## 3 Result and Discussion
The atom-resolved spin magnetic moments (AMMs) in the first three layers are plotted in Figure 5. In the Mn\({}_{2}\)CoAl bulk, each atom locates at a tetrahedral symmetry position, and each Co and Mn\({}^{\text{A}}\) atom has four Al and four Mn\({}^{\text{B}}\) as the nearest neighbors. While in the Mn\({}_{2}\)CoAl/Ag/Mn\({}_{2}\)CoAl heterostructures, an Ag atom takes the place of half of the nearest neighbors of the interface atom, reducing atomic coordination numbers at the interface. As a result, it breaks the periodic crystal field at the interface and the localization of the \(d\)-electron atom at the interface is enhanced. Therefore, AMMs of interface atoms are strengthened in various structures, and are larger than their corresponding bulk values. Besides, the relative distance between magnetic atoms could also affect the value of AMM. The maximum outward extension belongs to the interface Mn atom in the MnCo\({}^{\text{T}}\) structure, and it results in reduced hybridization and strengthened localization. Therefore, its AMM rises up to the highest value of 3.73 \(\mu_{\text{B}}\). The interface Mn atom in MnMn\({}^{\text{B1}}\) has a lower AMM than in MnCo\({}^{\text{B}}\), although they have a similar outward movement. This could be ascribed to the fact that the interface of MnMn\({}^{\text{B1}}\) is completely occupied by Mn atoms, and the interaction between Mn atoms is stronger than that between Co and Mn atoms. Such an explanation is also applied to the interface Mn atom in MnAl\({}^{\text{T}}\) and MnMn\({}^{\text{T2}}\), as well as MnAl\({}^{\text{B}}\) and MnMn\({}^{\text{B2}}\). Figure 4: The calculated phase diagram of the Mn\({}_{2}\)CoAl/Ag/Mn\({}_{2}\)CoAl (001) interface. The dashed lines denote the thermodynamically accessible region. Figure 5: Atom-resolved spin magnetic moment of magnetic atoms of various terminations. L1, L2, and L3 indicate the interface, subinterface, and next subinterface, respectively. The region with “*” stands for the replaced atom. Owing to the fact that subinterface atoms have small displacement, and the atom at the next subinterface maintains its position, AMMs of the subinterface and the next subinterface atoms could be compared to corresponding values in the bulk, revealing that atoms at deeper layers receive a minor interface effect. AMM of the Al atom presents negative values due to the fact that the \(sp\)-atom has a function of a bridge between local \(d\)-electron atoms according to the RKKY exchange model. Spin transportation of a spintronics device severely depends on interface spin polarization (ISP), which can be written as (D\({}_{\uparrow}-\)D\({}_{\downarrow}\))/(D\({}_{\uparrow}+\)D\({}_{\downarrow}\)), where the D\({}_{\uparrow}\) and D\({}_{\downarrow}\) respectively represent the majority spin density of states and minority spin density of states. First, we calculate the total density of states (DOS). It can be seen from Figure 6 that interface half-metallicity is not detected in various structures. The MnCo\({}^{\text{T}}\) interface displays the highest ISP of 78%, and the ISP of MnMn\({}^{\text{T1}}\) also exhibits a value as high as 45%; while the ISP of MnMn\({}^{\text{T2}}\), MnCo\({}^{\text{T}}\), and MnMn\({}^{\text{B1}}\) are only 26%, 33%, and 32%, respectively. The ISP of MnMn\({}^{\text{B2}}\) even descends to a poor value of 10%. Hence, it reveals that with different Co\({}_{2}\)MnSi/GaAs and CoFeMnSi/GaAs heterojunctions [27; 35], the interface containing the pure Mn atom in Mn\({}_{2}\)CoAl/Ag spin valves could not improve the ISP. Due to the reason that MnCo\({}^{\text{T}}\) and MnMn\({}^{\text{T1}}\) structures possess a high ISP, the project density of states (PDOS) in the interface, subinterface, and the next subinterface of these two terminated structures are further investigated and displayed in Figure 7. As for the interface magnetic atom, its majority spin band shifts to the lower energy region, while the minority spin band moves towards the higher energy region.