The discovery of topological states in two-dimensional (2D) magnetic systems has emerged as a frontier in condensed matter physics and material science. However, predicting band topology in 2D magnetic materials encounters significant challenges due to insufficient ground state information. To address this challenge, we develop an active learning framework that efficiently explores a size of over 13,000 in a comprehensive data set originating from 2265 potential 2D magnetic materials with different magnetic states. Our framework incorporates advanced surrogate models based on ensemble learning models and adaptive sampling strategies specifically designed to handle the inherent complexity of imbalanced topological classifications and diverse geometric structures. Through systematic screenings, 63 promising 2D magnetic topological materials with well-defined Fermi surfaces and stable magnetic configurations under ambient conditions are identified. Notably, we discover that CoO2 exhibits rich topological phase transitions, showcasing both insulating and semimetallic topological nontrivial phases under varying magnetic structures. First-principles calculations further reveal these phases are protected by the material's symmetry, with robust topological edge states remaining intact even under perturbation from edge onsite energy. Our framework provides a reliable methodology for the accelerated discovery of topological materials, with corresponding results paving pathways for the design of quantum devices.
Cao et al. (Thu,) studied this question.