Machine learning study of magnetism in uranium-based compounds

Actinide and lanthanide-based materials display exotic properties that originate from the presence of itinerant or localized $f$ electrons and include unconventional superconductivity and magnetism, hidden order, and heavy-fermion behavior. Due to the strongly correlated nature of the $5f$ electrons, magnetic properties of these compounds depend sensitively on applied magnetic field and pressure, as well as on chemical doping. However, precise connection between the structure and magnetism in actinide-based materials is currently unclear. In this investigation, we established such structure-property links by assembling and mining two datasets that aggregate, respectively, the results of high-throughput density functional theory simulations and experimental measurements for the families of uranium- and neptunium-based binary compounds. Various regression algorithms were utilized to identify correlations among accessible attributes (features or descriptors) of the material systems and predict their cation magnetic moments and general forms of magnetic ordering. Descriptors representing compound structural parameters and cation $f$-subshell occupation numbers were identified as most important for accurate predictions. The best machine learning model developed employs the random forest regression algorithm. It can predict both spin and orbit moment size with root-mean-square error of $0.17{\ensuremath{\mu}}_{\mathrm{B}}$ and $0.19{\ensuremath{\mu}}_{\mathrm{B}}$, respectively. The random forest classification algorithm is used to predict the ordering (paramagnetic, ferromagnetic, and antiferromagnetic) of such systems with 76% accuracy.