Accelerating the electronic-structure calculation of magnetic systems by equivariant neural networks

TL;DR

This paper introduces an equivariant deep learning framework that significantly accelerates electronic-structure calculations in magnetic systems by directly mapping magnetic configurations to Hamiltonian matrices, bypassing traditional iterative methods.

Contribution

The work develops a novel equivariant neural network model that incorporates physical constraints to efficiently predict Hamiltonians for complex magnetic structures, enabling rapid analysis of large superlattices.

Findings

High accuracy on diverse magnetic configurations

Effective prediction of electronic properties for large systems

Bypasses computationally intensive self-consistent calculations

Abstract

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.