First- and second-order phase transitions in RE6Co2Ga (RE = Ho, Dy or Gd) cryogenic magnetocaloric materials

link.springer.com link.springer.com Published online 16 August 2021 | https://doi.org/10.1007/s40843-021-1711-5 Sci China Mater 2021, 64(11): 2846–2857 First- and second-order phase transitions in RE6Co2Ga (RE = Ho, Dy or Gd) cryogenic magnetocaloric materials Dan Guo1,2, Luis M. Moreno-Ramírez2, Carlos Romero-Muñiz3,4, Yikun Zhang1*, Jia-Yan Law2*, Victorino Franco2, Jiang Wang1and Zhongming Ren1 ABSTRACT Rare-earth (RE) rich intermetallics crystallizing in orthorhombic Ho6Co2Ga-type crystal structure exhibit peculiar magnetic properties that are not widely reported for their magnetic ordering, order of magnetic phase transition, and related magnetocaloric behavior. By tuning the type of RE element in RE6Co2Ga (RE = Ho, Dy or Gd) compounds, metamagnetic anti-to-paramagnetic (AF to PM) phase transitions could be tuned to ferro-to-paramagnetic (FM to PM) phase transitions. Furthermore, the FM ground state for Gd6Co2Ga is confirmed by density functional theory calculations in addition to experimental observations. The field dependence magnetocaloric and Banerjee’s criteria demonstrate that Ho6Co2Ga and Dy6Co2Ga undergo a first-order phase transition in addition to a second-order phase transition, whereas only the latter is observed for Gd6Co2Ga. The two extreme alloys of the series, Ho6Co2Ga and Gd6Co2Ga, show maximum isothermal entropy change (|ΔSiso max(5 T)|) of 10.1 and 9.1 J kg−1 K−1 at 26 and 75 K, close to H2and N2liquefac- tion, respectively. This outstanding magnetocaloric effect performance makes the RE6Co2Ga series of potential for cryogenic magnetic refrigeration applications. Keywords: RE6Co2Ga compounds, magnetic phase transitions, magnetocaloric effect, rare-earth INTRODUCTION The pursuit of energy conservation and environmental protection has become the mainstream of modern society. The vapor-compression refrigeration, a widely used technology in transportation, and residential, commercial, and industrial refrigeration, can no longer meet the current development needs due to its low efficiency, adverse environmental impact, and noise of the compressor. Several researchers have shifted their focus to magnetic refrigeration (MR) based on the magnetocaloric effect (MCE) of magnetic materials due to their distinguished performance without relying on any hazardous or ozonedepleting refrigerant gas and noise-free advantage [1–7]. The use of natural gas as well as H2, He, N2, and O2, is widely extended with several scientific, industrial, and commercial purposes. Moreover, their consumption is expected to increase in future years. For better gas storage and transport, gas liquefaction is required despite being a complex process [8]. In recent years, it has been shown that MR technology could overcome some of the issues related to conventional methods [9,10]. Therefore, it is of significance to search for MCE materials suitable for cryogenic MR applications. The performance of MCE materials can be evaluated by the magnetic entropy change in an isothermal process (ΔSiso) and/or temperature change in an adiabatic process (ΔTad), which are correlated to thermomagnetic phase transitions of the materials. In general, MCE materials are classified into the order of thermomagnetic phase transitions they undergo. For those undergoing first-order phase transition (FOPT), they usually exhibit large ΔSiso values, but their accompanying thermal and magnetic hystereses can affect their cyclicality. On the other hand, for those exhibiting 1State Key Laboratory of Advanced Special Steels, Shanghai Key Laboratory of Advanced Ferrometallurgy, School of Materials Science and Engineering, Shanghai University, Shanghai 200072, China 2Departamento de Física de la Materia Condensada, ICMS-CSIC, Universidad de Sevilla, P.O. Box 1065, Sevilla 41080, Spain 3Department of Physical, Chemical and Natural Systems, Universidad Pablo de Olavide, Sevilla E-41013, Spain 4Departamento de Física Aplicada I, Universidad de Sevilla, Sevilla E-41012, Spain *Corresponding authors (emails: [email protected] (Zhang Y); [email protected] (Law JY)) ARTICLES SCIENCE CHINA Materials 2846 November 2021 | Vol.64 No.11 © The Author(s) 2021. This article is published with open access at link.springer.com. second-order phase transition (SOPT), while they exhibit no hysteresis, their ΔSiso values may be lower than those of FOPT materials [11–13]. In the past decade, a large number of MCE materials have been reported [14–20], among which rare-earth (RE) based alloys show great significance for MR applications at cryogenic temperatures. In particular, those crystallizing in orthorhombic Ho6Co2Ga-type structures (space group Immm) could exhibit both inverse (positive ΔSiso under magnetization process) and direct MCE (negative ΔSiso under magnetization process) despite showing peculiar and complex magnetic behavior [21–36]. For example, S-shaped curves of magnetization versus magnetic field M(H) were reported for RE6Cox(Al/Sn)y(x= 2.2–2.5 and y= 0.5–0.8), whereby all of them adopted the Ho6Co2Ga-type structure [21–23]. Inverse and direct MCE were then reported for isostructural Dy6Co2.5Sn0.5 [21] and RE6Co2.2Al0.8 (RE = Dy or Tb) [22], in which authors suggested that the magnetic ordering of Ho6Co2- Ga-type compounds is determined by the orthorhombically distorted octahedral RE sublattice, which in turn can yield similar magnetic structure and properties for such compounds despite their selection for the elements. Overall, these investigations centered on using compositions that can crystallize into orthorhombic Ho6Co2Ga- type structure; nevertheless, the studies on nominal RE6Co2Ga compositions, which are directly adopted from the structure itself, are less reported [24,25] and mainly on their crystal structures while their thermomagnetic and MCE properties have not been explored. Hence, in this paper, we aim to systematically investigate the influence of various RE elements on the structures, thermomagnetic phase transitions, and magnetocaloric properties of RE6Co2Ga-type compounds by changing RE from Ho to Dy and Gd. Using the recently developed criterion based on MCE [37] and the conventional Banerjee’s criterion [38], we report the nature of the order of magnetic phase transition undergone by these compounds. It is found that the Ho- and Dy-con- taining compounds exhibit low-temperature FOPT while the Gd-containing one exhibits SOPT. Density functional theory (DFT) calculations are performed for these compounds, further supporting the magnetic ordering observed from the experimental results. EXPERIMENTAL AND SIMULATION DETAILS Polycrystalline samples with nominal compositions of RE6Co2Ga (RE = Ho, Dy or Gd) were synthesized by arc melting from raw pure materials RE (99.9 %), Co (99.9 %) and Ga (99.999 %) in an argon atmosphere. Since RE elements could be easily volatilized during melting, 2 wt.% excess was added to ensure the nominal stoichiometry. The ingots were re-melted four times for good compositional homogeneity. They were sealed in a quartz tube filled with argon and then annealed in a muffle furnace at 600°C for seven days, followed by quenching with ice water. X-ray diffraction (XRD) patterns of the samples at room temperature were collected by a Bruker D8 diffractometer (Cu-Kα radiation) for studying their microstructures. Magnetization measurements were carried out using the vibrating sample magnetometer (VSM) option of the physical properties measurement system (PPMS-9). ΔSiso, one of the parameters to quantify the MCE of materials, was indirectly determined from the measured magnetic isotherms using thermodynamic Maxwell relation: S T H µ M T H TH( , ) = ( , ) d , (1) H H iso 0 0 where M,H, and Trepresent the magnetization, magnetic field, and temperature, respectively. In order to investigate the order of the phase transition by the novel MCE criterion, the field-dependent exponent of ΔSiso, was calculated from the following formula [37]: n T H S H ( , ) = dln dln . (2) iso In addition, DFT calculations were performed for unveiling the magnetic behavior of RE6Co2Ga compounds, whereby we exclusively focused on Gd6Co2Ga as the latest and the most sophisticated DFT methods are limited in accurately describing the complex magnetic behavior of some RE elements, such as Ho and Dy. For this purpose, we employed the standard Vienna Ab-initio Simulation Package (VASP) 5.4.1 [39], using plane waves to reproduce the one-electron wave functions with a kinetic energy cutoff of 400 eV for constructing the basis set and projected augmented wave pseudopotentials [40,41] for all the species involved. In particular, the valence electrons excluded in the pseudopotentials were 3d84s1(9) in Co, 4s24p1(3) in Ga and 5s25p64f75d16s2(18) in Gd. Thus, the f electrons of Gd were explicitly considered to properly describe its magnetism. The electronic exchange and correlation were modeled using a hybrid functional, namely the HSE06, which contained 25% of exact Hartree-Fock as exchange, following the implementation of the VASP code [42,43]. As a start, the standard Perdew- Burke-Ernzerhof (PBE) functional [44] was used but it was later found insufficient for such a complex system. In particular, it failed when resolving the on-site magnetism SCIENCE CHINA Materials ARTICLES November 2021 | Vol.64 No.11 2847 © The Author(s) 2021. This article is published with open access at link.springer.com. of the compound. As spin polarization was required for all calculations, we used the Vosko-Wilk-Nusair interpolation [45] for this task. Using the geometry provided by XRD data [24] for the analysis of the compound, structural optimizations using a conjugate gradient algorithm, sampling the reciprocal space with a 4 × 4 × 4 Monkhorst-pack grid, were performed until forces upon atoms were smaller than 0.01 eV Å−1, and each self-consistent electronic loop converged to a tolerance better than 10−4eV [46]. At PBE level, the obtained structure remains very similar to the experimental configuration with minimal displacement in atomic coordinates (only up to 0.1 Å in the worse scenario). This relaxed structure was further analyzed using the HSE06 hybrid functional. In all cases, we deal with a primitive 18-atom cell, which corresponds to a Niggli reduced cell. This is a quasi-rhombohedral unit cell (with a= 8.323Å, α= 107.25°, β= 109.96°, and γ= 111.23°) generated using the VESTA software [47]. It possesses a unit cell volume and a number of atoms that are small enough to allow calculations with hybrid functionals despite the high proportion of RE metals. Even in that case, we had to reduce the k-point grid to a 2 × 2 × 2 mesh due to the enormous computational demand. RESULTS AND DISCUSSION Crystal structure XRD patterns for the RE6Co2Ga (RE = Ho, Dy or Gd) series at room temperature and their corresponding Rietveld refinement results are shown in Fig. 1. The results show that all the samples successfully crystallize into a single phase Ho6Co2Ga-type structure. Details of the refined lattice parameters and the refinement factors are tabulated in Table 1, which shows that the cell volume and lattice parameters increase as RE changes from Ho to Dy and Gd. The ccell parameter for Dy6Co2Ga (9.8153 Å) is smaller than those for Dy6Co2.5Sn0.5 (9.8754 Å) and Dy6Co2Al (9.9265 Å), which is in line with Ref. [22] whereby authors predicted that lattice parameter cincreases from Ga to Sn and Al in RE6Co2X compounds. Fig. 2a and b illustrate the detailed crystal structures of the RE6Co2Ga compounds and the atomic environments of RE1, RE2, RE3, Co1, Co2, Ga1, and Ga2 sites. The Wyckoff sites of RE1, RE2, RE3 atoms are 8l, 8m, and 8n with the ..m, .m., and m.. point symmetry, respectively. Co1 and Co2 atoms occupy the Wyckoff sites of 4iand 4h with the mm2 and m2mpoint symmetry, respectively. Ga1 occupies the 2bsites with the mmm point symmetry and Ga2 occupies the 2dsites with the mmm point symmetry. Magnetic properties Fig. 3 displays the M(T) curves and their reciprocal susceptibility (1/χ=H/M) under a magnetic field of 0.5 T. Ho6Co2Ga (Fig. 3a) shows a magnetic phase transition from antiferromagnetic to paramagnetic (AF to PM) at around 16K and a plateau at 16–25 K, followed by a paramagnetic behavior. For Dy6Co2Ga in Fig. 3b, a phase transition from AF to PM is noticed at ~47 K, with the subsequent paramagnetic behavior at higher temperatures. Gd6Co2Ga shows three consecutive features at around 55, 78, and 129 K (pointed by the arrows), indicating three thermomagnetic phase transitions (Fig. 3c). The effective magnetic moment values (μeff) and paramagnetic Curie temperature (θP) were deduced by the fittings of the linear part of the 1/χ-Tplots, yielding: Figure 1 The XRD patterns and their corresponding Rietveld refinements for Ho6Co2Ga (a), Dy6Co2Ga (b), and Gd6Co2Ga (c). ARTICLES SCIENCE CHINA Materials 2848 November 2021 | Vol.64 No.11 © The Author(s) 2021. This article is published with open access at link.springer.com. μeff/f.u. = 29.105 ± 0.006 μB, 29.629 ± 0.007 μB, and 21.635 ± 0.020 μBfor Ho6Co2Ga, Dy6Co2Ga, and Gd6Co2Ga, respectively.Assuming the effective magnetic moment of Co atoms is 1.8 μB, the effective magnetic moment per RE atom for all three compounds can be calculated from µ µ µ= 6 × (RE) + 2 × (Co) eff eff 2 eff 2 , resulting in μeff(Ho) = 11.837 ± 0.002 μB,μeff(Dy) = 12.051 ± 0.003 μBand μeff(Gd) = 8.771 ± 0.008 μB. The calculated θPvalues are ~1.5, ~3.2, and ~99.1K for Ho6Co2Ga, Dy6Co2Ga, and Gd6Co2Ga, respectively. In the cases of Ho6Co2Ga and Dy6Co2Ga, the θPvalues are close to zero, which indicates that there are almost no ferromagnetic (FM) interactions in PM regions. The zero-field-cooled (ZFC) and field-cooled (FC) M(T) curves for H= 0.05 T of Ho6Co2Ga, Dy6Co2Ga, and Gd6Co2Ga are shown in Fig. S1. A small splitting in FC and ZFC M(T) curves for Gd6Co2Ga and Dy6Co2Ga is detected at low temperatures, which could probably be due to the domain wall pinning effects [48]. At higher temperatures, the ZFC and FC curves are well overlapped with each other for all the compounds, demonstrating no thermal hysteresis during their magnetic phase transitions. Such absence/negligible thermal hysteresis even in the first-order transformations for RE-based alloys makes these materials highly interesting from a technical point of view [49–51]. Fig. 4 displays the field dependence of magnetization measured at 3 K. Weak magnetic hysteresis can be observed in Ho6Co2Ga and Dy6Co2Ga, which is common in FOPT materials. For Gd6Co2Ga, there is no hysteresis, which is beneficial to practical applications. It can be seen Table 1 Refined lattice parameters and refinement factors for RE6Co2Ga compounds Parameter a(Å) b(Å) c(Å) V(Å3)α(˚)β(˚)γ(˚)Rp(%) Rwp (%) Rexp (%) χ2 Ho6Co2Ga 9.2710 9.4078 9.8153 856.09 90 90 90 5.59 7.07 6.03 1.37 Dy6Co2Ga 9.2891 9.4654 9.8439 865.53 90 90 90 7.48 9.48 8.79 1.16 Gd6Co2Ga 9.3863 9.5968 9.9799 898.97 90 90 90 8.46 10.9 9.75 1.25 Figure 2 (a) The crystal structures of RE6Co2Ga compounds; (b) atomic environments of RE1, RE2, RE3, Co1, Co2, Ga1, and Ga2 sites. SCIENCE CHINA Materials ARTICLES November 2021 | Vol.64 No.11 2849 © The Author(s) 2021. This article is published with open access at link.springer.com. that the magnetization isotherms for Ho6Co2Ga and Dy6Co2Ga compounds show a significant increase for certain applied magnetic fields (fields between 2 and 4.5 T for Ho6Co2Ga and Dy6Co2Ga, respectively), indicating the existence of metamagnetic transitions. This is in agreement with the S-shaped M(H) curves previously reported for isostructural Dy6Co2Al and Er6Co2Al compounds [23]. On the other hand, for Gd6Co2Ga, the M(H) shape indicates the FM character at 3 K. In addition to experimental observations, DFT calculations enable the determination of the distribution of the magnetic moments in Gd6Co2Ga by using hybrid functional (the standard generalized gradient approximation fails to describe this issue). In particular, a reasonable geometry very similar to the experimental result is successfully obtained from the calculations using the PBE functional, which suggests a strong FM ground state, or at least, a configuration with a high total magnetic moment. However, if we try to resolve the on-site magnetism, this simple approximation does not lead to a reasonable value for the magnetic moments of Gd atoms, being too small compared with the experimental observations. In addition, the spin moments associated with the Co atoms get unstable, assuming that they have some magnetic moments that are ferro- or antiferromagnetically coupled to the RE elements in the compound. Conversely, more advance functionals, such as the HSE06, which includes 25% of exact Hartree-Fock exchange, could properly reproduce the magnetic behavior of complex Gd6Co2Ga compound. Namely, we confirm that the magnetic ground state of Gd6Co2Ga corresponds to a state in which all Gd atoms have a strong magnetic moment of about 7.5 μB, pointing in the same direction whereas Co atoms couple in the opposite direction with a magnetic moment of around 1.8 μB. No magnetic moment is observed for Ga atoms. Only a minimal difference among Gd atoms belonging to different Wyckoff sites is found: the exact values are 7.49–7.51 μB(8l), 7.64–7.65 μB(8m), and 7.47 μB(8n). The same trend is also observed for Co atoms, whose magnetic moments are within the range of 1.77–1.78 μB. We have also calculated the spin-resolved projected density of states of the different species present in the Gd6Co2Ga compound as shown in Fig. 5. The strong magnetic moments observed for Gd atoms are reflected in their densities of states as strong localized states, mainly appearing around −4 eV spin up below the Fermi level. These states arise from the Gd f orbitals, resembling the fingerprint of the FM phase of pure Gd [52]. In the cases of Ho and Dy in RE6Co2Ga compounds, it is not possible to assume any trivial magnetic moment distribution for the constituent atoms that can be compatible with the experimental magnetic moments of RE Figure 3 Temperature dependence of magnetization (left-axis) and reciprocal susceptibility (right-axis) under a field of 0.5 T for Ho6Co2Ga (a), Dy6Co2Ga (b), and Gd6Co2Ga (c). Figure 4 The field dependence of magnetization measured at 3 K. ARTICLES SCIENCE CHINA Materials 2850 November 2021 | Vol.64 No.11 © The Author(s) 2021. This article is published with open access at link.springer.com. atoms. This suggests that the magnetic behavior of these two compounds is much more complex than the case of Gd, which could likely involve non-collinear behavior as reported in other isostructural compounds, such as Tb6Co2.2Al0.8 and Er6Ni2Sn [22,36]. The calculated total magnetic moment of Gd6Co2Ga lies between 41–45 μBper f.u., in good agreement with the experimental saturation magnetization values (43.35 μBper f.u. for Gd6Co2Ga at 7T obtained from Fig. 4). It is worth noting that the estimated value is 45 μBper f.u., while the summation over the individual contributions of the constituent atoms leads to 41.6 μBper f.u. The first estimation is supposed to be a more accurate value for the total magnetic moment. A large number of possible magnetic configurations as starting guesses for the electronic self-consistency calculation were performed but only two stable configurations were obtained. One is described above, and the second stable configuration is with the total FM solution, which is less energetically favorable. Other explored configurations include possible AFM couplings among Gd atoms belonging to different crystallographic sites, but none of them remain stable. It is interesting to note that the 18- atom primitive cell could still contain an even number for all species in all Wyckoff sites, which is a useful condition needed to properly study possible FM or AFM configurations. We did not find any other stable solution considering AFM couplings among Gd atoms. A similar analysis was also made at PBE level, without finding any reasonable conclusion. Overall, the results of DFT calculations are in good agreement with the experimental observations of Gd6Co2Ga. DFT reveals that the compound exhibits a relatively simple magnetic moment distribution (i.e., parallel Gd atoms with the FM ground state), which agrees with the significant and positive θPvalue (~99.1 K) of Gd6Co2Ga. Furthermore, the effective magnetic moment of Gd atoms determined by DFT and experimental results is in reasonable agreement with the theoretical value (7.94 μB). MCE and the order of phase transitions Fig. 6a–c show the isothermal M(H) curves used for calculating ΔSiso (shown in Fig. 6d–f) for the three studied compounds. Ho6Co2Ga and Dy6Co2Ga show inverse MCE at low temperatures while their direct MCE are at higher temperatures. In the case of Gd6Co2Ga compound, three direct MCE peaks (57, 75, and 131 K) are found in its ΔSiso(T) curves (being more visible for low magnetic field changes as shown in the inset of Fig. 6f), which correspond to the three phase transitions previously observed in Fig. 3. The most prominent magnetocaloric peak is the one at 75K. These observations are in agreement with the MCE reports of isostructural compounds, where inverse and direct MCE are found for Dy6Co2.2Al0.8 and Dy6Co2.5Sn0.5 and three observed transitions are in Gd6Co2.2Al0.8 [21,22]. It is worth noting that for low temperatures there is a change of sign for ΔSiso. More detailed studies are needed to identify the origin of that feature. The maximum values of |ΔSiso| under ΔHof 0–7 T are 15.8, 4.8, and 12.6 J kg−1K−1for Ho6Co2Ga, Dy6Co2Ga, and Gd6Co2Ga, respectively. It is worth highlighting that the peak temperatures of |ΔSiso| for the Ho6Co2Ga and Gd6Co2Ga compounds, 26 and 75 K, respectively, coincide with the desired range for H2and N2 liquefaction. To check the effect of the demagnetizing field on ΔSiso, we considered a demagnetizing factor (N) of 1/3 due to the shape of our samples. The maximum values of isothermal entropy change (ΔSisomax) as a function of the applied field (Hap) and the internal field (Hint = Hap −NM) for all the compounds are plotted in Fig. S2. Very minor difference can be observed when considering the applied or the internal magnetic field, indicating that the effect of the demagnetizing field can be neglected for the studied samples. The temperature-averaged magnetic entropy change (TEC), an appropriate parameter to evaluate the MCE materials, has been introduced by Griffith et al.[53] and can be calculated by the following equation: Figure 5 Spin-resolved projected density of states of each species (colored curves) and total density of states (black dotted curve) in Gd6Co2Ga calculated with DFT. The contributions of Co (blue) and Ga (red) have been multiplied by a factor to enhance visualization, since their contributions are very small. Contributions arising from the three different Gd sites of the crystal structure (green curves) are plotted together with the total Gd contribution. SCIENCE CHINA Materials ARTICLES November 2021 | Vol.64 No.11 2851 © The Author(s) 2021. This article is published with open access at link.springer.com. TT S T T TEC( ) = 1 max ( ) d , (3) TT T T T H T lift lift 2 +2, mid mid lift mid lift where ΔTlift is temperature span and Tmid is the central temperature whereby the TEC (ΔTlift) gets the maximum value for the given ΔTlift. The values of TEC (10) (ΔTlift = 10 K) under field change of 0–7 T are 14.9 J kg−1K−1for Ho6Co2Ga, 4.7 J kg−1K−1for Dy6Co2Ga and 12.5 J kg−1K−1 for Gd6Co2Ga, which are close to those of |ΔSisomax|. Another magnetocaloric parameter for a figure of merit is the relative cooling power (RCP), which is used to evaluate the cooling efficiency of MCE materials. It can be calculated by the following formula: S TRCP = × , (4) iso max FWHM where δTFWHM is the full width at half maximum of |ΔSiso|. The calculated values of RCP under ΔHof 0–7T are 532.6Jkg−1for Ho6Co2Ga, 256.9 J kg−1for Dy6Co2Ga, and 945.3 J kg−1for Gd6Co2Ga. Due to the three continuous phase transitions in Gd6Co2Ga, its refrigerant capacity is significantly higher than those of RE-based compounds reported in the literature. For comparison, the values of |ΔSiso max| and RCP of the studied RE6Co2Ga (RE = Ho, Dy or Gd) series versus those of other isostructural and promising RE-based magnetocaloric materials under a field change of 0–5 T are listed in Table 2 [14,21,22,54–62]. The MCE parameters for the present compounds (especially for Ho6Co2Ga and Gd6Co2Ga) studied in this work are competitive and even better than those of other reported materials, indicating their potential for cryogenic MR applications. In addition, the Ho6Co2Ga and Gd6Co2Ga compounds possess similar magnitudes of the isothermal entropy change within a temperature span of 50K. It has been raised that magnetocaloric composite material systems with the TCof phases in close proximity can aid performance optimization [63–66]. Therefore, it is worth exploring the MCE properties of a hypothetical composite of these two compounds. Assuming no interactions among the phases, the total values of ΔSiso for xHo6Co2Ga + (1−x)Gd6Co2Ga composite (xis the mass fraction of Ho6Co2Ga with 0 ≤x ≤1) for ΔHof 0–5 T were estimated as shown in Fig. 7. The optimal table-like MCE is found for x= 0.2, obtaining an RCP of 640 J kg−1, which is larger than those of Ho6Co2Ga and Gd6Co2Ga. In addition, the maximum temperature span has been found for x= 0.4, improving δTFWHM up to 90K, which is much larger than that of single Ho6Co2Ga and Gd6Co2Ga (29 and 68 K, respectively). Such a wide working temperature range (covering the H2and N2liquefaction temperature ranges) makes it Figure 6 The isothermal magnetization curves at selected temperatures for Ho6Co2Ga (a), Dy6Co2Ga (b), and Gd6Co2Ga (c). The isothermal magnetic entropy changes (ΔSiso) for Ho6Co2Ga (d), Dy6Co2Ga (e), and Gd6Co2Ga (f). The inset of (f) shows the ΔSiso-Tcurve in the range of 0–1 T for Gd6Co2Ga. ARTICLES SCIENCE CHINA Materials 2852 November 2021 | Vol.64 No.11 © The Author(s) 2021. This article is published with open access at link.springer.com. suitable for cryogenic refrigeration applications. In addition, these estimated phase fractions showing MCE optimization are in agreement with the reports of Ref. [67] in which the larger phase proportion of the higher TC phase will lead to RCP enhancement. Fig. 8a and b display the temperature dependence of ΔSiso (under ΔHof 0–1.5 and 0–2.0 T) and exponent n (under ΔHof 0–1.75 T) for the Ho6Co2Ga. It has been reported that the overshoot of nabove 2 near the transition temperature should be observed in the n(T) curves for FOPT materials [12]. For Ho6Co2Ga, it can be observed that nshows large values at low temperatures and in the region that MCE switches from inverse to direct (marked by the cyan box). For the former, the typical whole overshoot is not observed (due to the low transition temperature of Ho6Co2Ga), but still, nshows an increase above 2 within the inverse MCE region (below the transition temperature at 0 field), indicating the firstorder character of the AF-PM transition [68]. On the other hand, in the shadowed region, the large nvalues are due to the change of ΔSiso signs, unrelated to the order of phase transitions. In addition, the observed features marked by the gray box are related to the plateau observed in Fig. 3. The temperature dependence of ΔSiso and nfor Dy6Co2Ga under the same field change as Ho6Co2Ga are shown in Fig. 8c and d. The overshoot feature (n above 2) can also be clearly observed at low temperatures, which indicates the FOPT nature. Fig. 8e and f show the temperature dependence of ΔSiso (under ΔHof 0–3.0 and 0–4.0T) and exponent n(under ΔHof 0–3.5T) for Gd6Co2Ga. The n(T) curve shows three minima, which correspond to the three phase transitions aforementioned in the M(T) results (Fig. 3c). Gd6Co2Ga does not show any overshoot of n> 2 near the transition temperatures (except the shadowed region where MCE switches signs), Figure 7 Temperature dependence of ΔSiso for the hypothetical xHo6Co2Ga + (1−x)Gd6Co2Ga composite for ΔHof 0–5 T. Table 2 The phase transition temperatures Ttas well as the MCE parameters |ΔSiso max| and RCP for RE6Co2Ga compounds compared with some other magnetocaloric materials for cryogenic applications under ΔH= 0–5T Material Tt(K) |ΔSiso max| (J kg−1K−1)RCP (J kg−1) Refs. Direct MCE Inverse MCE Ho6Co2Ga 16 10.1 4.1 292 Present work Dy6Co2Ga 47 2.8 1.6 131 Present work Gd6Co2Ga 55/78/129 9.1 – 618 Present work Dy6Co2.2Al0.8 30 2.8 3.9 ~170 [22] Gd6Co2.2Al0.8 26/59/80 10.9 – ~760 [22] Dy6Co2.5Sn0.5 42 2.3 6.5 – [21] Gd11Ni4In941/92/135 2.8 ~1.0 171 [14] DyNiSi225 4.4 3.6 ~70 [54] GdCo2B2C 17 10.3 – 238 [55] Ho2CoGa310 13.8 – ~383 [56] Tm2Co2Ga 12 11.3 – 152 [57] EuAgCd 27 13.5 - 321 [58] HoCo0.3Ni1.7 27 18.6 – ~628 [59] GdZn285 8.8 – 530 [60] GdPdIn 90 4.64 – 464 [61] GdNi270 10.8 – ~518 [62] SCIENCE CHINA Materials ARTICLES November 2021 | Vol.64 No.11 2853 © The Author(s) 2021. This article is published with open access at link.springer.com. indicating that the nature of the phase transitions is of second-order. Near the peaks of ΔSiso,ndoes not show deep minima values below 1 as typically observed at the transition temperatures of single magnetic phase materials, which can be attributed to the mixed phase transitions present in the sample [12]. In addition, the field dependence of ΔSiso and the exponent nwere also investigated, as shown in Fig. S3. For Ho6Co2Ga and Dy6Co2Ga, we chose two temperatures below the inverse MCE peak: 9.5 and 9.0 K, respectively. An obvious overshoot of nabove 2 can be found for Ho6Co2Ga, evidencing that an AF-PM first-order metamagnetic phase transition occurred [68]. After the phase transition, ndecreases down to negative values due to the influence of the direct MCE associated with the FM phase [68]. It is worth noting that an overshoot (slightly above 2) can also be observed for Dy6Co2Ga at field changes around 3–4 T, also indicating the first-order character of the AF-PM transition. In the case of Gd6Co2Ga, two temperatures after the first two main ΔSiso peaks were chosen: 63 and 87 K. For both temperatures, the values of nare between 1 and 2 due to the coexistence of FM and PM phases. As the transformation begins (see the curve for 63 K), nincreases up to 2 followed by decreasing down to values close to 1, indicating the major FM contribution. No overshoot is observed for either temperature, reconfirming the second-order nature of both transitions. To further evaluate the nature of phase transition, we also studied the Arrott-plots (M2-H/M) for the three compounds, which are displayed in Fig. 9a–c. Negative slopes are observed for Ho6Co2Ga and Dy6Co2Ga (being more evident for the former), indicating FOPTs according to Banerjee’s criterion [38], which is in agreement with the exponent ncriterion. Whereas for Gd6Co2Ga, no negative slope or inflection point is observed, demonstrating the second-order nature of the phase transitions. It should be highlighted that there is good agreement between the analyses based on the exponent ncriterion and the conventional Banerjee’s criterion for this particular series of compounds. CONCLUSIONS The structural, magnetic, thermomagnetic, and magnetocaloric properties of RE6Co2Ga (RE = Ho, Dy or Gd) compounds were investigated. Rietveld refinement proved the compounds crystallize in single phase Ho6Co2Ga-type crystal structure (Immm space group). They exhibit complex and interesting magnetic behavior similar to literature work of isostructural RE6CoxAy compounds (A = Al/Sn, x= 2.2–2.5, and y=0.5–0.8). Using the conventional Banerjee’s criterion, novel MCE field dependence nfingerprint and DFT studies, the nature of the order of phase transitions, type of phase transitions, and magnetic ordering of such compounds are revealed. Ho6Co2Ga and Dy6Co2Ga are found to undergo a field-induced first-order AF to PM transition. Gd6Co2Ga exhibits FM to PM transition, with three consecutive features found to be of the second-order type. Its DFT calculations unveil its strong FM ground state in agreement with the obtained positive θPvalue and the observed saturated magnetization. By tuning Ho →Gd in RE6Co2Ga compounds, FOPT can be obtained in addition to the second-order FM-PM phase transitions: 1st and Figure 8 The temperature dependence of ΔSiso and exponent nunder different fields for Ho6Co2Ga (a, b), Dy6Co2Ga (c, d), Gd6Co2Ga (e, f). ARTICLES SCIENCE CHINA Materials 2854 November 2021 | Vol.64 No.11 © The Author(s) 2021. This article is published with open access at link.springer.com.