Magnetic phase transition and cryogenic magnetocaloric properties in the RE₆Ni_2.3In_0.7 (RE = Ho, Er, and Tm) compounds

The magnetic cooling^1–4 that relied on a magnetocaloric (MC) effect in magnetic solids was recognized as an effective new cooling technology with economic and environmental advantages to replace vapor-compression technology.^1–6 The magnetocaloric effect (MCE), known as an inherent thermodynamic response,^1–5 can be primarily expressed by the heat absorption or release (entropy or temperature changes) response to the variation of an external magnetic field. Thus, identifying prominent candidate materials with remarkable MC performances^3–17 is one of the most important prerequisites for magnetic cooling applications. Moreover, it was found that the magnetocaloric performances of the magnetic solid are closely correlated with their magnetic phase transition (MPT) properties.^4–24 As a consequence, various types of magnetic solids, including oxides, alloys, polymers, composites, and intermetallic compounds, have been investigated intensively within around the last 30 years with respect to their MC and MPT properties,^8–24 and this study aims to develop suitable MC candidate materials for applications and better elucidate their intrinsic magnetic characters. Among the identified candidate materials featuring remarkable MC performances, the rare-earth (RE)-containing magnetic solids are accounted for large proportions. For example, the famous giant MC materials of La(FeSi)₁₃H_y and Gd₅(Si,Ge)₄-based compounds^1,2 are attractive for room-temperature (RT) cooling applications. Large cryogenic MCE was recently reported in Gd₂MgTiO₆ and Gd₄Al₂O₉ oxides,^18,19 which are correlated with their unstable magnetic ground state. The pseudo-binary RE_1−xRE_xNi₂ and pseudo-ternary RE_1−xRE_xCoNi compounds^20–22 are found to be attractive candidates for MC hydrogen liquification. A large MCE was very recently reported in the GdCoC and Gd₂CuTiO₆ compounds,^23,24 which are correlated with their unique 4f–3d magnetic interactions. Detailed summaries of the MCE in RE-containing magnetic solids are provided in several review works^4–6 published recently. These aforementioned works indicated the highly potentials of RE-containing magnetic solids with remarkable MC performances, warranting further exploration.

The ternary RE-containing (621 phases) compounds^25–33 with a general formula of RE₆TM₂X (TM = 3d transition metals; X = Al, Ga, or In)^25–27 that crystallize mainly in an orthorhombic Ho₆Co₂Ga-type structure (space group Immm) aroused many research interest in recent years.^28–35 An important and special feature in the structure of 621 phase compounds^25–27 is that a certain mixture range of TM and X can happen at the X site, resulting in the formation of RE₆TM_2+xX_1−x phases.^25–35 Previous investigations on the 621 phase compounds²⁸ indicated that most of them display one or more cryogenic MPTs.^27–35 Despite their magnetism mainly originated from the RE elements, the MPT order types and temperatures of these RE₆TM_2+xX_1−x compounds are also strongly dependent on the other constituting elements.^25–28 For example, three successive MPTs at ∼35, ∼17, and ∼7 K were found in an Er₆Ni₂Sn compound. The Gd₆Co_2.2In_0.8 compound²⁹ reveals two successive MPTs at ∼66 and ∼34 K. Also, only a single MPT from paramagnetic to antiferromagnetic (AFM) at ∼42 K was observed in a Tb₆Co_2.35Sn_0.65 compound.³⁰ Moreover, the MPT and MC properties in RE₆Co_2.2Al_0.8 compounds were determined by Morozkin et al.,³² in which a large MCE in Gd₆Co_2.2Al_0.8 around ∼75 K with the maximum magnetic entropy change (−ΔS_M^max) of 10.89 J/kg K (magnetic entropy change Δμ₀H = 0–5 T) was observed. A large cryogenic MCE was also reported in RE₆Co_2.2In_0.8 compounds³⁴ around their MPT temperatures with the −ΔS_M^max values of 20.4, 9.6, and 11.8 J/kg K for Ho₆Co_2.2In_0.8, Tb₆Co_2.2In_0.8, and Gd₆Co_2.2In_0.8 under Δμ₀H of 0–7 T, respectively. The MPT and MC properties in RE₆Co₂Ga compounds³⁵ were recently determined by Guo et al., in which the Ho₆Co₂Ga/Gd₆Co₂Ga composites show large −ΔS_M^max values in a wide temperature range. Given the reported large cryogenic MCE in some RE₆TM_2+xX_1−x compounds, herein, we fabricated the RE₆Ni_2.3In_0.7 compounds and determined their magnetic, MPT, and MC properties by experimental determination and theoretical calculations. The deduced MC parameters of the present RE₆Ni_2.3In_0.7 compounds are comparable with some recently updated RE-containing magnetic solids, making them considerable for applications.

Polycrystalline RE₆Ni_2.3In_0.7 (RE = Ho, Er, and Tm) samples were prepared by a typical arc-melting route from a high-purity metal of RE (99.9%), Ni (99.99%), and In (99.99%). The alloy ingots were all melted four times followed by flipping over after each melting to achieve better homogeneity. The obtained alloy ingots were then directly sealed in the evacuated quartz crucible. Finally, the quartz crucibles with the alloy ingots were annealed at 1013 K for one week. The structural characters of RE₆Ni_2.3In_0.7 compounds were determined by powder x-ray diffraction (XRD, Rigaku, SmartLab-9KW) at RT. The magnetization (M) data of RE₆Ni_2.3In_0.7 compounds were collected by a magnetic property measurement system (MPMS, QD, Model3) with temperature ranges of 3–300 K (sweeping rate of 3 K/min) and the magnetic field up to 7 T (sweeping rate of 250 Oe/s).

The atomic-level first-principles DFT calculations for RE₆Ni_2.3In_0.7 compounds were performed using commercialized VASP software. The electronic exchange and correlation of RE₆Ni_2.3In_0.7 compounds were modeled by Perdew–Burke–Ernzerhof functional^36–38 within spin-polarized generalized gradient approximation. The valence electron contributions in pseudopotentials are [4f¹¹ 6s²] for Ho, [4f¹² 6s²] for Er, [4f¹³ 6s²] for Tm, [3d⁸ 4s²] for Ni, and [5s² 5p¹] for In, respectively. Structural optimizations were conducted using the conjugate gradient algorithm until the Hellman–Feynman forces and self-consistent electronic loops were converged to lower than 0.01 eV/Å and 10⁻⁴ eV, respectively. Also, the k-point grid using the Monkhorst–Pack method is set as 4 × 4 × 3 for calculations.

The experimental obtained XRD patterns at RT of the RE₆Ni_2.3ln_0.7 (RE = Ho, Er, and Tm) compounds and corresponding Rietveld refinement profiles fitted by FullProf³⁹ are presented in Figs. 1(a)–1(c). Evidently, all of these RE₆Ni_2.3ln_0.7 compounds exhibit similar behaviors, apart from a small amount of secondary phase of Er₃Ni₂In (∼3.19 wt. %) and Tm₃Ni₂In (∼7.15 wt. %) in the corresponding RE₆Ni_2.3ln_0.7 compounds, and the main diffraction peaks of these RE₆Ni_2.3ln_0.7 compounds can be all indexed and well-fitted by a Ho₆Co₂Ga-type structure with an orthogonal Immm space group. The obtained reliability factors, including the R_p, R_wp, and R_exp, are 2.06%, 2.85%, and 1.2% for Ho₆Ni_2.3ln_0.7; 3.79%, 5.42%, and 1.07% for Er₆Ni_2.3ln_0.7; and 3.52%, 4.8%, and 1.06% for Tm₆Ni_2.3ln_0.7, respectively. These low values of all reliability factors verify the reliability of the fittings. The determined lattice constants of a, b, c, and V are 9.321, 9.497, 9.888 Å, and 875.30 ų for Ho₆Ni_2.3ln_0.7; 9.246, 9.413, 9.832 Å, and 855.70 ų for Er₆Ni_2.3ln_0.7; and 9.225, 9.401, 9.830 Å, and 852.50 ų for Tm₆Ni_2.3ln_0.7, respectively. All of these lattice constants show decrease trends with an increase in the RE atomic number, adhering the contraction law of RE elements. The schematic crystal structure of RE₆Ni_2.3ln_0.7 compounds is presented in Fig. 1(d). The RE atoms occupied at three different Wyckoff sites of 8n, 8m, and 8l, as shown by different colors. The RE1 atom forms grid locating within xy planes. Similarly, the RE2 and RE3 atoms form grids locating within xz and yz planes, respectively. The Ni atom occupied at two different Wyckoff sites of 4j and 4g, while the Al atom occupied at the 2c site. Additionally, the remaining Al and Ni atoms share the 2a Wyckoff site. Additionally, six RE atoms form an octahedron [see Fig. 1(e)], and there are eight such octahedrons in the unit cell. These octahedrons connect via RE1, RE2, and RE3 atoms along the z axis, y axis, and x axis, respectively, forming a typical three-dimensional network structure.

To investigate the magnetic and MPT properties of RE₆Ni_2.3ln_0.7 compounds, temperature-dependent M(T) curves were determined. The resulting M(T) and inverse susceptibility 1/χ(T) curves of RE₆Ni_2.3ln_0.7 compounds under an external magnetic field (μ₀H) of 1 T are presented in Fig. 2, and the corresponding M(T) curves under μ₀H of 0.1 T for RE₆Ni_2.3ln_0.7 compounds in field-cooled (FC) and zero-field-cooled (ZFC) modes are presented in the inset. All of these RE₆Ni_2.3ln_0.7 compounds evidently exhibit cryogenic magnetic orderings. Specifically, two successive low-temperature MPTs at T_M of ∼10.6 and ∼33.0 K can be noted for Ho₆Ni_2.3ln_0.7. Only a single MPT from a paramagnetic (PM) to an AFM state was identified at T_M of ∼11.0 K for Er₆Ni_2.3ln_0.7, whereas the Tm₆Ni_2.3ln_0.7 shows the MPT around T_M of ∼7.6 K from a PM to ferromagnetic (FM) state. The small deviations that observed below T_M in present RE₆Ni_2.3ln_0.7 compounds are probably attributed to the existence of domain-wall pinning effects and/or the indication spin-freezing. Moreover, the 1/χ(T) curves of present Ho₆Ni_2.3ln_0.7 and Er₆Ni_2.3ln_0.7 compounds above 120 K, as presented in Fig. 2, generally show linear behavior, i.e., obeying the Curie–Weiss law of $χ(T)= C/(T− θ P)$ and $C=N ( μ B μ eff ) 2/3 κ B$⁠, in which θ_P and μ_eff represent the paramagnetic Curie temperature and the effective magnetic moment, respectively. The linear fitting of 1/χ(T) curves resulted in the μ_eff values of 10.40, 9.46, and 7.33 μ_B/f.u. for Ho₆Ni_2.3ln_0.7, Er₆Ni_2.3ln_0.7, and Tm₆Ni_2.3ln_0.7, respectively, and the slight difference for Tm₆Ni_2.3ln_0.7 with those of theoretical values by only considering the free RE³⁺ ions is probably due to the existence of an impurity phase.

In an attempt to shed some light on the ground state properties of RE₆Ni_2.3ln_0.7 compounds, the spin-polarized DFT calculations^36–38 were conducted. The stability of the crystal structure was first checked, and the orthorhombic Ho₆Co₂Ga-type structure (space group Immm) assumed from the XRD refinement was selected as the initial structure for optimization. The differences between optimized and experimental results of all the RE₆Ni_2.3In_0.7 compounds are less than 1.0%, suggesting that the optimized crystal structure is logical and accessible. Then, the total energy (E_tot) with different potential magnetic structures of RE₆Ni_2.3ln_0.7 compounds was calculated by using the optimized structural parameters to decide their magnetic ground state. The arrangements of RE atoms by setting the spin directions (spin-up or spin-down) and, therefore, four magnetic configurations are constructed, including FM, A-AFM, C-AFM, and G-AFM states, as presented in Fig. 3. The corresponding calculated E_tot values are −276.9681, −276.0709, −277.3717, and −277.3759 eV/f.u. for Ho₆Ni_2.3In_0.7; −249.0665, −249.93017, −249.6143, and −250.2607 eV/f.u. for Er₆Ni_2.3In_0.7; and −228.51133, −227.1848, −227.8451, and −227.6089 eV/f.u. for Tm₆Ni_2.3In_0.7, respectively. Apparently, the lowest E_tot of Ho₆Ni_2.3In_0.7, Er₆Ni_2.3In_0.7, and Tm₆Ni_2.3In_0.7 corresponds to G-AFM, G-AFM, and FM state, respectively. Moreover, the total density of states (DOS) and partial DOS of each element in RE₆Ni_2.3ln_0.7 compounds were also calculated, as presented in Figs. 4(a)–4(c), to further understand their electronic and magnetic ground state properties. The DOS of these RE₆Ni_2.3ln_0.7 compounds crosses the Fermi level without creating a bandgap, illustrating the metallic nature of them. The DOS of Ho₆Ni_2.3In_0.7 and Er₆Ni_2.3In_0.7 have the symmetric splitting, indicating the AFM ground state, whereas polarization splitting for Tm₆Ni_2.3In_0.7 indicates the FM ground state. Obviously, the partial DOS of RE-4f orbits show obvious splitting behavior and mainly controlled the total DOS of RE₆Ni_2.3ln_0.7 compounds, suggesting the spontaneous polarization of RE³⁺ ions and the realization of large magnetic moments. These calculation results are well-consistent with those of aforementioned magnetization determination, which further proved vital roles of RE³⁺ ions in magnetism for these RE₆Ni_2.3ln_0.7 compounds.

Additionally, the M(μ₀H) look at 2 K and series M(μ₀H) curves of RE₆Ni_2.3ln_0.7 compounds were determined, which are given in Figs. 5(a) and 5(b)–5(d), respectively. Generally, only very tiny differences during M(μ₀H) loops at 2 K, as displayed in the inset of Fig. 5(a), can be observed. Specifically, the values of M have linear increasing behavior with an increase in μ₀H of Ho₆Ni_2.3ln_0.7 and Er₆Ni_2.3ln_0.7 in the curves below T_N under low-μ₀H, then show quick rises in M under medium-μ₀H, and exhibit saturation-like behavior under high-μ₀H regions. These behaviors in Ho₆Ni_2.3ln_0.7 and Er₆Ni_2.3ln_0.7 compounds are quite similar with those of recently reported RE₂Ga₂Mg⁴⁰ and RE₂O₂SO₄⁴¹ compounds, in which a typical μ₀H-induced metamagnetic transition arisen from AFM to FM-like state occurred, whereas the M values increased abruptly with a rise in μ₀H of Tm₆Ni_2.3ln_0.7 under low-μ₀H regions and then show saturation-like characters under high-μ₀H regions at low temperatures, illustrating a typical FM state. Moreover, for the curves well above T_M, nearly linear relations between M and μ₀H can be noted in all of the present RE₆Ni_2.3ln_0.7 compounds, illustrating the PM states. Moreover, it was found that the magnetocaloric performances of the magnetic solid are closely correlated with their MPT properties,^4–10 which could be determined primarily from the slopes⁴² in the curves of the Arrott plot (M² vs μ₀H/M) based on the Banerjee criterion.⁴² The exhibition of positive or negative values in the slope, in principle, corresponds to the second-order or first-order type MPT.⁴² Thus, we directly transferred the M(μ₀H) data to Arrott plot curves, which are given in Figs. 6(a)–6(c), in which clearly negative slopes can be identified for Ho₆Ni_2.3ln_0.7 and Er₆Ni_2.3ln_0.7, illustrating first-order type MPT(s) at low temperatures, whereas only positive slopes can be found for Tm₆Ni_2.3ln_0.7, illustrating second-order type MPT.

The resultant −ΔS_M(T) curves of present RE₆Ni_2.3ln_0.7 compounds are given in Figs. 7(a)–7(c). Generally, the MCE can be divided into two different types, i.e., the direct-type (or conventional) MCE and the inverse-type MCE.^4–6,40,41 The material heats up when μ₀H is applied for the direct MCE, which can be usually observed in the traditional FM-ordered materials,^20–23 whereas the material cools down when μ₀H is applied for the inverse MCE, which has been reported for some materials with special AFM ordered.^4–6,40,41 An obvious crossover in −ΔS_M(T) curves for Ho₆Ni_2.3ln_0.7 and Er₆Ni_2.3ln_0.7 under low Δμ₀H can be noted; e.g., it changes from negative −ΔS_M values (inverse MCE) to positive −ΔS_M values (direct MCE) with the rise in temperature. The observed inverse MCE of Ho₆Ni_2.3ln_0.7 and Er₆Ni_2.3ln_0.7 further confirms the AFM states in these compounds, and the direct MCE is believed to be related to their μ₀H-induced FM-like states. The maximum value of negative −ΔS_M (−ΔS_M^max) referring the inverse MCE is −1.54 J/kg K for Ho₆Ni_2.3ln_0.7 under Δμ₀H of 0–3 T and −1.03 J/kg K for Er₆Ni_2.3ln_0.7 under Δμ₀H of 0–2 T, respectively. Moreover, only positive –ΔS_M values can be observed within the present tested μ₀H and T regions for Tm₆Ni_2.3ln_0.7, which are consistent well with its FM state. Moreover, the positive −ΔS_M^max values of these RE₆Ni_2.3ln_0.7 compounds that refer to direct MCE are deduced to be 2.54 and 9.66 J/kg K for Ho₆Ni_2.3ln_0.7, 4.13 and 13.93 J/kg K for Er₆Ni_2.3ln_0.7, and 9.60 and 17.59 J/kg K for Tm₆Ni_2.3ln_0.7, under Δμ₀H of 0–3 and 0–7 T, respectively. Evidently, the Tm₆Ni_2.3ln_0.7 exhibits the largest direct MCE, which is probably related to its FM ground state and larger magnetic moments. Additionally, the MPT order types can also be simply determined from the signs of exponent n, which was proposed recently by Franco et al.,^43,44 and the values of n were evaluated by $n( T , μ 0 H)= d ln | Δ S T | d ln μ 0 H$⁠. The resultant n(T) curves of RE₆Ni_2.3ln_0.7 compounds are presented in Figs. 8(a)–8(c). Generally, n > 2 is a first-order type MPT; otherwise, it will be of second-order type MPT.^43,44 Obvious overshoots with n above 2 can be observed for Ho₆Ni_2.3ln_0.7 and Er₆Ni_2.3ln_0.7, further proving the first-order type MPT, whereas no overshoot with n above 2 can be found for Tm₆Ni_2.3ln_0.7, further proving the second-order type MPT. The relative cooling power (⁠ $RCP=| Δ S M max|×δTFWHM$⁠)^4–6 and the temperature-averaged entropy change (⁠ $TEC ( Δ T lift)$ $= 1 Δ T lift max T mid⁡ { ∫ T mid − Δ T lift 2 T mid + Δ T lift 2 Δ S M ( T ) Δ μ 0 H , T d T }$⁠)⁴⁵ with proper lifted temperatures (ΔT_lift) of present RE₆Ni_2.3ln_0.7 compounds were also determined. The T_mid denotes the central temperature where TEC(ΔT_lift) exhibits its maximum. The resultant RCP values are deduced to be 67.85 and 344.09 J/kg for Ho₆Ni_2.3ln_0.7, 86.87 and 388.71 J/kg for Er₆Ni_2.3ln_0.7, and 119.24 and 371.17 J/kg for Tm₆Ni_2.3ln_0.7 under Δμ₀H of 0–3 and 0–7 T, respectively. The TEC(5) and TEC(10) values (Δμ₀H = 0–7 T) are 9.48 and 9.27 J/kg K for Ho₆Ni_2.3ln_0.7, 13.45 and 13.01 J/kg K for Er₆Ni_2.3ln_0.7, and 17.07 and 16.17 J/kg K for Tm₆Ni_2.3ln_0.7, respectively. Interestingly, the deduced MC parameters of these RE₆Ni_2.3ln_0.7 compounds, especially for Tm₆Ni_2.3ln_0.7, are evidently better than the reported RE₆TM_2+xX_1−x compounds^32–35 and also comparable to some recently updated RE-containing magnetic solids, such as the RE₂Ga₂Mg,^40, RE₂RuIn,^46, RE₂Cr₂C₃,⁴⁷ and RE₅Ni₂Sb⁴⁸ compounds, as well as the RE₂MgTiO₆,^49, RE₂O₂SO₄,^41, REOCl,^14, RE₂Ti₂O₇,⁵⁰ and RE₂BaZnO₅ oxides,⁵¹ with remarkable cryogenic performances, making the Tm₆Ni_2.3ln_0.7 compound considerable for applications.

In summary, three polycrystalline RE₆Ni_2.3ln_0.7 (RE = Ho, Er, and Tm) samples were fabricated and investigated their structure, magnetic, and magnetocaloric properties by experimental determination and theoretical calculations. All of these RE₆Ni_2.3ln_0.7 compounds crystallize in a Ho₆Co₂Ga-type structure with an orthogonal Immm space group and magnetically ordered at low temperatures. Large cryogenic MCE and remarkable performances were realized in these RE₆Ni_2.3ln_0.7 compounds. Moreover, their MC parameters under Δμ₀H of 0–7 T, including the –ΔS_M^max, RCP, and TEC(5), reach 9.66 J/kg K, 344.09 J/kg, and 9.48 J/kg K for Ho₆Ni_2.3In_0.7; 13.93 J/kg K, 388.71 J/kg, and 13.46 J/kg K for Er₆Ni_2.3In_0.7; and 17.59 J/kg K, 371.17 J/kg, and 17.07 J/kg K for Tm₆Ni_2.3In_0.7, respectively, which are comparable to some recently updated RE-containing magnetic solids with remarkable cryogenic performances.

The present work was supported by the National Natural Science Foundation of China (No. 52071197). The authors also acknowledge the Supercomputing Center of Hangzhou Dianzi University for providing computing resources.

The authors have no conflicts to disclose.

Yang Xie: Data curation (equal); Investigation (equal); Validation (equal); Writing – original draft (equal). Jinyi Wang: Data curation (equal); Investigation (equal); Visualization (equal). Fuyu Yang: Data curation (equal); Investigation (equal); Validation (equal). Jiayu Ying: Data curation (equal); Investigation (equal); Validation (equal); Visualization (equal). Yikun Zhang: Conceptualization (equal); Funding acquisition (equal); Project administration (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).

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