This study delves into the phonon spectra, martensitic transformations, and magnetic properties of Ni₂MnGa, Ni₂MnAl, and Pd₂MnZ (Z = Ga, Ge, As) alloys. Focusing on Ni₂MnGa, we observe a martensitic transformation at 202 K, closely related to a pre-transformation phase at 260 K, reflecting the compound's sensitivity to temperature and external influences. Investigations into supercell size and geometry reveal a significant impact on the martensitic elasticity and stability of the TA₂ phonon mode in Ni₂MnGa and Ni₂MnAl. Chemical and structural disorders, especially in Ni₂MnGa, show pronounced effects on crystallographic structures and superelastic properties. Computational analysis using VASP software with PBE and SCAN methodologies highlights differences in the TA₂ phonon mode, indicating the complexities in metallic properties and structural instabilities. The Pd₂MnZ series exhibits diverse magnetic and martensitic behaviours, with the theoretical study underscoring the influence of valence electrons on compound stability. These provide a deeper understanding of the relationship between atomic-level phenomena and macroscopic properties in these complex alloys, paving the way for future research and applications in advanced material science.
