Title: Machine Learning Study of the Magnetic Ordering in 2D Materials

Abstract: Magnetic materials have been applied in a large variety of technologies, from data storage to quantum devices. The development of 2D materials has opened new arenas for magnetic compounds, even when classical theories discourage their examination. Here we propose a machine-learning-based strategy to predict and understand magnetic ordering in 2D materials. This strategy couples the prediction of the existence of magnetism in 2D materials using random forest and the SHAP method with material maps defined by atomic features predicting the magnetic ordering (ferromagnetic or antiferromagnetic). While the random forest model predicts magnetism with an accuracy of 86%, the material maps obtained by the SISSO method have an accuracy of about 90% in predicting the magnetic ordering. Our model indicates that 3d transition metals, halides, and structural clusters with regular transition metals sublattices have a positive contribution in the total weight deciding the existence of magnetism in 2D compounds. This behavior is associated with the competition between crystal field and exchange splitting. The machine learning model also indicates that the atomic SOC is a determinant feature for the identification of the patterns separating ferro- from antiferro-magnetic order. The proposed strategy is used to identify novel 2D magnetic compounds which, together with the fundamental trends in the chemical and structural space, paves novel routes for experimental exploration.