Magnetic refrigeration, leveraging the magnetocaloric effect (MCE), offers an eco-friendly alternative to conventional gas-cycle refrigeration. The MCE relies on the entropy change in materials upon applying/removing magnetic fields. While substantial research has identified materials with large MCEs near room temperature (e.g., Gd₅(Si₁₋ₓGeₓ)₂, La(Fe,Si)₁₂, MnFeP₁₋ₓAsₓ, and NiMn Heusler alloys), the need for efficient cooling near the hydrogen liquefaction temperature (20.3 K) remains unmet. Liquid hydrogen is crucial for green fuel, rocket propellant, and space exploration. MCE-based refrigeration is well-suited for this application, driving the search for materials exhibiting a significant MCE at cryogenic temperatures. This study employs machine learning (ML) as a data-driven approach to identify promising candidates. Unlike previous work primarily focused on first-principles calculations for non-rare-earth systems, this research uses machine learning on a large dataset from the MagneticMaterials database to predict materials with high MCE properties, particularly around 20 K. The model successfully identified HoB₂ as a potential candidate, leading to its synthesis and experimental characterization.

The authors reviewed existing literature on magnetocaloric materials, primarily focusing on the peak values of magnetic entropy change (ΔSM) for a 5 T field change. Data was compiled from the MagneticMaterials database, encompassing a vast number of materials. This dataset, along with the known limitations of other predictive methods like first-principles calculations (particularly for rare-earth systems), provided the motivation for using machine learning for material selection.

The research employed a three-stage machine learning approach (Figure 1): (a) Data acquisition from 219 journal articles in the MagneticMaterials database, resulting in 1644 data points after processing. (b) Feature extraction from material compositions utilizing XenonPy: composite features (combining 58 elemental properties using seven featureizers - weighted average, sum, variance, geometric mean, harmonic mean, max and min pooling), counting features (amount of each atomic species), and experimental field change features. This yielded 408 features after removing redundant ones. (c) Model construction and optimization using a gradient boosted tree algorithm (XGBoost) and Bayesian optimization (HyperOpt), minimizing the mean absolute error (MAE) using cross-validation. The optimized model achieved an MAE of 1.8 kg·K⁻¹. HoB₂ was identified as a potential candidate. Polycrystalline HoB₂ was synthesized using arc-melting under an argon atmosphere, followed by annealing. X-ray diffraction confirmed the main phase structure. Magnetic measurements were conducted using a SQUID magnetometer (MPMS XL), and specific heat measurements using a PPMS system. The magnetic entropy change (ΔSM) was calculated using the Maxwell relation (equation 1), and the adiabatic temperature change (ΔTad) was determined from specific heat measurements.

Experimental measurements on the synthesized HoB₂ revealed a ferromagnetic transition at a Curie temperature (Tc) of 15 K (Figure 2a). The material shows negligible magnetic hysteresis (Figure 2b). Isothermal magnetization (M-T) curves for various fields (Figure 2c) were used to calculate ΔSM (Figure 2d), revealing a gigantic magnetic entropy change of |ΔSM| = 40.1 J kg⁻¹ K⁻¹ (0.35 J cm⁻³ K⁻¹) for a 5 T field change near Tc. This is, to the authors' knowledge, the highest value reported near the hydrogen liquefaction temperature. Specific heat measurements (Figure 3a) showed two peaks, one at ~11 K (possibly a spin-reorientation transition) and another at Tc=15 K. The entropy curves at different applied fields (Figure 3b) were obtained by combining zero-field entropy data from specific heat measurements with the calculated |ΔSM| values. The adiabatic temperature change (ΔTad) was derived from these entropy curves.

The discovery of a gigantic MCE in HoB₂ near the hydrogen liquefaction temperature validates the effectiveness of the machine-learning approach for identifying novel magnetocaloric materials. The high |ΔSM| value makes HoB₂ a highly promising candidate for hydrogen liquefaction and low-temperature refrigeration applications. The additional peak observed in specific heat and ΔSM curves warrants further investigation to understand its physical origin. The results highlight the potential of data-driven approaches in accelerating materials discovery in the field of magnetocaloric refrigeration.

This study successfully demonstrated the use of machine learning to identify a material with a gigantic magnetocaloric effect. HoB₂ exhibits exceptional MCE properties, making it a strong candidate for cryogenic refrigeration. Future studies should focus on clarifying the origin of the secondary peak observed in the specific heat and entropy data and exploring the potential of HoB₂ in practical refrigeration applications.

The study focused on polycrystalline samples of HoB₂. Further investigation into single-crystal samples would provide more detailed information about the material's properties. The physical origin of the secondary peak observed in the specific heat and ΔSM needs further investigation. The model's prediction accuracy relies on the quality and quantity of data used for training, so the generalization capabilities might be improved with larger and more diverse datasets.