First-Principles Study of Mg-Induced Phase Stabilization in Ga$_2$O$_3$ polymorphs

In this study, we investigate the effect of Mg incorporation on the relative phase stability of the four primary Ga$_2$O$_3$ polymorphs using density functional theory (DFT) calculations, with the goal of rationalizing experimental observations suggesting that diffusion from MgAl$_2$O$_4$ substrates contributes to relative stabilization of the $γ$ phase. Mg incorporation is modeled up to 25% of Ga sites within supercells derived from fully relaxed unit cells of each polymorph. Our results show that while $β$-Ga$_2$O$_3$ remains the thermodynamically most stable phase, the enthalpic differences between polymorphs decrease with increasing Mg content. The inherently disordered $γ$ phase, with its high configurational entropy, becomes less energetically unfavorable under Mg substitution, suggesting that entropy-driven stabilization may facilitate its formation under high-temperature and/or nonequilibrium growth conditions such as those previously reported. These findings provide a thermodynamic rationale for the experimental observation of the $γ$ phase during epitaxial growth on MgAl$_2$O$_4$ spinel substrates.