Learning crystal field parameters using convolutional neural networks

• Published in: arXiv.org
• Main Authors: Berthusen, Noah F, Sizyuk, Yuriy, Scheurer, Mathias S, Orth, Peter P
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 18.05.2021
• Subjects: Algorithms; Angular momentum; Artificial neural networks; Crystals; Integers; Machine learning; Magnetic materials; Magnetic permeability; Mathematical analysis; Neural networks; Parameters; Physics - Computational Physics; Physics - Statistical Mechanics; Physics - Strongly Correlated Electrons; Rare earth elements; Wavelet transforms
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2011.12911

We present a deep machine learning algorithm to extract crystal field (CF) Stevens parameters from thermodynamic data of rare-earth magnetic materials. The algorithm employs a two-dimensional convolutional neural network (CNN) that is trained on magnetization, magnetic susceptibility and specific heat data that is calculated theoretically within the single-ion approximation and further processed using a standard wavelet transformation. We apply the method to crystal fields of cubic, hexagonal and tetragonal symmetry and for both integer and half-integer total angular momentum values \(J\) of the ground state multiplet. We evaluate its performance on both theoretically generated synthetic and previously published experimental data on CeAgSb\(_2\), PrAgSb\(_2\) and PrMg\(_2\)Cu\(_9\), and find that it can reliably and accurately extract the CF parameters for all site symmetries and values of \(J\) considered. This demonstrates that CNNs provide an unbiased approach to extracting CF parameters that avoids tedious multi-parameter fitting procedures.