Machine Learning of Magnetoelectric Multipoles

In this work, we have developed and implemented equivariant neural networks to help understand and discover new magnetoelectric multiferroics, a class of energy materials with application in energy-efficient memory devices. Magnetoelectric multiferroics are materials exhibiting simultaneous spontaneous switchable electric polarization (ferroelectricity) and magnetization (ferromagnetism or other types of magnetic ordering). A bottleneck in the design of these materials is evaluating their linear magnetoelectricity, which we addressed by using the irreducible representations of their magnetoelectric multipole tensor. We achieved this by constructing efficient symmetry-preserving neural networks (leveraging the e3nn library) that can learn scalar, vector, and tensorial quantities. Next, we employed our methodology to predict new crystal structures and magnetic orientations that maximize linear magnetoelectricity in the BiFeO$_3$ phase space. Not only our work provide a framework to discover new multiferroics, but it will also provide new data-driven frameworks for materials design by enabling the efficient prediction of materials properties with complex forms.