Highly reversible magnetocaloric effect in Gd₅Si_0.25Ge_3.75 and Gd₅Si_0.5Ge_3.5 under moderate magnetic fields for hydrogen liquefaction

Abstract

For magnetic cooling with the goal of hydrogen liquefaction, magnetocaloric materials with outstanding magnetic-entropy and adiabatic temperature changes (ΔS_T and ΔT_ad) are required, covering the temperature range from liquid nitrogen to the condensation point of hydrogen at 20 K. Although second-order rare-earth-based intermetallic compounds show large ΔS_T and ΔT_ad near 20 K, their performance decreases drastically with increasing temperature. Here, compounds with first-order transition can be beneficial, if the reversibility of the magnetocaloric effect is ensured. In this work, we report that Gd₅Si_0.25Ge_3.75 and Gd₅Si_0.5Ge_3.5 exhibit highly reversible magnetocaloric effects near 55 and 80 K, respectively, in a magnetic field of 5 T despite significant thermal hysteresis. The high reversibility originates from the rapid shift of the transition temperature with magnetic field. Since superconducting coils are widely used to generate magnetic fields up to 5 T in existing magnetic refrigeration prototypes, this work proves that first-order magnetocaloric materials with significant thermal hysteresis can be promising candidates for hydrogen liquefaction in moderate magnetic fields.

Introduction

Hydrogen has the highest gravimetric energy density among all chemical fuels (about 120 and 140 MJ kg⁻¹ for lower and higher heating values, respectively). It is environmentally friendly and considered for transportation, use in households, industry, and as an energy storage medium^1,2,3. On the other hand, the low density of hydrogen gas leads to an extremely low energy density in relation to volume, which is why high pressures are required to store significant amounts of H₂⁴. Alternatively, hydrogen can be stored and transported as a liquid at atmospheric pressure with almost twice the volumetric energy density compared to gaseous storage of 700 bar⁵. However, the liquefaction is a very energy-intensive process and requires about one-third of a lower heating value^6,7. Due to the low efficiency of conventional expansion-based cooling methods at cryogenic temperatures below 100 K, the alternative technology of magnetic cooling has attracted significant interest after a number of discoveries that demonstrated the viability of this idea⁸. Magnetic refrigeration employs environment-friendly solid-state cooling based on magnetic materials. The device efficiency is directly related to the thermal-magnetic properties of the material, the so-called magnetocaloric effect, which scales with the magnetic field. Despite their cost, superconducting magnets can generate sufficiently strong fields to maximize the useful power of magnetic refrigerators. For the industrial scale, where larger magnetized volumes are required, superconducting coils can even be more cost-efficient than fields produced by permanent magnets, plus they allow for higher field strengths^9,10. This is why many groups use superconducting solenoids with up to 5 T for their cryogenic prototypes^{11,12,13,14,15,16}.

The cooling principle is based on the magnetocaloric effect, known for many years¹⁷, but the search for suitable materials with the best properties for application began to gain momentum, especially after the discovery of the giant magnetocaloric effect in Gd₅Si₂Ge₂¹⁸. Dozens of potential material families, such as Heusler alloys^19,20,21, Laves phases^{3,22,23,24,25,26,27,28,29}, rare-earth metals^30,31, FeRh^32,33,34, La-Fe-Si^35,36,37, and others³⁸, demonstrating application potential for magnetocaloric cooling both for cryogenics and room temperature. Still, the Gd-Si-Ge family occupies a special place in this list^39,40.

The phase diagram of Gd₅Si_xGe_1−x as a function of temperature and silicon concentration x was presented in refs. ^41,42,43. For Ge-rich compositions below x = 1.2, the high-temperature phase corresponds to the Sm₅Ge₄-type orthorhombic O(II) structure (space group Pnma). At silicon concentrations below 1, a second-order transition from a paramagnetic (PM) to an antiferromagnetic (AFM) state appears at the Néel temperature T_N (from about 128 K for x = 0 to 140 K for x ≈ 1)⁴³. A further first-order phase transition into the Gd₅Si₄-type orthorhombic O(I) structure (space group Pnma) with ferromagnetic (FM) order occurs below the Curie point, which depends almost linearly on x being T_C ≈ 165 K for x = 1.2 and reducing to 20 K when x is close to zero. In the binary compound Gd₅Ge₄, the AFM-FM magnetostructural transition does not occur. Below 20 K, the material behaves as magnetic glass due to a kinetic arrest (KA)^44,45,46. A transition into the FM phase can be induced at about 20 K by applying a magnetic field of about 1 T. Chattopadhyay et al. showed the formation of FM clusters at 1 T, randomly distributed in the AFM matrix, using Hall-probe microscopy, which evidences a heterogeneous magnetic state with glassy behavior⁴⁷.

Although the O(I) and O(II) crystal structures are very similar, there exist decisive differences^{42,48,49,50,51,52}. For simplifying the description, Smith et al.⁵³ proposed considering the structure of these compounds in terms of so-called slabs, which are flat structural blocks of subnanometer thickness and infinite width in the ac plane (Fig. 1). Each slab consists of five layers of only R (Gd) atoms, only T (T = Ge, Si) atoms, or a combination C of them, lining up as a TRCRT sequence. These slabs are highly robust against deformations, whereas external stimuli promote their relative movements and allow for the only possible structural change⁵⁴. The distances between the slabs play a crucial role in forming interslab T–T bonds, which influence interlayer ordering through RKKY interactions between the gadolinium magnetic moments⁵⁰. In the case of the O(I) structure, the T–T bonds are formed and lead to FM order; for the O(II) structure, the bonds are broken, and the magnetic order is AFM. Controlling the interslab distances via silicon substitution allows the transition temperatures to be tuned. Temperature variation, as well as the application of magnetic field and pressure, induce the first-order magnetostructural transition, leading to giant magnetocaloric effects, giant magnetostriction^55,56,57, and giant magnetoresistance^58,59,60.

Fig. 1: Crystal structure.

Schematic representation of a the O(I) Sm₅Ge₄-type and b the O(I) Gd₅Si₄-type orthorhombic structures. The purple boxes show the orthorhombic unit cells with the ab plane lying in the plane of the figure. The dashed gray boxes highlight slabs of highly stable structural blocks that consist of layers formed by rare-earth atoms (R), transition-metal elements (T), and their combinations (C). Relative movements of the slabs (gray arrows) change the interatomic distances between the atoms from the T layers and a strengthening of interslab T–T bonds (orange double lines in (b)). Adapted from Figure 6 in ref. ³⁹.

At the same time, such a transition is accompanied by thermal hysteresis, which leads to irreversibility effects, i.e., an incomplete transition when applying and removing an external stimulus. One of the ways to solve this problem is the application of a multicaloric cycle, when the return to the initial state after application and removal of a magnetic field can be provided by uniaxial stress^19,61,62. Another approach is to search for compounds with giant magnetocaloric effects and minimal irreversibility. Guided by the latter, in this paper, we present the results of our study on the adiabatic temperature change ΔT_ad and the isothermal entropy change ΔS_T as well as irreversibilities in the Gd₅Si_xGe_1−x family for compounds with x = 0, 0.25, and 0.5, in which we observe a large magnetocaloric effect between 20 and 100 K. This is particularly promising when it comes to cryogenic applications working with liquid-nitrogen pre-cooling. These three materials can be used to form a stack that allows magnetocaloric cooling down from 77 K to the boiling point of hydrogen.

Results and discussion

Figure 2a–c shows temperature-dependent magnetization data for Gd₅Ge₄, Gd₅Si_0.25Ge_3.75, and Gd₅Si_0.5Ge_3.5, respectively. All three samples reveal similar features in the M(T) data. Between 110 and 130 K, there are cusps due to the second-order PM-AFM transition, as indicated by gray dotted lines, which connect the positions of this feature in different fields. The first-order AFM-FM magnetostructural transitions are accompanied by thermal hysteresis and rapid changes in magnetization. Based on these features observed during cooling, we present the phase diagrams in the insets of Fig. 2a–c.

Fig. 2: Magnetization end isothermal entropy change.

Temperature-dependent magnetization of a Gd₅Ge₄, b Gd₅Si_0.25Ge_3.75, and c Gd₅Si_0.5Ge_3.5. During cooling and heating, the data were measured under various applied magnetic fields up to 10 T. Arrows around the thermal hysteresis indicate the sweep directions. The gray dotted lines indicate the second-order PM-AFM transitions. The insets in (a–c) show phase diagrams based on the magnetization features extracted from cool-down sweeps. The isothermal entropy changes for d Gd₅Ge₄, e Gd₅Si_0.25Ge_3.75, and f Gd₅Si_0.5Ge_3.5 are calculated from the magnetization data using Eq. (1). Light thick lines show the envelopes of the reversible areas of ΔS_T peaks, formed by the overlapping area of up and down sweeps.

For Gd₅Ge₄, we found additional features (marked by A and KA) that are not present in Gd₅Si_0.25Ge_3.75 and Gd₅Si_0.5Ge_3.5. A splitting of the magnetostructural AFM-FM transition appears in magnetic fields at about 8 T (green area in the inset of Fig. 2a). This additional phase originates from antiferromagnetic short-range correlations in the main ferromagnetic matrix (phase A) as reported in ref. ⁶³. Another feature appears in the heating curve in 1 T. With increasing temperature, the magnetization rises around 15 K, reaches a maximum at around 20 K, and then drops at 26 K. We attribute this behavior to the kinetic-arrest (KA) phase mentioned above. The KA area, reported by S. B. Roy et al. in ref. ⁴⁴, is depicted in yellow in the inset of Fig. 2a. The shape of the heating curve in 1 T is similar to that reported in ref. ⁵⁹.

When germanium is substituted by silicon, there are no signs for the presence of the KA and A phases, at least in the measured magnetic-field ranges. There are only the two second-order PM-AFM and first-order AFM-FM transitions (inset in Fig. 2b). The inset in Fig. 2c shows the feature positions obtained from the cooling curves for all three samples. The PM-AFM transition depends only weakly on the Si concentration, with very similar Néel temperatures (T_N ≈ 127 K for Gd₅Ge₄, 128 K for Gd₅Si_0.25Ge_3.75, and 130 K for Gd₅Si_0.5Ge_3.5). The PM-AFM transition shifts to lower temperatures with increasing magnetic field. In contrast, the magnetostructural AFM-FM transition temperatures increase with increasing silicon concentration and increasing magnetic field.

The magnetization at 5 T and 10 K reaches similar values of 185 Am² kg⁻¹ for all three compounds. Among the samples investigated, Gd₅Si_0.25Ge_3.75 shows the lowest saturation field of less than 1 T. At 0.25 T, the magnetization already reaches about 135 Am² kg⁻¹ at low temperatures, whereas for Gd₅Si_0.5Ge_3.5 this value is about 70 Am² kg⁻¹. Gd₅Ge₄ is in the KA phase up to 1 T and temperatures below 20 K, with a magnetization of not more than 62 Am² kg⁻¹.

In most materials with a first-order transition, the magnetization changes sharply but continuously, which is why we can use the Maxwell relation to estimate the magnetocaloric effect^64,65. From Maxwell relations, we can calculate the isothermal entropy change ΔS_T for a variation of the magnetic field ΔH = H_f − H_i using

$$\Delta {S}_{T}(T,\Delta H)={\mu }_{0}\int_{{H}_{{{{{\rm{i}}}}}}}^{{H}_{{{{{\rm{f}}}}}}}{\left(\frac{\partial M}{\partial T}\right)}_{H,p}dH.$$

(1)

Based on our magnetization measurements, we interpolated the data in 2 K steps and calculated ΔS_T using Eq. (1) (Fig. 2d–f). Here, we observe a characteristic behavior of first-order transitions with an almost unchanged low-temperature peak edge of ΔS_T. With increasing magnetic field, this peak grows and expands toward higher temperatures. All three samples show clear hysteresis, evidenced by the shift of the ΔS_T peaks between the heating and cooling curves. The overlapping area of these peaks for each magnetic field reflects the reversibility region (indicated by light thick lines in Fig. 2d–f). The influence of phase A on ΔS_T at 10 T for Gd₅Ge₄ leads to the appearance of a second maximum.

In view of the large magnetization change with temperature and magnetic field of Gd₅Si_0.25Ge_3.75 (Fig. 2b), it is not surprising that this compound exhibits a significant value of ΔS_T ≈ −23 J kg⁻¹ K⁻¹ already at 1 T. Apparently, the kinetic arrest causes that ΔS_T for Gd₅Ge₄ does not even reach  −2 J kg⁻¹ K⁻¹ at 1 T. Beyond the KA phase, above 1 T, ΔS_T gradually increases, reaching about  −24 J kg⁻¹ K⁻¹ at 5 T and  −30 J kg⁻¹ K⁻¹ at 10 T. For Gd₅Si_0.25Ge_3.75, ΔS_T reaches  −36 J kg⁻¹ K⁻¹ at 5 T and  −40 J kg⁻¹ K⁻¹ at 10 T. For Gd₅Si_0.5Ge_3.5, ΔS_T reaches  −37 J kg⁻¹ K⁻¹ at 5 T. Increasing the silicon concentration reduces the width of the AFM phase and, therefore, the full width at half maximum (FWHM) of the ΔS_T peak. For example, in 5 T the FWHM is about 24, 22, and 18 K for the silicon concentrations x = 0, 0.25, and 0.5, respectively.

We further measured the magnetic-field dependences of ΔT_ad for selected starting temperatures T₀ and maximum fields using pulsed magnetic fields (Fig. 3a–c). The arrows indicate the field-sweep directions. The first-order nature of the transition is reflected by the large hysteresis in most of the ΔT_ad curves. Depending on T₀, the critical fields triggering the magnetocaloric effect shift (see phase diagrams in Fig. 2). For example, for Gd₅Ge₄ at T₀ = 52 K (green curves in Fig. 3a) in fields up to 5 T, ΔT_ad remains almost zero. For higher field, ΔT_ad increases strongly until reaching a complete transition to the ferromagnetic phase, where ΔT_ad saturates. For further analysis, we determined the adiabatic temperature change at maximum field, $\Delta {T}_{ad}^{max}$. For some T₀, due to irreversibility, the final temperature after the field pulse is $\Delta {T}_{ad}^{fin}$, marked by an open circle for T₀ = 8 K in Fig. 3a. Figure 3d–f shows $\Delta {T}_{ad}^{max}$ and $\Delta {T}_{ad}^{fin}$ as a function of T₀ obtained from our pulse-field data with maximum fields of 5, 10.9, and 22.6 T. For illustration, the hatched areas highlight the irreversible region below $\Delta {T}_{ad}^{fin}$. For each of the samples, these regions are nearly identical, independent of the maximum field and appear close to the zero-field AFM-FM magnetostructural transition. For Gd₅Ge₄, we observe an anomalous increase of both $\Delta {T}_{ad}^{max}$ and $\Delta {T}_{ad}^{fin}$ below about 20 K. Since ΔS_T, obtained from the magnetization data, is close to zero (Fig. 2d), there should also be no ΔT_ad. Indeed, the large values of ΔT_ad are associated with dissipative losses as previously discussed in ref. ⁶⁶. Whether the formation of the KA phase is the cause for this behavior is not clear and is not the subject of this paper.

Fig. 3: Adiabatic temperature change.

Magnetic-field dependences of adiabatic temperature changes ΔT_ad measured during various magnetic-field pulses up to 22.6 T for a Gd₅Ge₄, b Gd₅Si_0.25Ge_3.75, and c Gd₅Si_0.5Ge_3.5. Colors denote different starting temperatures T₀. Arrows indicate up and down field sweeps. d–f Extracted ΔT_ad values at maximum magnetic field ($\Delta {T}_{ad}^{max}$, filled circles) and immediately after each field pulse ($\Delta {T}_{ad}^{fin}$, open circles) as a function of initial temperature. Hatched areas below $\Delta {T}_{ad}^{fin}$ correspond to irreversibilities.

Otherwise, ΔT_ad for the three compounds is in line with the above-described behavior of ΔS_T. At 130 K, Gd₅Ge₄ and Gd₅Si_0.25Ge_3.75 show weak peaks associated with the second-order PM-AFM transition. At 22.6 T, $\Delta {T}_{ad}^{max}$ is about 5 and 6.5 K for Gd₅Ge₄ and Gd₅Si_0.25Ge_3.75, respectively. For Gd₅Si_0.5Ge_3.5, the $\Delta {T}_{ad}^{max}$ peak merges with the magnetostructural peak at 22.6 T. For Gd₅Ge₄, $\Delta {T}_{ad}^{max}$ shows a broad peak associated with the AFM-FM transition, reaching about 10.2 K in 22.6 T. At this field, we also could observe a peak splitting due to the appearance of phase A.

For Gd₅Si_0.25Ge_3.75 and Gd₅Si_0.5Ge_3.5, we find much narrower, but larger $\Delta {T}_{ad}^{max}$ peaks. At 22.6 T, the adiabatic temperature change reaches about 19 K for both compounds, and about 15 K at 10.9 T. Most interestingly, at 5 T, Gd₅Si_0.5Ge_3.5 demonstrates $\Delta {T}_{ad}^{max}=8.7\,{{{{\rm{K}}}}}$ and $\Delta {T}_{ad}^{fin}=1.5\,{{{{\rm{K}}}}}$ at T₀ = 82 K. At T₀ = 55 K, Gd₅Si_0.25Ge_3.75 shows a giant effect of 13 K, while $\Delta {T}_{ad}^{fin}$ is only 0.9 K, which reflects a minor influence of the irreversibility. However, already at T₀ = 50 K, the irreversibility becomes important with $\Delta {T}_{ad}^{max}=3.9\,{{{{\rm{K}}}}}$ and $\Delta {T}_{ad}^{fin}=1.4\,{{{{\rm{K}}}}}$. The silicon-doped samples show impressive $\Delta {S}_{T}^{max}$ and $\Delta {T}_{ad}^{max}$ values (Fig. 4) in 2 and 5 T, surpassing the results for compounds with similar transition temperatures, such as TbFeSi and DyFeSi ($\Delta {S}_{T}^{max}=17.5$ and 17.4 J kg⁻¹ K⁻¹, $\Delta {T}_{ad}^{max}=8.2$ and 7.1 K in 5 T, respectively)⁶⁷, EuO (17.5 J kg⁻¹ K⁻¹, 6.8 K)⁶⁸, DyAl₂ (16.8 J kg⁻¹ K⁻¹, 6.4 K)⁶⁹, HoCo₂ (23.6 J kg⁻¹ K⁻¹, 6.9 K)²³, Eu₂In (34 J kg⁻¹ K⁻¹)⁷⁰, and HoGa (17.1 J kg⁻¹ K⁻¹)⁷¹. At the same time, kinetic arrest and irreversibilities lead to a reduced magnetocaloric effect and Gd₅Ge₄ is inferior to materials with low transition temperatures, such as ErCo₂ ($\Delta {S}_{T}^{max}=35.9\,{{{{\rm{J}}}}}\,{{{{{\rm{kg}}}}}}^{-1}\,{{{{{\rm{K}}}}}}^{-1}$, $\Delta {T}_{ad}^{max}=7.6\,{{{{\rm{K}}}}}$)²³, HoB₂ (40.1 J kg⁻¹ K⁻¹, 12 K)⁷², and ErAl₂ (37.8 J kg⁻¹ K⁻¹, 9.8 K)³.

Fig. 4: Comparison of magnetocaloric materials.

Comparison of $\Delta {S}_{T}^{\max }$ and $\Delta {T}_{{{{{\rm{ad}}}}}}^{\max }$ values for the Gd₅Si_xGe_1−x family from the present work (stars) with literature data from refs. ^{3, 23, 67,68,69,70,71,72, 76,77,78,79,80} showing a large magnetocaloric effect at cryogenic temperatures under magnetic-field application of 2 (left) and 5 T (right).

In addition, for a more objective comparison of materials, we evaluated the temperature-averaged entropy change (TEC)⁷³ using ΔS_T(T) data of our samples and materials from the literature mentioned above and summarized this in Table 1. Most of the materials from that list demonstrate no significant thermal hysteresis. However, this is different for the Gd-Si-Ge system, since it reduces the efficiency of the magnetocaloric thermodynamic cycle in cooling devices. For this reason, we evaluated TEC for our samples on the basis of both sets of data, ΔS_T(T) during the heating protocol and for the reversible process (overlapping areas of heating and cooling curves). The results are presented in Table 1 for temperature spans of 3 and 10 K in magnetic fields of 1, 2, and 5 T. For the sake of clarity, we sorted the materials according to their transition temperatures and applied a color scheme to reflect the TEC values.

Table 1 Temperature-averaged entropy change

Griffith et al. showed for Gd₅Si_0.5Ge_3.5 values for TEC(3 K) and TEC(10 K) in 1 T of 20 and 11 J kg⁻¹ K⁻¹, respectively, which is higher compared to our estimates from the heating curves (12.4 and 37.8 J kg⁻¹ K⁻¹, respectively)⁷³. However, details on the calculation of the TEC parameter were not provided in that work. In order to avoid overestimates of the material efficiency, we focus on the TEC calculations derived from reversible ΔS_T curves, which is critical especially at low magnetic-field changes, whereas in 5 T the resulting TEC values differ little between reversible part of ΔS_T(T) and under heating protocol.

In 1 T, TEC(3 K) and TEC(10 K) for Si-doped samples are inferior to some other compounds. Thus, ErCo₂ shows about one and a half times higher values of 19.2 and 9.1 9.1 J kg⁻¹ K⁻¹ compared to Gd₅Si_0.25Ge_3.75 (11.7 and 5.9 J kg⁻¹ K⁻¹). HoCo₂ has more than two times higher values than Gd₅Si_0.5Ge_3.5. However, at the same time, these values are comparable and even superior to the TEC values of other materials shown in Table 1. Much higher TEC values are achieved in 5 T, where Gd₅Si_xGe_4−x compounds have impressive ΔS_T peak widths. Especially Gd₅Si_0.5Ge_3.5 and related Gd₄ScGe₄ stand out in the nitrogen boiling point region. These materials have the advantage of a wide temperature window with a large magnetocaloric effect, making them suitable for use in devices using such moderately high magnetic fields.

In this work, we have studied the magnetocaloric effect in three members of the Gd₅Si_xGe_1−x family in high fields. In these compounds, a large magnetocaloric effect arises from the rapid shift of the AFM-FM transition temperatures with magnetic field. Changing the silicon concentration x allows fine-tuning of the Curie point and the choice of a preferred operating temperature range for magnetic cooling. Direct measurements of ΔT_ad show that Gd₅Si_0.25Ge_3.75 exhibits almost fully reversible ΔT_ad curves under moderate pulsed magnetic fields of 5 T and higher. Despite the presence of strongly increasing irreversibilities at temperatures below 30 K, Gd₅Ge₄ still shows reasonable ΔT_ad and ΔS_T values in magnetic fields above 2 T. Considering the better cost efficiency of superconducting solenoids on a large scale, moderate fields up to 5 T are common in cryogenic magnetocaloric prototypes. In light of this, the materials discussed here, in particular the silicone-containing compounds, are very attractive for magnetic hydrogen liquefaction.

Methods

We prepared our Gd₅Ge₄, Gd₅Si_0.25Ge_3.75, and Gd₅Si_0.5Ge_3.5 samples by arc melting high-purity Gd (99.9%), Si (99.9999%), and Ge (99.9999%) from chemPUR. To ensure good homogeneity, we melted the samples five times. The ingots were flipped before each melting step. The sufficient quality of the samples was confirmed by X-ray powder diffraction (Stadi P, Stoe & Cie GmbH) and backscattered electron imaging (Tescan Vega 3 scanning electron microscope). We performed the magnetic measurements using a vibrating sample magnetometer and a Quantum Design physical property measurement system (PPMS). We measured during up and down temperature sweeps at constant magnetic field. For Gd₅Ge₄ and Gd₅Si_0.25Ge_3.75, we determined the magnetization in fields up to 10 T, for Gd₅Si_0.25Ge_3.75 up to 5 T. We did a smoothing of the M(T) curves and interpolated the data for temperature steps of 2K to reduce the noise in ∂M(T)/∂T and to make ΔS_T(T) smoother. We measured the adiabatic temperature changes ΔT_ad at the Dresden High Magnetic Field Laboratory (HLD) using pulsed magnetic fields of different amplitudes up to about 22.6 T. We glued thin chromel-constantan thermocouples between two pieces of the samples using silver paste, allowing the determination of the sample temperature during the short magnetic pulse of about 100 ms⁷⁴. Due to the irreversibility in the region of the magnetostructural transitions of the studied compounds, we applied a discontinuous measurement protocol of cycling the sample temperatures before each field pulse. We heated the sample to above the transition and then cooled it in zero field to the initial temperature T₀ before we applied the magnetic-field pulse. A more detailed description can be found in ref. ⁷⁵.