First-Principles and Machine Learning Investigation of Pressure-Induced Elastic, Electronic, and Magnetic Behavior in FeZrTiX (X = Al, Si) Heusler Alloys

Abstract

In this study, we investigate the structural, electronic, magnetic, and elastic properties of quaternary Heusler alloys FeZrTiX (X = Al, Si) using first-principles calculations based on density functional theory (DFT). The pressure-dependent behavior of these compounds is explored over the range of 0-50 GPa to evaluate their potential for spintronic applications. Our results reveal that the band gap of FeZrTiAl decreases with increasing pressure, while FeZrTiSi exhibits halfmetallic behavior beyond 20 GPa-an essential trait for spintronic devices due to the emergence of 100% spin polarization. The total magnetic moment shows minimal variation under pressure, indicating robust and stable magnetic ordering. The elastic constants remain positive throughout the applied pressure range and satisfy the Born mechanical stability criteria, confirming mechanical integrity. Additionally, the Debye temperature increases with pressure, suggesting enhanced lattice stiffness. To complement the DFT insights, machine learning (ML) approaches were employed to predict the scalar band gap of FeZrTiAl and FeZrTiSi. ML models demonstrated good predictive performance as evaluated by the coefficient of determination (R 2 ) and root mean square error (RMSE), capturing trends consistent with DFT calculations. As expected for spinpolarized half-metallic systems, ML predicted scalar band gaps were lower than DFT spinresolved band gaps, reflecting averaging over spin channels by the models.These combined first-principles and ML results demonstrate that FeZrTiAl and FeZrTiSi possess pressure-tunable magneto-electronic properties, mechanical robustness, and half-metallicity, making them promising candidates for next-generation spintronic applications.