Deep-learning electronic-structure calculation of magnetic superstructures

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)×{I,T}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E(3)\times \{I,{{{\mathcal{T}}}}\}$$\end{document}), 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. A deep learning ab initio method for studying magnetic materials is developed, reducing the computational cost and opening opportunities to predict the electronic properties of magnetic superstructures, such as magnetic skyrmions.