AI-accelerated Discovery of Altermagnetic Materials

TL;DR

The paper addresses the challenge of discovering altermagnetic materials, a recently proposed magnetic phase with limited known examples. It introduces an AI search engine that pre-trains a crystal-structure graph neural network with an optimal transport-based Wasserstein decoder and then fine-tunes on a small set of positive samples, guided by symmetry analysis and validated by first-principles calculations. From 91,649 candidate materials, the method discovers 50 new altermagnetic materials (16 metals, 34 insulators), including 4 i-wave altermagnets, with verification via density functional theory. The approach demonstrates few-shot capability and outperforms expert screening, offering a scalable pathway to accelerate discovery of materials with targeted spin and topological properties.

Abstract

Altermagnetism, a new magnetic phase, has been theoretically proposed and experimentally verified to be distinct from ferromagnetism and antiferromagnetism. Although altermagnets have been found to possess many exotic physical properties, the limited availability of known altermagnetic materials hinders the study of such properties. Hence, discovering more types of altermagnetic materials with different properties is crucial for a comprehensive understanding of altermagnetism and thus facilitating new applications in the next generation information technologies, e.g., storage devices and high-sensitivity sensors. Since each altermagnetic material has a unique crystal structure, we propose an automated discovery approach empowered by an AI search engine that employs a pre-trained graph neural network to learn the intrinsic features of the material crystal structure, followed by fine-tuning a classifier with limited positive samples to predict the altermagnetism probability of a given material candidate. Finally, we successfully discovered 50 new altermagnetic materials that cover metals, semiconductors, and insulators confirmed by the first-principles electronic structure calculations. The wide range of electronic structural characteristics reveals that various novel physical properties manifest in these newly discovered altermagnetic materials, e.g., anomalous Hall effect, anomalous Kerr effect, and topological property. Noteworthy, we discovered 4 $i$-wave altermagnetic materials for the first time. Overall, the AI search engine performs much better than human experts and suggests a set of new altermagnetic materials with unique properties, outlining its potential for accelerated discovery of the materials with targeted properties.

Figures (6)

• Figure 1: Workflow of the pre-trained model for searching altermagnetic materials.a, Construction of candidate material datasets using high-throughput screening and symmetry analysis (see Supplementary Appendix Fig. S.1 for details). b, The pre-training autoencoder framework for crystal materials. The input of the model is the crystal structure. Each crystal structure can be represented as a multi-edge graph neural network (GNN). The encoder is built by the graph convolutional neural network. The decoder is built on the Waterstein neighborhood reconstruction. c, The fine-tuning procedure with loading pre-training stage weight matrix. d, The prediction procedure by inputting candidate materials. e, Validation of the altermagnetic property via the first principle electronic structure calculations.
• Figure 2: The network architectures of the auto-encoder and the classifier.a, Details of the auto-encoder model. The encoder consists of three graph convolution layers denoted by $\phi^{(1)}, \phi^{(2)}, \phi^{(3)}$, whose input are node features $h_i^{(t)}$ and neighbors features $H_{\mathcal{N}_i}^{(t)}$, where $t=0,1,2$, respectively. The decoder is composed of a decoder module $\psi_s$ for reconstructing initial node features and three decoder modules $\psi_p^{(1)}, \psi_p^{(2)}, \psi_p^{(3)}$ for reconstructing neighborhood set of node features. We minimize the weighted sum of the reconstruction loss functions for both decoder modules. b, Details of the $\psi_p$ module in the decoder. The $\psi_p$ module includes three MLPs ($\chi_{\mu}, \chi_{\sigma}$ and $\chi_{p}$) and a Gaussian sampler, while the $\psi_s$ module is composed of a single MLP. c, Details of the classifier model. The node features $h_i^{(0)}$ and the neighborhood set of node features $H_{\mathcal{N}_i}^{(0)}$ are fed into the pre-trained encoder. The output node features ${h}_i^{(3)}$ are then transformed to a latent vector ${h}_g$ by a pooling layer. Finally, another MLP and softmax module is designed to output the probability that quantifies whether the material is altermagnetic.
• Figure 3: The crystal and electronic structure of the altermagnets.a, The NdB$_2$C$_2$ crystal primitive cell with magnetic structure. b and c, The electronic band structure of altermagnetic NdB$_2$C$_2$. The electronic structure is calculated under correlation interaction $\rm{U= 5~eV}$. d, The Sc$_2$MnIr$_5$B$_2$ crystal primitive cell with magnetic structure. e and f, The electronic band structure of altermagnetic Sc$_2$MnIr$_5$B$_2$ without and with SOC, respectively. The electronic structure is calculated under correlation interaction $\rm{U= 4~eV}$. g, The Mg$_2$NiIr$_5$B$_2$ crystal primitive cell with magnetic structure. h and i, The electronic band structure of altermagnetic Mg$_2$NiIr$_5$B$_2$ without and with SOC, respectively. The electronic structure is calculated under correlation interaction $\rm{U= 6.56~eV}$. The red and blue lines represent spin-up and spin-down energy bands, respectively.
• Figure 4: The crystal and electronic structure of the altermagnet FeHO$_2$ (31).a, The crystal primitive cell of the altermagnetic FeHO$_2$ (31). b--e, Four significant magnetic structure of FeHO$_2$ (31). The arrows represent the magnetic moments of Fe. f, The Brillouin zone (BZ) with high-symmetry points and lines of altermagnetic FeHO$_2$ (31). g, The relative energy of four significant magnetic states with the variation of correlation interaction U. h and i, The electronic band structure of FeHO$_2$ (31) without SOC. The red and blue lines represent the spin-up and spin-down energy bands, respectively. The electronic structure is calculated under correlation interaction $\rm{U= 4~eV}$.
• Figure 5: The crystal and electronic structure of the altermagnetic $\text{Nb}_2\text{Fe}\text{B}_2$.a, The side view of altermagnetic $\text{Nb}_2\text{Fe}\text{B}_2$. b, The top view of altermagnetic $\text{Nb}_2\text{Fe}\text{B}_2$. c, The Brillouin zone (BZ) with high-symmetry points of altermagnetic $\text{Nb}_2\text{Fe}\text{B}_2$. The cyan plane represents the nodal surface of BZ. The m represents the mirror symmetry $M_y$. d, The anisotropic spin-charge density deriving from an anisotropic crystal field. e, The electronic band structure along high-symmetry directions without spin-orbit coupling (SOC). f, The electronic band structure along non-high-symmetry directions without SOC. The red and blue lines represent the spin-up and spin-down energy bands, respectively. The electronic structure is calculated under correlation interaction $\rm{U= 4.82~eV}$.