Broadening Hard-Magnet Discovery Beyond Symmetry Constraints via Unified Effective Anisotropy

Machine-learning-driven discovery of rare-earth-lean hard magnets has advanced rapidly, yet existing pipelines have remained constrained either to a fixed composition family or to a single crystal-system class, leaving most compositional and structural space unexplored. We address both limitations by introducing a unified effective anisotropy constant, K_eff, defined consistently across all seven crystal systems, equal to the conventional K₁ in uniaxial cases and-as established here by symmetry-based derivation and density functional theory calculations-designed to approximate the minimum magnetization-reversal barrier that governs the hardness parameter κ in orthorhombic, monoclinic, and triclinic systems, with symmetry-dependent accuracy quantified by angular DFT sampling. With this descriptor, we assemble a magnetocrystalline-anisotropy database and train a two-stage classification-regression pipeline that screens structures without symmetry prefiltering. Applied to Materials Project entries, it recovers established hard magnets and uncovers rare-earth-free κ > 1 candidates in orthorhombic and monoclinic classes-beyond most previous symmetry-restricted screens. Complementing this search, a fine-tuned diffusion model proposes five DFT-confirmed rare-earth-free candidates, four absent from the Materials Project: refinements of a known Pt hard-magnet chemistry plus the noble-metal-free TaFe₃, three of them phonon-stable. These results show that a physically unified anisotropy descriptor can substantially broaden data-driven hard-magnet discovery using established machine-learning and generative workflows.