Pressure and spin effect on the stability, electronic and mechanic properties of three equiatomic quaternary Heusler (FeVHfZ, Z = Al, Si, and Ge) compounds

In this paper, three equiatomic quaternary  Heusler compounds   −  FeVHfZ (Z = Al, Si, and Ge)  −  are investigated for their structural, magnetic, electronic, mechanic, and lattice dynamic properties under pressure effect. These compounds are optimized for under three structural types and three magnetic phases:  β  is the most stable structure with ferromagnetic phase. The electronic properties reveal that FeVHfAl is a half-metal, and that FeVHfSi and FeVHfGe are spin gapless semiconductors. In addition to  electronic band structure , possible hybridization and partial density of states are presented. Furthermore, the mechanical properties are studied, and the three-dimensional direction-dependent mechanical properties are visualized under varying pressure effects. Our results reveal the half-metal and spin gapless semiconductor nature of the ferromagnetic FeVHfZ compounds, making them promising materials for spintronics applications.