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

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.