Uncovering critical temperature dependence in Heusler magnets via explicit machine learning

TL;DR

This paper uses interpretable machine learning to analyze and explicitly model how the critical temperature $T_c$ depends on chemical composition and magnetic moments in Heusler magnets, providing insights into material design.

Contribution

It introduces the hierarchical dependence extraction (HDE) method to explicitly model $T_c$ dependence on material features in Heusler compounds, enhancing interpretability and understanding.

Findings

$T_c$ mainly depends on Fe, Co, and Mn proportions.

HDE achieves accuracy comparable to other ML methods.

HDE expression of $T_c$ aligns with phase transition theories.

Abstract

We employ interpretable explicit machine learning to analyze the material dependence of the magnetic transition temperature $T_c$ in ferromagnetic and ferrimagnetic Heusler compounds. For around 200 compounds, we consider both experimental $T_c$ and calculated $T_c$ using \textit{ab initio} determination of magnetic interactions together with a Monte-Carlo solution. We use the hierarchical dependence extraction (HDE) procedure [Mor\'ee and Arita, Phys. Rev. B 110, 014502 (2024)] to extract the dependencies of $T_c$ on chemical proportions and magnetic moments from the main order to the higher order, and construct an explicit expression of $T_c$ from these dependencies. The main results are: (a) $T_c$ is mainly controlled by the proportions of Fe, Co, and Mn, and increases with these proportions, consistent with previous machine learning analyses of ferromagnetic materials. (b) The HDE describes $T_c$ with an accuracy that is comparable to that of other machine learning procedures. (c) The HDE expression of $T_c$ can be interpreted as a generalized order parameter that increases with increasing magnetization amplitude, in qualitative agreement with various theories of phase transitions. These results strengthen our understanding of the material dependence of $T_c$ in collinear Heusler magnets and motivate the further use of HDE in material design.