  Complex spin-spin interactions in magnets can often lead to magnetic
superlattices with complex local magnetic arrangements, and many of the
magnetic superlattices have been found to possess non-trivial topological
electronic properties. Due to the huge size and complex magnetic moment
arrangement of the magnetic superlattices, it is a great challenge to perform a
direct DFT calculation on them. In this work, an equivariant deep learning
framework is designed to accelerate the electronic calculation of magnetic
systems by exploiting both the equivariant constraints of the magnetic
Hamiltonian matrix and the physical rules of spin-spin interactions. This
framework can bypass the costly self-consistent iterations and build a direct
mapping from a magnetic configuration to the ab initio Hamiltonian matrix.
After training on the magnets with random magnetic configurations, our model
achieved high accuracy on the test structures outside the training set, such as
spin spiral and non-collinear antiferromagnetic configurations. The trained
model is also used to predict the energy bands of a skyrmion configuration of
NiBrI containing thousands of atoms, showing the high efficiency of our model
on large magnetic superlattices.
