Interpretable machine learning of magnetic transition temperature in Heusler magnets via hierarchical dependence extraction

Abstract

We employ interpretable machine learning to analyze the material dependence of the magnetic transition temperature $T_c$ in ferromagnetic and ferrimagnetic Heusler compounds. For over 200 candidate materials with the same $F\overline{4}3m$ crystal structure but different chemical formulae and lattice constants, we consider both experimental $T_c$ and those computed via classical Monte Carlo simulations using magnetic interactions derived from ab initio calculations. We use the hierarchical dependence extraction (HDE) procedure [Mor\'ee and Arita, Phys. Rev. B 110, 014502 (2024)] to determine how $T_c$ depends on chemical composition and magnetic moments, from leading to higher-order effects, and use these dependencies to construct an explicit expression for $T_c$. Our results show that the HDE framework predicts $T_c$ with accuracy comparable to other machine-learning approaches such as neural network and random forest algorithms while remaining fully interpretable. $T_c$ is primarily governed by the proportions of Fe, Co, and Mn, increasing systematically with their concentration. These findings clarify how chemical composition and magnetic moments influence $T_c$ in collinear Heusler alloys and support the use of the HDE for computationally guided discovery of new functional materials with tailored $T_c$ values.