Machine-learning-guided discovery of the gigantic magnetocaloric effect in HoB₂ near the hydrogen liquefaction temperature

The study addresses the need for efficient, environmentally friendly cooling technologies, focusing on magnetocaloric materials suitable for operation near the hydrogen liquefaction temperature (20.3 K). Magnetic refrigeration relies on magnetic entropy change (ΔSM) and adiabatic temperature change (ΔTad), with peak performance typically near a material’s magnetic transition temperature. While significant progress has been made at room temperature, there is growing demand for high-performance materials around 20 K for hydrogen liquefaction and other cryogenic applications. The research question is whether data-driven machine learning can guide the discovery of materials with large magnetocaloric effects near ~20 K. The authors compile magnetocaloric data, build a predictive model for ΔSM, screen candidate materials, and experimentally evaluate the highlighted candidate HoB₂ to validate the approach and identify a strong refrigerant near the target temperature range.

Prior work has demonstrated giant MCEs near room temperature in materials such as Gd₅(Si₁−ₓGeₓ)₄, La(Fe,Si)₁₃, and MnFeP₁−ₓAsₓ, and research has also expanded to systems like NiMn Heusler alloys. For cryogenic applications, Gd₃Ga₅O₁₂ (GGG) is widely used, and MCE-based prototypes have shown suitability for hydrogen liquefaction. Machine learning has been successfully applied to related materials problems (e.g., predicting Curie temperatures, designing permanent magnets and Heusler alloys), but ML approaches specifically targeting MCE prediction have been limited, largely to first-principles studies in non-rare-earth systems. An autogenerated database (MagneticMaterials) and recent reviews have amassed data on magnetic and MCE properties, enabling a data-driven screening strategy to identify promising, yet unexplored, MCE materials.

Data acquisition and ML model: The authors screened 219 journal articles (via MagneticMaterials and literature) to extract magnetocaloric properties, focusing on reported peak |ΔSM| for field changes μ0ΔH ≤ 5 T, yielding 1,644 data points. Features were generated from chemical formulas using XenonPy: (1) composite features from 58 elemental properties via seven featureizers (weighted average, weighted sum, weighted variance, geometric mean, harmonic mean, max pooling, min pooling), (2) element-counting features for elements H (Z=1) through Pu (Z=94), and (3) the experimental field change value. After cleaning, the final feature vector comprised 408 features (343 composite, 64 counting, plus the field-change feature). A gradient-boosted tree model (XGBoost) was trained on 80% of the data; Bayesian optimization with HyperOpt tuned hyperparameters using cross-validated MAE. The final model achieved an MAE of ~1.8 J kg⁻¹ K⁻¹ on the 20% test split. Screening with this model highlighted HoB₂ as a promising candidate near TC ≈ 15–20 K. Sample synthesis and characterization: Polycrystalline Ho–B compound corresponding to HoB₂ was synthesized by arc melting Ho (99.9%) and B (99.5%) under Ar on a water-cooled copper hearth, with multiple flips/remelts for homogeneity, followed by annealing at 1000 °C for 24 h in evacuated quartz and water quenching. X-ray diffraction confirmed the target phase as the main component. Magnetic and thermodynamic measurements: Magnetization was measured using a SQUID magnetometer (MPMS-XL). Specific heat was measured using a PPMS with heat capacity option. Isothermal magnetization and temperature-dependent magnetization were collected over 0–5 T to evaluate |ΔSM| via the Maxwell relation ΔSM = μ0 ∫(∂M/∂T)_H dH. For thermodynamic analysis, zero-field specific heat Cp(T) was integrated to obtain S(T) = ∫(Cp/T) dT from Tmin = 1.8 K. Entropy curves under field were constructed by adding |ΔSM|(T, μ0ΔH) derived from magnetization to S(T, 0 T), enabling estimation of adiabatic temperature change ΔTad from isentropes.

- Machine learning model trained on 1,644 data points (μ0ΔH ≤ 5 T) predicted ΔSM with test MAE ≈ 1.8 J kg⁻¹ K⁻¹ and identified HoB₂ as a top candidate near ~20 K. - Experimental evaluation found a gigantic peak magnetic entropy change |ΔSM| = 40.1 J kg⁻¹ K⁻¹ (0.35 J cm⁻³ K⁻¹) at μ0ΔH = 5 T near the ferromagnetic Curie temperature TC = 15 K. - Magnetization showed ferromagnetic ordering at TC ≈ 15 K and negligible magnetic hysteresis at low temperature (e.g., 5 K), favorable for refrigeration cycles. - Specific heat revealed two anomalies: a lower-temperature peak around ~11 K (likely a spin-reorientation transition analogous to DyB₂) and a main transition at TC ≈ 15 K; entropy curves enabled estimation of ΔTad from combined calorimetry and magnetization data. - The reported |ΔSM| is, to the authors’ knowledge, the highest near the hydrogen liquefaction temperature, positioning HoB₂ as a strong candidate for hydrogen liquefaction and low-temperature magnetic cooling.

The ML-guided workflow effectively targeted materials with large magnetocaloric responses near the desired cryogenic temperature range, addressing the challenge of exploring a vast compositional space with limited experimental bandwidth. By prioritizing HoB₂, the approach led to experimental confirmation of an exceptionally large |ΔSM| at 5 T near TC = 15 K, aligning well with needs for hydrogen liquefaction (~20.3 K). The negligible hysteresis minimizes energy losses and improves reversibility, both critical for efficient magnetic refrigeration. The combined magnetization- and calorimetry-based analysis further supports robust estimates of entropy changes and adiabatic temperature shifts relevant for practical cycle design. The findings validate ML as a powerful guide for magnetocaloric materials discovery and establish HoB₂ as a promising refrigerant material for cryogenic cooling applications, especially hydrogen liquefaction.

This work demonstrates a machine-learning-driven strategy to discover high-performance magnetocaloric materials near cryogenic temperatures. Training an XGBoost model on a curated dataset of 1,644 entries enabled screening and selection of HoB₂, which was synthesized and experimentally shown to exhibit a record-high |ΔSM| of 40.1 J kg⁻¹ K⁻¹ at 5 T near TC = 15 K—among the best reported near the hydrogen liquefaction temperature. The approach bridges data-driven prediction and experimental validation, accelerating materials discovery. Future work could (i) expand datasets and feature representations to further improve predictive accuracy, (ii) investigate the physical origin of the observed lower-temperature anomaly (~11 K) and its influence on MCE performance, (iii) optimize processing/microstructure to tailor hysteresis and thermal conductivity, and (iv) explore compositional tuning around HoB₂ and related borides to adjust TC toward exactly 20.3 K and enhance ΔTad and refrigerant capacity.

- Dataset limitations: Although sizable, the 1,644-point dataset may not cover all chemistries or measurement conditions; reported |ΔSM| values from literature can be heterogeneous in quality and methodology. - Model scope: Features are composition-based with an added field-change input; they do not explicitly capture crystallography, microstructure, or processing history, which can affect MCE. - Field range: Training and experiments were limited to μ0ΔH ≤ 5 T for compatibility; performance at other fields remains to be assessed. - Physical interpretation: The origin of the lower-temperature specific heat peak (~11 K), likely a spin-reorientation transition, remains unconfirmed and could influence operational behavior. - Temperature targeting: While TC = 15 K is close to 20.3 K, further tuning may be needed for optimal hydrogen liquefaction cycles.