaction, which is consistent with previously reported data [46]. A linear trend is observed from the 1/χ-T curves (Fig. 2a), indicating that all the samples obey the Curie-Weiss law in the PM region: P where θ P is the PM Curie temperature and C is the Curie con-

SCIENCE CHINA Materials
stant which can be expressed by the following formula:  [51]. This shows that the RE elements play a major magnetic contribution in these compounds. In addition, the θ P is determined from the intercept of the fittings with the temperature axis, obtaining 29.3, 11.4, and 7.5 K for DyNiGa 2 , HoNiGa 2 , and ErNiGa 2 , respectively. The positive values of θ P prove the FM ground state in the studied series. For exploring the magnetocaloric performance of these compounds, magnetization isotherms were measured at different temperatures around T C (displayed in Fig. 3). It is observed that all samples show FM characteristic at low temperatures (T < T C ) whereas PM characteristic at high temperatures (T > T C ), in agreement with the previous M-T results. In addition, M(H) loops measured for the three samples show negligible magnetic hysteresis (coercivity values of 30 mT for DyNiGa 2 , 20 mT for HoNiGa 2 and 10 mT for ErNiGa 2 ). Using these isothermal magnetization curves, the isothermal entropy change (ΔS iso ) can be indirectly determined based on thermodynamic Maxwell relations from: H H iso 0 0 The calculated |ΔS iso | values versus temperature for the studied compounds are plotted in Fig. 4a-c under several selected magnetic field changes (ΔH). For all the compounds, the values of |ΔS iso | gradually increase as ΔH increases. For ΔH of 0-5 T, the maximum |ΔS iso | values (|ΔS iso max |) and their corresponding peak temperatures (T peak ) are found to be 6.2 J kg −1 K −1 and 41.5 K, 10.4 J kg −1 K −1 and 24.5 K, as well as 11.4 J kg −1 K −1 and 12.0 K for Dy-, Ho-, and Er-containing samples, respectively. It is highlighted that in the case of the Ho-containing compound, the magnetocaloric response is within the range of the H 2 liquefaction temperature (20.4 K). For the Er-containing sample, its T peak shifts to higher temperatures gradually with increasing external field in contrast to DyNiGa 2 and HoNiGa 2 whose T peak remains unaffected with fields. This can be ascribed to the

ARTICLES
critical exponents deviating from mean field for ErNiGa 2 [52]. When ΔH increases to 0-7 T, the T peak value obtained for ErNiGa 2 is 18 K, which is close to the H 2 liquefaction temperature.
To quantify the cooling efficiency of the compounds, the relative cooling power (RCP) is calculated by the following equation: where δT FWHM is the full temperature width at a half maximum of the |ΔS iso | peak. For 0-5 T, the RCP values are 275 J kg −1 for DyNiGa 2 , 302 J kg −1 for HoNiGa 2 , as well as 238 J kg −1 for ErNiGa 2 , respectively. Additionally, the values of δT FWHM are 44.6, 29.1, and 20.9 K for Dy-, Ho-, and Er-containing samples, respectively.
Griffith et al. [53] proposed the temperature-averaged magnetic entropy change (TEC) as another figure of merit to evaluate the magnetocaloric performance of the materials. For a given temperature span (ΔT lift ), the TEC(ΔT lift ) can be estimated using the following formula:  Fig. 4d. This indicates that the compounds can properly operate as magnetic refrigerant (e.g., in active magnetic regenerator (AMR) cycles) with a working span of 5 K with performance close to their maximums.
It can be observed that while the maximum MC response of HoNiGa 2 compound is slightly above the H 2 liquefaction temperature, that of ErNiGa 2 is slightly below. Therefore, it is worth studying the existence of a composite material based on both HoNiGa 2 and ErNiGa 2 , which would operate in a broad temperature range around the desired H 2 liquefaction temperature. Moreover, composites with two or more phases were found to be helpful in obtaining table-like MCE which is required for an ideal Ericsson cycle [27,[54][55][56][57]. To explore this, we estimate the total values of |ΔS iso | and TEC(ΔT lift = 10, 15, and 20 K) under ΔH of 0-5 T for the xHoNiGa 2 + (1−x)ErNiGa 2 composite (where x is the mass fraction of the HoNiGa 2 compound in the composite, being 0 ≤x ≤ 1). This magnitude is selected as it is equivalent to the average value of magnetic entropy change over a wide temperature range (i.e., ∆T lift ), which is more representative for MCE performance evaluation. We found an optimal table-like MCE for x = 0.5 composite, having an isothermal entropy change of 8.7 J kg −1 K −1 with the temperature range of 11-25 K as presented in Fig. 5a, showing the potential of this composite for Ericsson cycle MR. Fig. 5b displays the |ΔS iso max | and TEC values as a function of the composite composition. It can be observed that the TEC values for 10, 15, and 20 K working span for x = 0.5 and 0.6 composites are much closer to  As MCE response is linked to the nature of magnetic transitions, it is thus important to determine the order of phase transitions for practical applications mainly to take into account the reversibility of the response. To confirm the nature of magnetic transitions, the Arrott plots (i.e., M 2 versus H/M curves) were constructed by applying the Banerjee's criterion [58] (Fig. 6a-c). It can be inferred that the three compounds undergo a second-order phase transition (SOPT) since all isotherms show positive slopes, according to the Banerjee's criterion.
In addition, Franco et al. [52] have introduced a criterion that a universal curve could be achieved for magnetocaloric materials undergoing SOPT upon rescaling the ΔS iso vs. T curves for different ΔH. For the universal curve construction, the magnetic entropy change axis and temperature axis were changed to ΔS iso (T)/ΔS iso max and θ, respectively, where θ was defined independently below and above T C as follows:

T T T T T T T T T T T T
where T r1 and T r2 (T r1 < T C < T r2 ) denote two reference temperatures and their corresponding ΔS iso (T r1 )/ΔS iso max = ΔS iso (T r2 )/ ΔS iso max = 0.6. Fig. 6d-f present the normalized ΔS iso (T)/ΔS iso max vs. θ curves for the DyNiGa 2 , HoNiGa 2 , and ErNiGa 2 compounds, respectively. It can be observed that all rescaled curves are unaffected by the magnetic field and collapse onto a universal curve, revealing the SOPT nature for the three studied samples. These results are in excellent agreement to those of the Banerjee's criterion. Fig. 7 displays the |ΔS iso max | and RCP values of the studied samples and their T t indicated by the color legend. For comparison, other RETMX 2 systems and some recently reported cryogenic materials falling in the range of the H 2 liquefaction temperature have been included. It can be seen that the magnetocaloric parameters of our studied MgCuAl 2 -type gallides are much larger than those of the NdNiGa 2 -type ones, which can be attributed to the favored FM ground state. In addition, the present samples also show competitive cooling efficiency com-pared with the isostructural MgCuAl 2 -type aluminides, CeNiSi 2type silicides, and some other materials, making them potential candidates for cryogenic applications.

CONCLUSIONS
HRENiGa 2 series (with HRE = Dy, Ho, and Er) crystallizing in the MgCuAl 2 -type crystal structure were successfully synthesized by arc melting. Rietveld refinement results show that all the samples are almost single-phase (99 wt% of the main phase). All three compounds undergo an FM-PM magnetic phase transition at low temperatures, around 46.0, 26.0, and 11.0 K for Dy-, Ho-, and Er-containing samples, respectively. The second order nature of the magnetic phase transitions was verified by the Banerjee's criterion and magnetocaloric universal curve method. Regarding the magnetocaloric response, the maximum |ΔS iso | values for 0-5 T are 6.2, 10.4, and 11.4 J kg −1 K −1 for Dy, Ho, and Er, respectively. The temperature span of these responses, quantified by δT FWHM values, are 44.6 K for DyNiGa 2 , 29.1 K for HoNiGa 2 , and 20.9 K for ErNiGa 2 , showing good cooling performance in a broad temperature range. This has also been checked by the TEC(5) parameter, which shows values rather close to their maximum capabilities (around 99%-97%). For HoNiGa 2 and ErNiGa 2 compounds, their peak temperatures of maximum isothermal entropy changes are close to the H 2 liquefaction temperature, making them of great value for magnetocaloric liquefaction systems. Moreover, we illustrate the excellent magnetocaloric performance of a hypothetical HoNi-Ga 2 and ErNiGa 2 composite which would exhibit a notable tablelike MCE in a broad temperature range around the desired H 2 liquefaction temperature (8.7 J kg −1 K −1 around 11-25 K).  Magnetocaloric parameters (|ΔS iso max | and RCP) for the HRENiGa 2 compounds compared with other RETX 2 systems [34,41,44,48,49] and some recently reported cryogenic materials [59][60][61] for 0-5 T. The color legend on the right indicates the different T t for each sample.