Machine learning magnetism classifiers from atomic coordinates.

The determination of magnetic structure poses a long-standing challenge in condensed matter physics and materials science. Experimental techniques such as neutron diffraction are resource-limited and require complex structure refinement protocols, while computational approaches such as first-principles density functional theory (DFT) need additional semi-empirical correction, and reliable prediction is still largely limited to collinear magnetism. Here, we present a machine learning model that aims to classify the magnetic structure by inputting atomic coordinates containing transition metal and rare earth elements. By building a Euclidean equivariant neural network that preserves the crystallographic symmetry, the magnetic structure (ferromagnetic, antiferromagnetic, and non-magnetic) and magnetic propagation vector (zero or non-zero) can be predicted with an average accuracy of 77.8% and 73.6%. In particular, a 91% accuracy is reached when predicting no magnetic ordering even if the structure contains magnetic element(s). Our work represents one step forward to solving the grand challenge of full magnetic structure determination.