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Machine Learning Approach to Predict the Curie Temperature of Fe- and Pt-Based Alloys

Svitlana Ponomarova, Oleksandr Ponomarov, Yurii Koval

TL;DR

This work addresses predicting the Curie/Néel temperature for Fe- and Pt-based ternary alloys by developing a data-driven ML pipeline that explicitly incorporates composition and atomic ordering via a high-dimensional feature set $f(c_{Fe}, c_{Pt}, c_{Pd}, r_{Fe}, r_{Pt}, r_{Pd}, s_{Fe}, s_{Pt}, s_{Pd}, Z_{Fe}, Z_{Pt}, Z_{Pd}, \eta)$. Using Azure ML and Monte Carlo cross-validation, the Voting Ensemble emerges as the top predictor with a normalized RMSE of $NRMSE=0.051$, outperforming other regressors on a 100-row experimental dataset. The study analyzes Fe-Pt-Pd systems with Pd up to 5 at.% in both ordered ($L1_2$) and disordered states, revealing that Pd substitution effects on Tc depend on ordering, and that Tc trends align with binary FePt data. A thermodynamic model is developed to relate the free energy $f(c_{Fe}, c_{Pt}, c_{Pd}, \eta)$ to the observed Tc behavior, highlighting a critical Pd concentration where configurational free-energy extrema occur. The approach generalizes to other multicomponent alloys and provides a computational pathway for rapid, data-driven design of magnetic materials, with practical implications for spintronics and data storage.

Abstract

Various techniques can be employed to determine the temperature of magnetic transformation, whether it be the Curie or Neel temperature. The standard procedure typically involves creating alloys with defined compositions and performing measurements experimentally. Alternatively, these temperatures can be predicted based on a material known physical and chemical properties prior to experiments. We identified an optimal feature set and selected the most effective algorithm. Our findings show that the Voting Ensemble model, when combined with Monte Carlo cross-validation, achieves the highest prediction accuracy. The normalized root mean squared error serves as the primary performance metric. For implementation, we utilize the Azure Machine Learning framework for its robust computational and integration capabilities. This approach offers an efficient and reliable strategy for designing and predicting the Curie temperature of ternary alloys. The paper also highlights potential applications of the model and its extensions for other systems.

Machine Learning Approach to Predict the Curie Temperature of Fe- and Pt-Based Alloys

TL;DR

This work addresses predicting the Curie/Néel temperature for Fe- and Pt-based ternary alloys by developing a data-driven ML pipeline that explicitly incorporates composition and atomic ordering via a high-dimensional feature set . Using Azure ML and Monte Carlo cross-validation, the Voting Ensemble emerges as the top predictor with a normalized RMSE of , outperforming other regressors on a 100-row experimental dataset. The study analyzes Fe-Pt-Pd systems with Pd up to 5 at.% in both ordered () and disordered states, revealing that Pd substitution effects on Tc depend on ordering, and that Tc trends align with binary FePt data. A thermodynamic model is developed to relate the free energy to the observed Tc behavior, highlighting a critical Pd concentration where configurational free-energy extrema occur. The approach generalizes to other multicomponent alloys and provides a computational pathway for rapid, data-driven design of magnetic materials, with practical implications for spintronics and data storage.

Abstract

Various techniques can be employed to determine the temperature of magnetic transformation, whether it be the Curie or Neel temperature. The standard procedure typically involves creating alloys with defined compositions and performing measurements experimentally. Alternatively, these temperatures can be predicted based on a material known physical and chemical properties prior to experiments. We identified an optimal feature set and selected the most effective algorithm. Our findings show that the Voting Ensemble model, when combined with Monte Carlo cross-validation, achieves the highest prediction accuracy. The normalized root mean squared error serves as the primary performance metric. For implementation, we utilize the Azure Machine Learning framework for its robust computational and integration capabilities. This approach offers an efficient and reliable strategy for designing and predicting the Curie temperature of ternary alloys. The paper also highlights potential applications of the model and its extensions for other systems.

Paper Structure

This paper contains 17 sections, 5 equations, 8 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Motivation
  3. Contribution
  4. Paper Structure
  5. Related works
  6. Computational technique
  7. Results and Discussion
  8. Object of research
  9. Prediction of Curie temperature in Fe-Pt-Pd
  10. Thermodynamic analysis
  11. Summary
  12. Model applications
  13. Conflict of interest
  14. Acknowledgment
  15. Data Availability Statement
  16. ...and 2 more sections

Figures (8)

  • Figure 1: Operational Workflow Overview for ML Models
  • Figure 2: Curie temperature for $Fe_{75}Pt_{25-X}Pd_X$ where Pd replaces Pt atoms
  • Figure 3: Curie temperature for $Fe_{75-X}Pt_{25}Pd_X$ where Pd replaces Fe atoms
  • Figure 4: Disordered state for Fe-Pt alloys
  • Figure 5: Atomic ordering in Fe-Pt alloys
  • ...and 3 more figures