Predicting crystal spin Hall conductivity using a multi-modal transformer with real-space and reciprocal-space fingerprints
Phys. Rev. Materials 9, 093804 – Published 24 September, 2025
DOI: https://doi.org/10.1103/jn3l-hp93
Abstract
Traditional machine learning models for material structure-property prediction primarily rely on real-space crystallographic features. It fails to capture reciprocal-space electron interactions, limiting their ability to capture emergent spin-, orbital-, and momentum-related properties, such as the spin Hall effect. Here, we propose a multimodal transformer architecture to synergize heterogeneous information obtained from both real-space (atomic crystal structures) and reciprocal-space (electronic structures) for predicting intrinsic spin Hall conductivity in crystals. The framework explicitly encodes spin-orbit coupling (SOC) effect through atomic-scale SOC-aware embeddings in the atom representation and employs a symmetry-adapted transformer module. The crystal symmetry priors guide cross-modal attention to preserve the efficiency of modal fusion. Our model demonstrates a significant 22% performance improvement in spin Hall conductivity prediction compared to conventional material property prediction models with single-modality real-space features. Finally, our density functional theory (DFT) calculations further validate the advanced performance of the multimodal SHCTransformer model.
Physics Subject Headings (PhySH)
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This article appears in the following collection:
Machine Learning for Materials Discovery and Understanding
The Editors of Physical Review Materials are pleased to present the Collection on Machine Learning for Materials Discovery and Understanding, highlighting cutting-edge advances in machine learning method development and applications for materials discovery and fundamental understanding of the structure-property-function relationship. The Collection is being guest-edited by Deyu Lu of Brookhaven National Laboratory (USA) and Jinlan Wang of Southeast University (China). Every article published in this collection underwent a rigorous peer review process, adhering to the same high standards applied to all papers. The Physical Review Materials editorial team managed the peer review and made all editorial decisions.
