Structure-Property Relationships and Machine Learning for Magnetic Susceptibility Prediction in Quantum Materials: An Elastic Net Regression Approach

This study investigates the structure-property relationships and machine learning prediction capabilities for twenty quantum materials that exhibit exotic electronic and magnetic phenomena at cryogenic temperatures. The materials exhibit lattice constants ranging from 3.4 to 4.3 angstroms, electron mobilities ranging from 800-2100 cm²/V·s, band gaps of 0-0.7 eV, band sensitivities of 20-130 (×10⁻ ⁶ ), and critical temperatures ranging from 6-32 K. Statistical analysis reveals exceptionally strong positive correlations (0.93-0.97) between lattice constant, electron mobility, magnetic susceptibility, and critical temperature, while the band gap exhibits strong negative correlations (-0.84 to - 0.93) with all other parameters. These relationships reflect fundamental quantum mechanical principles: expanded lattices facilitate electron wave function delocalization, simultaneously enhancing mobility, magnetic response, and phase transition temperatures. Materials with zero band gaps consistently exhibit superior properties, reaching mobilities greater than 2000 cm²/V·s and susceptibilities greater than 110 (×10⁻ ⁶ ). Elastic net regression successfully uses these relationships to predict magnetic susceptibility, achieving a training R² of 0.99 with an RMSE of 3.34. However, the study suffers from important experimental limitations, in particular the insufficiently large experimental set of only two samples, making the reported experimental R² of 0.88 statistically unreliable. Validation curve analysis identifies the optimal regularization strength (alpha ≈ 0.001- 0.01), where model performance peaks. The dataset reveals clear material hierarchies, with a peak performance of 4.3 Å, suitable for advanced quantum applications, and small lattice constants that severely limit the functionality. This research demonstrates that quantum materials follow predictable structure-property relationships suitable for machine learning prediction, although robust validation requires significantly larger datasets with appropriately sized test sets that implement cross-validation procedures. Key words: Quantum materials, elastic net recoil, structure-property relationships, electron mobility, magnetic susceptibility, critical temperature, machine learning prediction