## 3 Results and Discussion
### Pressure Effect of VFeScZ (Z = Sb, As, P)  
Based on the above analysis and discussion, we can find that the VFeScSb and VFeScP are typical ferromagnetic semiconductors with band gap widths of about 0.372 eV and 0.172 eV, respectively, when they stay in the ground state. However, the VFeScAs is predicted to be a half-metal, because the Fermi level of VFeScAs is at the edge of the spin-up gap and the spin-down semiconductor gap is slightly damaged. The detection from the structure indicates that the stability of the alloy with type-I structure will be further enhanced with the decrease of the lattice constant. Generally, external pressure on the alloy system is a possible way to decreasing lattice. Therefore, in this subsection, we conduct a specific discussion to detailly reveal the pressure effect on electrons and magnetism in the type-I VFeScZ (Z = Sb, As, P) alloy. As shown in Figure 7, we can find that in VFeScZ the lattice constant slowly decreases and the total energy linearly enhances with increasing pressure. This change is characterized by the linear decrease in the volume of the whole system because of pressure, which makes the bonding between the atoms shorter and the interaction between them stronger. As a result, the energy and lattice constant will linearly change in the alloy system until the novel phase change occurs. In Figure 7, the data is recorded within the pressure range from 0 GPa to the phase transformation point. Figure 6: Energy band diagram of (**a**) VFeScSb, (**b**) VFeScAs, and (**c**) VFeScP with type-I structure. Figure 7: Lattice constant (\(L\)) and the energy change, (\(\Delta E\)) in type-I (**a**) VFeScSb, (**b**) VFeScAs, and (**c**) VFeScP as a function of pressures. \(\Delta E\) is the relative energy with respect to zero pressure. The DOS and PDOS of VFeScZ under different pressures are shown in Figure 8. For the VFeScSb, see Figure 8a, when the pressure increases, the spin-down band gradually moves toward the low energy orientation and the spin-up band quickly shifts to the high energy region, which causes the indirect band gap width determined by the valence band top and the conduction band bottom to decrease. As the pressure increases to 50 GPa, the spin-down valence band moves near the Fermi level. With increasing pressure, the spin-up conduction band continues to move toward the high-energy region, while the spin-down valence band almost keeps still. When the pressure is increased to 132 GPa, in the type-I VFeScSb alloy, the semiconductor gap gets close to zero at the Fermi level. Therefore, we can judge that the type-I VFeScSb will be transformed from ferromagnetic semiconductor to SGS under external pressure of about 132 GPa. For the type-I VFeScAs alloy, see Figure 8b, along with the increase of pressure it was found that the position of the spin-down conducting band did not change with respect to the Fermi level, while the spin-up band moves rapidly toward the high energy region. This results in a remarkable shrink of the semiconductor gap. When the pressure is near 58 GPa, the gap width of the type-I VFeScAs system almost becomes zero, indicating the phase transition from ferromagnetic semiconductor to SGS. Similar behavior is seen in the type-I VFeScP alloy, as shown in Figure 8c. With the increase of pressure, the spin-up valence band moves toward the high energy region continuously, and the spin-down conduction band moves slightly toward the Fermi surface until it touches the Fermi level as the pressure continues to increase. Obviously, when the pressure reaches 32 GPa, the VFeScSb alloy system becomes a typical SGS. In order to understand the mechanism of the band gap width changing with the increase of pressure, the indirect band gap of semiconductor at different pressures are detected and plotted in Figure 9. It is seen that the semiconductor gap decreases gradually and finally becomes 0 for type-I VFeScSb and VFeScP alloys.