提出可连续调控的对称性破缺指标，实现巨反磁自旋分裂材料设计。
Continuous PT-Symmetry Breaking as a Design Variable for Giant Altermagnetic Spin Splitting
- 引入MSBI指标量化晶格中反平行磁畴的PT对称性破缺程度。
- 通过组合优化找到三种新候选材料，自旋分裂能达1.297 eV以上。
- 无需密度泛函计算，直接通过晶体结构预测高自旋分裂材料。
磁点群分析虽能分类反磁体，但仅给出二元对称性判断，无法直接获取自旋分裂能（SSE），需依赖自旋极化密度泛函理论（DFT）。本文突破此二元限制，将亚晶格对称性破缺提升为可连续调节的、无需DFT的标量——基元对称性破缺指数（MSBI），可直接从晶体坐标量化反平行磁基元间的$$\mathcal{PT}\u0024$对称性破缺。基于3,851个已标注的二元结构训练的XGBoost模型，结合SHAP分析识别出三个主导描述符：MSBI（对称性破缺轴）、基元填充率MPF（超交换轴）和$\u0024p/d\u0024$电子比（共价轴），每项均可对应实验可调参数。在相同P$6_3$/mmc母体晶格中，控制组分使VO–CrSb的自旋分裂能提升七倍。基于三轴空间的贝叶斯优化，经独立DFT验证，成功复现$\alpha$-NiS（SSE=0.823 eV）作为对称性预测的交叉验证，并发现三种此前未被识别的高自旋分裂候选材料：平面正方形FeS（1.297 eV）、八面体CoS（1.103 eV）和FeAs（1.089 eV），均达到或超过CrSb水平。提出平面正方形Fe–S为可迁移的高自旋分裂配位构型，推动反磁体设计从对称性分类迈向连续定量优化。
原文摘要 · Abstract (English)
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.
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