Learning crystal field parameters using convolutional neural networks

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 twodimensional 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 PrAgSb2 and PrMg2Cu9, 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.

Deep Learning Quantum States for Hamiltonian Estimation

“…Recently, Berthusen et al utilized CNN to extract the crystal field Stevens parameters from the thermodynamic data, which illustrates the validity of CNN-based method in deducing physical information. [35] Goh et al put forward a deep CNN model named Chemception to predict chemical properties with the 2D drawings of molecules. [36] Laanait et al utilized an encoder-decode architecture with convolutional layers to generate the local electron density of material by learning from the diffraction patterns.…”

“…Similar idea has been used in Ref. [35], where the thermodynamic data (specific heat and others) are transformed to images by wavelet transformation before being fed to the CNN. The state-image map we use is known as Qubism, [39] where the obtained images are of fractals [see some examples in Fig.…”