Deep-learning electronic-structure calculation of magnetic superstructures

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Ab initio studies of magnetic superstructures are indispensable to research on emergent quantum materials, but are currently bottlenecked by the formidable computational cost. Here, to break this bottleneck, we have developed a deep equivariant neural network framework to represent the density functional theory Hamiltonian of magnetic materials for efficient electronic-structure calculation. A neural network architecture incorporating a priori knowledge of fundamental physical principles, especially the nearsightedness principle and the equivariance requirements of Euclidean and time-reversal symmetries (E(3)times {I,{{{mathcal{T}}}}}), is designed, which is critical to capture the subtle magnetic effects. Systematic experiments on spin-spiral, nanotube and moiré magnets were performed, making the challenging study of magnetic skyrmions feasible.