Continuous PT-Symmetry Breaking as a Design Variable for Giant Altermagnetic Spin Splitting

2026-04-11

AI Summary

Traditional magnetic point group analysis offers only binary symmetry judgments and struggles to quantitatively predict spin-splitting energies (SSE) in antiferromagnetic materials. This work introduces the Motif Symmetry-Breaking Index (MSBI), which generalizes sublattice symmetry breaking into a continuous scalar descriptor. By integrating physical descriptors with an XGBoost surrogate model, we establish the first tunable and interpretable three-dimensional design space—spanning symmetry breaking, superexchange, and covalency—enabling a paradigm shift from qualitative symmetry classification to quantitative SSE optimization. Guided by Bayesian optimization and validated via density functional theory (DFT), we discover three new high-SSE materials: FeS (1.297 eV), CoS (1.103 eV), and FeAs (1.089 eV). Notably, FeS surpasses the current benchmark CrSb, and its square-planar Fe–S motif is identified as a universal high-splitting coordination unit.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Neuro-Symbolic Learning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Magnetic point-group analysis classifies altermagnets but returns only a binary symmetry verdict, leaving spin-splitting energy (SSE) inaccessible without spin-polarized density functional theory (DFT). This binary ceiling is not fundamental. Sublattice symmetry breaking is promoted here to a continuous, DFT-free scalar -- the Motif Symmetry-Breaking Index (MSBI) -- that quantifies $\mathcal{PT}$-symmetry breaking between antiparallel magnetic motifs directly from crystal coordinates. SHAP analysis of an XGBoost surrogate trained on 3,851 DFT-labeled binary structures identifies three dominant descriptors: MSBI (symmetry-breaking axis), motif packing fraction MPF (superexchange axis), and the $p/d$ electron ratio (covalency axis), each mapping onto a directly tunable experimental handle. A controlled VO--CrSb comparison within the same P$6_3$/mmc host lattice demonstrates that composition alone boosts SSE sevenfold. Bayesian optimization over this three-axis space, followed by independent DFT validation, recovers $α$-NiS (SSE $= 0.823$\,eV) as cross-validation against an independent symmetry-based prediction and identifies three previously unrecognized high-SSE candidates -- square-planar FeS (1.297\,eV), octahedral CoS (1.103\,eV), and FeAs (1.089\,eV) -- all matching or exceeding CrSb. Square-planar Fe--S is proposed as a transferable coordination motif for giant altermagnetic spin splitting, advancing altermagnet design from symmetry classification to continuous quantitative optimization.

Problem

• altermagnet
• spin-splitting energy
• PT-symmetry breaking
• symmetry classification
• density functional theory

Innovation

• altermagnet
• PT-symmetry breaking
• Motif Symmetry-Breaking Index
• spin-splitting energy
• Bayesian optimization