Deep-learning electronic-structure calculation of magnetic superstructures

Magnetic superstructures — from spin spirals to skyrmions — host rich quantum phenomena but are notoriously hard to simulate with first-principles methods. We extended the DeepH framework to magnetic materials by designing neural networks that rigorously respect Euclidean and time-reversal symmetries, and by learning from diverse magnetic configurations generated via constrained DFT. The method (xDeepH) successfully predicts electronic structures of magnetic skyrmions in moiré-twisted CrI₃, revealing how skyrmions can suppress flat bands — a coupling previously inaccessible to ab initio studies.