## 3 Results and Discussion
From 0 to 40 GPa, elastic anisotropy factor A becomes smaller and smaller, and the anisotropic characteristics of GaFe(CN)\({}_{6}\) become more obvious. At the same time, the bulk modulus increases from 104.3 to 208.8 GPa, and the Debye temperature reaches 798.5 K. The increase in pressure makes the atoms more closely linked, which makes the compound's stiffness. The spin-polarized band structures and density of states of GaFe(CN)\({}_{6}\) at 0 GPa are depicted in Figure 1:4 It can be clearly seen that the conduction band minimum (CBM) and valence band maximum (VBM) in majority-spin are located at the same highly symmetric G-point, and a band gap of 4.01 eV is formed between the conduction band and the valence band, indicating that this spin direction has insulator behavior. The bands pass through the Fermi level in minority-spin to exhibit a metallic feature. According to the band theory of quantum solid, GaFe(CN)\({}_{6}\) is a half-metal with 100% spin polarization. Figure 6 presents the total and local density of state of GaFe(CN)\({}_{6}\) at 0 GPa. It can be clearly seen that the half-metallic behavior of GaFe(CN)\({}_{6}\) is mainly due to the formation of spin splitting in the vicinity of the Fermi level by the 3d states of the Fe atom and the 2p states of the N atom. The 3d states of the Fe atom and the 2p states of the N atom have obvious spin hybridization in the energy range of \(-\)1.01 to 0.35 eV. The 3d state of the Fe atom is also the most important contributor to the total density of GaFe(CN)\({}_{6}\). From the magnetic properties generated by spin splitting, it can be inferred that Fe atoms are also the main source of GaFe(CN)\({}_{6}\) magnetic moment. In the energy range of \(-\)2.7 to \(-\)1.01 eV, the density of states is mainly derived from the C-2p, N-2p, and Ga-4P states, and the 3d of the Fe atom has little contribution in this region. Figure 1:5 Elastic modulus of GaFe(CN)\({}_{6}\) under different pressures. Figure 1:6 Band structure and density of states (DOS) of GaFe(CN)\({}_{6}\) at 0 GPa. The electronic structure calculation of pressure from 0 to 40 GPa shows that the minority-spin direction of GaFe(CN)\({}_{6}\) always shows metallic behavior. In this case, the physical properties of GaFe(CN)\({}_{6}\) under pressure are basically determined by the majority-spin electronic states. Figure 7 depicts the CBM and VBM in majority-spin of GaFe(CN)\({}_{6}\) as a function of pressure. With the increase of pressure, both CBM and VBM move towards high energy. Once the pressure is greater than 35 GPa, VBM will cross the Fermi level and make GaFe(CN)\({}_{6}\) majority-spin also show metallic behavior. In this way, the half-metallicity of GaFe(CN)\({}_{6}\) will disappear. It is worth noting that, as can be seen from Figure 7, the density of states across the Fermi level at 40 GPa is very low. This means that the material may not be able to hold enough free electrons and therefore has poor conductivity or metallicity. The effect of pressure on the electronic structure of GaFe(CN)\({}_{6}\) can also be confirmed by Figure 1:7 In Figure 8, we can see that the minority-spin electronic states are hardly affected by external pressures. A slightly more obvious feature is that the conduction band in the high energy region moves toward a higher energy position as the pressure increases. However, this does not change the metallicity of the minority-spin direction. The electronic structure in majority-spin changes are consistent with the analysis in Figure 1:8 When the pressure is 40 GPa, the valence band in majority-spin crosses the Fermi level. Figure 1:9 Total and local density of states of GaFe(CN)\({}_{6}\) at 0 GPa. Figure 2.0 Conduction band minimum (CBM) and valence band maximum (VBM) of GaFe(CN)\({}_{6}\) in majority-spin under different pressures. At 0 GPa, the total magnetic moment per formula unit of GaFe(CN)\({}_{6}\) is 1.0 \(\upmu_{\text{B}}\), which is very consistent with the characteristic that the molecular magnetic moment of half-metallic magnetic materials is an integral value.