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[GADO Mohamed Gaber Abdelsaid](https://orcid.org/0000-0002-5293-5532), SHIRAI Tsuyoshi, [NATSUME Kyohei](https://orcid.org/0000-0003-3949-6923), [UCHIDA Akira](https://orcid.org/0000-0002-9193-054X), Takenori Numazawa, [KAMIYA Koji](https://orcid.org/0000-0002-6765-4485)

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[SURVEYING DIFFERENT MAGNETOCALORIC MATERIALS USING AN ACTIVE MAGNETIC REGENERATIVE REFRIGERATOR (AMRR) FOR HYDROGEN LIQUEFACTION](https://mdr.nims.go.jp/datasets/a95e5d3e-a5c9-4522-b314-f232ddd78ca7)

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THERMAG XI 2026 | 11th IIR International Conference on Caloric Cooling and Applications of Caloric Materials | June 7–11, 2026 | Ljubljana, Slovenia    DOI: 10.18462/iir.[organisers to request DOI from IIR].XXXX SURVEYING DIFFERENT MAGNETOCALORIC MATERIALS USING AN ACTIVE MAGNETIC REGENERATIVE REFRIGERATOR (AMRR) FOR HYDROGEN LIQUEFACTION Mohamed G. Gado*, Tsuyoshi Shirai, Kyohei Natsume, Akira Uchida,  Takenori Numazawa, Koji Kamiya  National Institute for Materials Science   Tsukuba, 305-0003, Japan, mohamed.gado@nims.go.jp ABSTRACT Hydrogen serves as a key clean energy carrier for decarbonization. Liquefied hydrogen offers high volumetric energy density for efficient storage and transport. However, its low liquefaction temperature of 20 K makes the process energy-intensive. This study investigates magnetic refrigeration as a potential method to enhance hydrogen liquefaction efficiency. Utilizing the magnetocaloric effect (MCE), magnetic refrigeration enables an efficient cooling cycle, which reduces energy consumption in the liquefaction process. Herein, granular HoAl2 particles have been proposed, given their significant specific heat and strong MCE. To boost the temperature span, an Active Magnetic Regenerative Refrigerator (AMRR) is deployed. In the present study, different magnetocaloric materials have been utilized to examine the hydrogen liquefaction efficiency in comparison to HoAl2. The cooling power and coefficient of performance are systematically evaluated using heat transfer, fluid flow, and magnetic field cycling of the numerical AMRR model. Accordingly, the hydrogen liquefaction efficiency (𝜂𝐼𝐼) and hydrogen yield are evaluated, under an applied magnetic field of 5 T to quantify their impact on system-level performance. The results show a potential second-law efficiency (𝜂𝐼𝐼) over 60% and cooling capacity over 100 W using HoAl2 under an operating range of 20-30 K. On the other hand, ErAl2 can achieve a 𝜂𝐼𝐼 over 40% and cooling capacity over 40 W under the operating range of 10-20 K. Taking advantage of those materials will eventually upgrade hydrogen utilization and push boundaries toward achieving a hydrogen society.    Keywords: Magnetic refrigeration, Hydrogen liquefaction, strong MCE 1. INTRODUCTION Green hydrogen, generated through electrolyzers powered by renewable energy sources, represents a critical instrument for climate change mitigation by enabling the decarbonization of energy-intensive sectors. In particular, traditional coal-based steel production is responsible for about 7% of global carbon dioxide emissions, and hydrogen presents a more sustainable and lower-carbon alternative (Gado, 2026). Hydrogen is decreasing reliance on conventional fossil fuels through the facilitation of domestically produced renewable hydrogen (Kavousighahfarokhi et al., 2026). It also plays a central role in Power-to-X pathways, fostering sectoral integration across the electricity, transportation, and industrial domains. Besides the hydrogen industrial relevance, it can effectively work as an energy storage carrier, which can contribute to grid stability and efficient energy management in buildings (Li and Deusen, 2025; Mastoi et al., 2025). Compared to the hydrogen gaseous form, liquid hydrogen exhibits substantially greater volumetric energy density, as liquefaction reduces its volume by nearly three orders of magnitude, making it effectively suitable for storage and transport (Gado et al., 2025). Nevertheless, hydrogen liquefaction is energy-intensive due to  THERMAG XI 2026 | 11th IIR International Conference on Caloric Cooling and Applications of Caloric Materials | June 7–11, 2026 | Ljubljana, Slovenia   its low liquefaction temperature of 20 K (Matsumoto et al., 2011). Therefore, boosting the efficiency of hydrogen liquefaction is crucial for advancing the technological and commercial development of the hydrogen value chain. After hydrogen liquefaction by Sir James Dewar in 1898, multiple liquefaction systems have been developed. Conventional methods encompass Joule–Thomson and turbine expansion systems (e.g., the Linde–Hampson, Claude, Brayton, Collins, and mixed refrigerant cycles). Adversely, they are energy-intensive, requiring about 10–20 kWh/kg (Zhang et al., 2023), and achieve overall liquefaction efficiencies of only about 20–30% (Matsumoto et al., 2009). By contrast, magnetic refrigeration has recently emerged as a promising substitute for conventional liquefaction systems. This solid-state cooling technology operates based on the magnetocaloric effect (MCE), whereby the temperature of a magnetic material changes in response to variations in the magnetic field. (Gschneidner and Pecharsky, 2008; Pecharsky and Gschneidner Jr, 1999). Magnetic refrigeration systems are considered efficient, compact, and environmentally friendly, as they do not rely on ozone-depleting or greenhouse gases such as chlorofluorocarbons (CFCs) and hydrofluorocarbons (HFCs). Figure 1 shows the classifications of magnetic refrigeration systems, namely adiabatic demagnetization refrigeration (ADR), Carnot magnetic refrigeration (CMR), and active magnetic regenerative refrigeration (AMRR). The ADR systems were successfully used to attain an ultra-low temperature of 0.25 K (Giauque and MacDougall, 1935). ADR systems operate based on the Carnot cycle and are widely applied in advanced technologies, including quantum computing and space instrumentation (Shirron, 2014). Similarly, CMR systems, which are also based on the Carnot cycle, have been explored for hydrogen liquefaction. Several studies have investigated the feasibility of CMR systems. For example, Ohira et al. liquified hydrogen using a pulsed magnet, reaching a second-law efficiency (𝜂𝐼𝐼) of 37% with a cooling capacity of 0.4 W (Ohira et al., 2000). In addition, Kamiya et al. (Kamiya et al., 2007) developed a hydrogen liquefaction system using a reciprocating CMR system operating under a stationary magnetic field.  Figure 1: Classification of magnetic refrigeration systems. Regarding the latest developments in producing liquid hydrogen using AMRR, Jeong et al. (Jeong et al., 1994) developed an AMRR system operating between 4.2 and 1.8 K, achieving continuous cooling to 1.8 K by alternately driving reciprocating flow through two regenerators with a superconducting coil. More recently, Kamiya et al. (Kamiya et al., 2025) assessed a hydrogen liquefier magnetized by a superconducting magnet, reporting a cooling capacity of 7.34 W with a 𝜂𝐼𝐼  of 60.5%. Magnetic RefrigerationAdiabatic Demagnetization Refrigeration (ADR)Carnot Magnetic Refrigeration (CMR)Active Magnetic Regenerative Refrigeration (AMR)Continuous ADRSingle-shot ADRPulsed MagnetCMRReciprocatingCMRPulsed Magnet AMRReciprocating AMRRotating CMRRotatingAMRNo moving partsNo moving parts THERMAG XI 2026 | 11th IIR International Conference on Caloric Cooling and Applications of Caloric Materials | June 7–11, 2026 | Ljubljana, Slovenia   The importance of the present study is to highlight new magnetocaloric material candidates for hydrogen liquefaction. The deployment of HoAl2 indicated a significant hydrogen production yield. Meanwhile, ErAl2 showed an appreciable potential to provide further lower cryogenic temperatures than HoAl2. 2. WORKING PRINCIPLES OF THE AMRR CYCLE FOR HYDROGEN LIQUEFACTION In magnetic refrigeration systems, as illustrated in Fig. 2, subjecting a magnetic field to a magnetic refrigerant causes it to release heat, while removing the magnetic field allows it to absorb heat. The magnetization process is analogous to compression in conventional gas refrigeration, and demagnetization is comparable to expansion. In gas-based systems, cooling performance mainly depends on the gas compression ratio. Similarly, in magnetic refrigeration, the entropy change induced by magnetization serves a comparable function to the compression ratio in determining refrigeration capacity.  Figure 2: Schematic diagram of the AMRR cycle. The AMRR cycle includes four stages, namely, (i) magnetization, (ii) cold-to-hot blow, (iii) demagnetization, and (iv) hot-cold blow (cf. Fig. 3). During the cold-to-hot end blow, the helium flow is allowed to reject heat to the hot-end heat exchanger (HHEX). During the hot-to-cold blow, helium gas is used to cover a cooling load via the cold-end heat exchanger (CHEX). Consecutive cycle operations enable a quasi-continuous cooling effect, which can be used for hydrogen liquefaction.  Figure 3: Schematic diagram of the AMRR cycle. Extensive research has been carried out on different candidates of magnetocaloric materials for hydrogen liquefaction. Amongst them, HoAl2 and ErAl2 possess a strong magnetocaloric effect near the liquefaction temperature of hydrogen (20.3 K) (Gado et al., 2026). Each candidate has its local operating temperature range between the heat rejection and absorption reservoirs. In Fig. 4, HoAl2 shows a strong MCE near the (a) MagnetizationCold endHot end(b) Cold-to-hot blowCold endHot end(c) DemagnetizationCold endHot endMagnetHeMCMCHEX(d) Hot-to-cold blowCold endHot endHHEX THERMAG XI 2026 | 11th IIR International Conference on Caloric Cooling and Applications of Caloric Materials | June 7–11, 2026 | Ljubljana, Slovenia   hot-end temperature of 30 K. Besides, it has a wide distribution of MCE, making it more suitable for hydrogen liquefaction applications. Mainly, at a magnetic field change of 5 T, both ErAl2 and HoAl2 show significant isothermal entropy changes that vary with temperature. For ErAl2, ΔS increases rapidly with temperature, reaching a maximum of about 33 J/kg·K near 10–12 K, and then gradually decreases at higher temperatures. In contrast, HoAl2 exhibits its peak ΔS of around 28–29 J/kg·K at a higher temperature of about 28–30 K, after which it steadily declines. This behavior reflects how each material responds to the applied magnetic field, with the largest entropy changes occurring near their respective magnetic transition temperatures. However, HoAl2 can be more expensive than ErAl2.  Figure 4: Isothermal entropy changes for HoAl2 and ErAl2. 3. COMPUTATIONAL ANALYSIS 3.1. NbTi superconducting magnet design Magnetizing the MCM is produced using a NbTi superconducting magnet, two sets of coils (cf. Fig. 5a). The main coils provide the magnetic field of the magnet set, while the shield coils are used to curtail the effect of the magnet field and the top and bottom, enabling reduced stroke movement. Fig. 5b shows the magnetic field contours, which demonstrate the capability of generating a magnetic field over 5 T.  Figure 5: (a) Superconducting magnet layout, and (b) magnetic field contours.  6431025B (T)(b) Magnetic field contours(a) Superconducting magnet layoutShield coil1Shield coil2Main coil1Main coil2Superconducting magnet set THERMAG XI 2026 | 11th IIR International Conference on Caloric Cooling and Applications of Caloric Materials | June 7–11, 2026 | Ljubljana, Slovenia   3.2. Magnetocaloric materials The main characteristics of HoAl2 and ErAl2 are shown in Fig. 6, including the specific entropy and heat capacity. Meanwhile, Table 1 lists their respective density and thermal conductivity. (a) (b)   (c) (d)   Figure 6. (a) specific entropy of HoAl2, (b) specific heat of HoAl2, (c) specific entropy of ErAl2, and (d) specific heat of ErAl2, at different magnetic densities (Hashimoto et al., 1986).   Table 2 Physical properties of HoAl2 and ErAl2 (Lopatina et al., 2022; Yamamoto et al., 2022). Property HoAl2 ErAl2 Density (kg/m3) 6220 6250 Thermal conductivity (W/m K) 2 1 3.3. AMRR thermos-fluid coupling 3.3.1. Continuity equation (compressed flow) 𝜕(𝜌𝑓)𝜕𝑡+ 𝛻. (𝜌𝑓  𝑢)  = 0 Eq. (1) 3.3.2. Momentum equation 1𝜀𝑏𝜕(𝜌𝑓  𝑢)𝜕𝑡+1𝜀𝑏2 𝜌𝑓  𝑢 . 𝛻𝑢  =  −∇𝑝 +𝜇𝑓𝜀𝑏∇2𝑢 − 𝜇𝑓𝜅𝑢 Eq. (2) here, εb and μf stand for the porosity of the AMRR bed and HTF dynamic viscosity, respectively.   THERMAG XI 2026 | 11th IIR International Conference on Caloric Cooling and Applications of Caloric Materials | June 7–11, 2026 | Ljubljana, Slovenia   3.3.3. Energy equation (1 − 𝜀𝑏) 𝜌𝑠 𝐶𝑝,𝑠𝜕𝑇𝑠𝜕𝑡=  ∇ ⋅ [(1 − ε) 𝑘𝑠 ∇𝑇𝑠] + 𝐴𝑠ℎ𝑠𝑓  (𝑇𝑓 − 𝑇𝑠) + (1 − 𝜀𝑏) 𝑄𝑆   Eq. (3) 𝜌𝑓  𝐶𝑝,𝑓  (𝜕𝑇𝑓𝜕𝑡+  𝑢 . 𝛻𝑇𝑓) = 𝑘𝑓  ∇2𝑇𝑓 +  𝐴𝑠ℎ𝑠𝑓𝜀𝑏(𝑇𝑠 − 𝑇𝑓)  Eq. (4) here, Ts refers to the MCM temperature, and Tf stands for the HTF temperature. The MCM density, specific heat, and thermal conductivity are assigned as ρs, Cp,s, and ks. 3.3.4. The magnetocaloric source term 𝑄𝑆 = − 𝜌𝑠 𝑇𝑠  𝜕𝑆𝜕𝐵 𝐵̇    Eq. (5) where 𝐵̇ is the magnetic field ramp rate. Eventually, Table 3 categorized the main characteristics of the AMRR system. Table 3 Main characteristics of the AMRR system. AMRR characteristics HoAl2 ErAl2 TH 30 (K) 20 (K) TC 20 (K) 10 (K)  𝜀𝑏  0.392 (–) 0.392 (–) 𝑑p 300 (μm) 300 (μm) 3.3.5. Performance indicators In this section, different performance indicators are evaluated, namely (Zheng et al., 2024): Cooling power: 𝑄𝐶  =1𝑡𝑐𝑦𝑐𝑙𝑒∫ 𝑚̇𝑓  𝐶𝑝,𝑓  (𝑇𝐶  −  𝑇𝐶,𝑜𝑢𝑡)𝑡𝑐𝑦𝑐𝑙𝑒0 𝑑𝑡 Eq. (6) Rejected heat (Zheng et al., 2024): 𝑄𝐻  =1𝑡𝑐𝑦𝑐𝑙𝑒∫ 𝑚̇𝑓  𝐶𝑝,𝑓  (𝑇𝐻,𝑜𝑢𝑡  − 𝑇𝐻)𝑡𝑐𝑦𝑐𝑙𝑒0 𝑑𝑡 Eq. (7) Coefficient of performance: 𝐶𝑂𝑃 =𝑄𝐶 𝑄𝐻  −  𝑄𝐶 Eq. (8) Second-law efficiency (𝜂𝐼𝐼): 𝜂𝐼𝐼 =𝐶𝑂𝑃𝐶𝑂𝑃𝐶𝑎𝑟𝑛𝑜𝑡× 100% Eq. (9) Hydrogen liquefaction rate: 𝑚̇𝐻2 =𝑄𝐶Δℎtotal Eq. (10)  THERMAG XI 2026 | 11th IIR International Conference on Caloric Cooling and Applications of Caloric Materials | June 7–11, 2026 | Ljubljana, Slovenia   The total enthalpy difference: Δℎtotal = (ℎ80𝐾,0.25𝑀𝑃𝑎 − ℎ𝑥=1,0.25𝑀𝑃𝑎 ) + (ℎ𝑥=1,0.25𝑀𝑃𝑎 − ℎ𝑥=0,0.25𝑀𝑃𝑎) Eq. (11) herein, 𝑥 denotes the vapor quality. Besides, hydrogen gas is presumably kept initially at 30 K and 0.25 MPa. 4. RESULTS AND DISCUSSION The following section presents the potential application of HoAl and ErAl2. For HoAl2, it is examined with the best operating range of 20-30 K, whereas ErAl2 is examined with 10-20 K. Also, the impact of the helium mass flow rate is sensitively investigated with 80-160 g/s. Figure 7 illustrates the transient behavior of a magnetic refrigeration system over one complete operating cycle of approximately 14.6 seconds, showing temperature evolution at the hot and cold ends (top row) and the corresponding cooling power (bottom row) for two different operating conditions. The cycle is divided into four stages: magnetization (Mag), cold-to-hot heat transfer (C→H), demagnetization (Demag), and hot-to-cold heat transfer (H→C). During magnetization, the hot-end temperature rises due to the MCE, while the cold-end exhibits a smaller temperature rise (because of the lower effect of the magnetic flux). During demagnetization, the hot-end temperature decreases, and the cold end cools further (due to the significant effect of magnetic flux reduction). In Fig. 7b, for ErAl2, a sharper temperature drop at the cold end and a larger temperature span compared to HoAl2 are shown, which indicates the stronger MCE at the cold end (at 20 K) for ErAl2. Figs. 7c and d show the cooling power evolution for HoAl2 and ErAl2, respectively. It can be seen that HoAl2 shows a higher cooling power peak than ErAl2.  Figure 7. Cycle evolution of AMRR temperature and cooling capacity for HoAl2 and ErAl2.   THERMAG XI 2026 | 11th IIR International Conference on Caloric Cooling and Applications of Caloric Materials | June 7–11, 2026 | Ljubljana, Slovenia   Figure 8 compares the performance of ErAl₂ and HoAl₂ magnetic refrigerants with the variation in helium mass flow rate (ṁ = 80–160 g/s), evaluating Qc, COP, 𝜂𝐼𝐼, and hydrogen yield. The Qc increases steadily with mass flow rate for both materials; however, HoAl₂ consistently delivers significantly higher cooling power. ErAl₂ rises from approximately 22 W to 41 W, while HoAl₂ increases from about 55 W to 112 W, indicating nearly 2.5–3 times greater cooling capacity across the range. The COP behavior differs between the two materials. For ErAl₂, COP decreases gradually from about 0.39 to 0.32 as mass flow rate increases, showing reduced thermodynamic efficiency at higher flow rates. By contrast, HoAl₂ exhibits much higher efficiency, with a COP of over 1.22 near 120–140 g/s.   Similarly, the 𝜂𝐼𝐼 decreases from roughly 39% to 32% with increasing flow rate ErAl₂. Whereas HoAl₂ increases from 52% to about 61% at 120–140 g/s and then marginally declines. Accordingly, HoAl₂ demonstrates superior performance due to the proximity of its transition temperature (about 27 K) to the heat rejection temperature of 30 K. Meanwhile, hydrogen daily yield increases nearly linearly with mass flow rate for both materials. ErAl₂ rises from approximately 4.0 to 7.45 kg/day, while HoAl₂ increases from about 9.9 to 20.1 kg/day, almost doubling the hydrogen output compared to ErAl₂. Overall, HoAl₂ outperforms ErAl₂ in cooling capacity, efficiency, 𝜂𝐼𝐼, and hydrogen production across all tested mass flow rates.  Figure 8. Impact of the He mass flow rate on the AMRR cooling power, COP, 𝜂𝐼𝐼, and hydrogen yield, for HoAl2 and ErAl2.  THERMAG XI 2026 | 11th IIR International Conference on Caloric Cooling and Applications of Caloric Materials | June 7–11, 2026 | Ljubljana, Slovenia   5. CONCLUSIONS A quantitative comparison was developed using HoAl2 and ErAl2 to examine the potential for efficient hydrogen liquefaction. Based on the aforementioned findings, the following concluding points can be inferred: • HoAl2 can optimally work within the operating range of 20-30 K and flow rate range of 80-160 g/s, highlighting a cooling throughput of 112 W, a coefficient of performance of 1.2, and 𝜂𝐼𝐼 of 61%. • ErAl2 has a significant magnetic effect at temperatures below 20 K, operating down to 13 K, below the hydrogen triple point. ACKNOWLEDGEMENTS This work was supported by the JST-Mirai Program Grant Number JPMJMI18A3, Japan. We also acknowledge the financial support provided by the Japan Society for the Promotion of Science (JSPS). NOMENCLATURE As Specific surface area of particles (m²·m⁻³) 𝑆 Entropy (J·kg⁻¹·K⁻¹) B Magnetic flux density (T) 𝑡 Time (s) 𝐶𝑝,𝑓 Specific heat capacity of fluid (J·kg⁻¹·K⁻¹) 𝑡𝑐𝑦𝑐𝑙𝑒  AMRR cycle time (s) 𝐶𝑝,𝑠  Specific heat capacity of solid (J·kg⁻¹·K⁻¹) 𝑇 Temperature (K) 𝑑𝑝 Particle diameter (mm) 𝑇𝑓  Fluid temperature (K) ℎ𝑠𝑓  Solid–fluid heat transfer coefficient (W·m⁻²·K⁻¹) 𝑇𝑠  Solid temperature (K) ℎ Specific enthalpy (J·kg⁻¹) 𝑇𝐻 Hot-end temperature (K) 𝑘𝑓  Thermal conductivity of fluid (W·m⁻¹·K⁻¹) 𝑇𝐶  Cold-end temperature (K) 𝑘𝑠  Thermal conductivity of solid (W·m⁻¹·K⁻¹) 𝑇𝐻,𝑜𝑢𝑡  Fluid outlet temperature at hot end (K) 𝑚̇𝑓 Mass flow rate of fluid (kg·s⁻¹) 𝑇𝐶,𝑜𝑢𝑡  Fluid outlet temperature at cold end (K) 𝑚̇𝐻2 Hydrogen liquefaction rate (kg·s⁻¹) 𝑢 Superficial fluid velocity vector (m·s⁻¹) 𝑄𝐶 Cooling power (W) 𝑉 Molar volume (m³·mol⁻¹) 𝑄𝐻 Rejected heat (W) 𝑥 Vapor quality (–) 𝑄𝑆 Magnetocaloric heat source (W·m⁻3) Δℎ𝑡𝑜𝑡𝑎𝑙  Total enthalpy difference (J·kg⁻¹) 𝑅 Universal gas constant (J·mol⁻¹·K⁻¹)   REFERENCES Gado, M.G., 2026. 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