Abstract
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 JJ of the ground state multiplet. We evaluate its performance on both theoretically generated synthetic and previously published experimental data on CeAgSb_22, PrAgSb_22 and PrMg_22Cu_99, and find that it can reliably and accurately extract the CF parameters for all site symmetries and values of JJ considered. This demonstrates that CNNs provide an unbiased approach to extracting CF parameters that avoids tedious multi-parameter fitting procedures.
Highlights
We find that our convolutional neural network (CNN) architecture generalizes well for moderately large training data sets and for all site symmetries and values of J considered
Focusing on the ground state multiplet of a single-ion with a definite total angular momentum J, we show how to expand the crystal field (CF) Hamiltonian for a given J and point symmetry group G in terms of operator equivalents, as first introduced by Stevens [5]
The behavior of the quality of the CNN predictions across different input parameters can be largely understood on physical grounds such as arising from energy level crossings, from the smallness of certain CF parameters or from the ratio of the energy bandwidth to the maximal temperature scale
Summary
Rare-earth magnets often exhibit rich magnetic behaviors as a result of various competing energy scales that include spin-orbit coupling, crystal field (CF) and Zeeman energies as well as magnetic exchange interactions [1,2,3,4]. We train the CNN on thermodynamic data for different site symmetries (cubic m3 ̄m, hexagonal 6 ̄m2, tetragonal 4mm) and different values of angular momentum J = 4 and J = 15/2 This corresponds to the rare-earth ions Pr3+ (J = 4) and Er3+ (J = 15/2) in different crystalline environments. We find that our CNN architecture generalizes well for moderately large training data sets and for all site symmetries and values of J considered It provides good estimates of the Stevens parameters from experimental data.
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