Determining the anisotropy field of permanent magnets: A comparison of current methodologies

Abstract

With the exponential rise of data-driven materials research strategies, datasets play a crucial role in developing models and predicting material properties. However, machine learning requires accurate datasets and well-defined descriptors to ensure reliable predictions. In the field of energy applications, the demand for high-performance and sustainable permanent magnets is growing, and machine learning has the potential to accelerate the discovery of new compounds. One of the key criteria for achieving hard magnetic properties is the magnetocrystalline anisotropy field ($H_A$). Ideally, and if available, $H_A$ is determined using single crystals of a defined shape. However, growing phase-pure single crystals is not always feasible for certain hard magnetic compounds due to phase stability challenges. In this study, we compare and evaluate the most commonly used methodologies for estimating the anisotropy field using Ce${}_2$Fe₁₄B as a case study. Specifically, we compare different methods – including hard-axis saturation, magnetization area, Sucksmith–Thompson, the law of approach to saturation, and singular point detection – applied to single crystals, aligned polycrystals, and isotropic polycrystals. Our results show that for single crystals, almost all methods provide accurate results within a 2% relative error when the demagnetizing field is properly accounted for. However, for aligned polycrystalline powders, the highest errors are observed, reaching up to 17% compared to single-crystal data. In contrast, for bulk polycrystalline samples, only the singular point detection method using a pulse magnetometer with second derivative analysis enables an accurate estimation of the anisotropy field. These findings are particularly relevant for materials scientists seeking to use reliable descriptors in machine learning datasets and to accurately estimate the anisotropy field to accelerate new hard magnet discovery.