## 1 Introduction
The neighbor X atoms occupy the locations at (0, 0, 0) and (0.25, 0.25, 0.25), the residual Y enters (0.5, 0.5, 0.5), and Z is located at (0.75, 0.75, 0.75). Given the different surroundings of neighboring X atoms, the d-states hybridization must be remodulated according to magnetic atomic electronegativity. Such remodulation results in novel magnetism and electronic properties and surface or interface behaviors. Given that high Curie temperature and magnetism follow the Slater-Pauling rule, the Cu\({}_{2}\)MnAl-type Heusler alloys have received attention in earlier studies. Many Cu\({}_{2}\)MnAl-type Heusler alloys, such as Co\({}_{2}\)MnX (X = Si, Ge, Sn) [25], Mn\({}_{2}\)CoZ (Z = Al, Ga, In, Si, Ge, Sn, Sb), [26] and Cr\({}_{2}\)MnZ (Z = P, As, Sb, and Bi) [27], have been predicted with half-metallicity from theoretical ab initio calculations and experimental investigations. TMR experiments of the classic Heusler compound MTJs highlighted significant magnetoresistive effects of these junctions and their potential applications [21; 22; 28]. However, inverse Ti-based Heusler alloys, such as Ti\({}_{2}\)VAl [29], Ti\({}_{2}\)FeIn [30], and Ti\({}_{2}\)MnGa [31], have been previously predicted with \"ideal\" half-metallicity in the bulk phase from first-principle calculations. The relatively high experimental TMR values of approximately 262% at a low temperature and 159% at room temperature have been reported for the Fe-based inverse Heusler Fe\({}_{2}\)CoSi/MgO/Co\({}_{3}\)Fe [32]. However, research on the MTJs of inverse Heusler alloys is still in its infancy. Moreover, to the best of our knowledge, the theoretical or experimental evidence supporting high spin polarization in MTJs for inverse Heusler alloy systems remains scarce. In our previous work, the inverse Heusler alloy Ti\({}_{2}\)CoAl was intensively studied owing to its theoretical 100% spin polarization in the bulk phase from first-principle calculations. The doping effects of d-electrons on the electronic structure and magnetism of the inverse Heusler alloy Ti\({}_{2}\)CoAl were also investigated by substituting Nb and V atoms with Ti(A) and Ti(B) atoms. The doped compounds Ti\({}_{1.25}\)V\({}_{0.75}\)CoAl and Ti\({}_{1.5}\)Nb\({}_{0.5}\)CoAl effectively inhibited the spin-flip excitation and were shown to be promising candidates for spintronic applications [33]. We also investigated the effect of swap, antisite, and vacancy defects on the inverse Heusler alloy Ti\({}_{2}\)CoAl. A Ti vacancy and a high spin polarization of around 95% were observed in the Co-Al swap [12]. For Heusler MTJ applications, evidence of high spin polarization on the surface are crucial because the potential surface states appearing in the minority spin gap can easily destruct the \"ideal\" spin polarization in the bulk phase, as has been reported many times in Cu\({}_{2}\)MnAl-type Heusler alloys. Moreover, (100) surfaces have been comprehensively detected for the Ti\({}_{2}\)CoAl system by researchers. Given the surface states, the calculated surfaces failed to preserve the half-metallicity observed in the bulk, and high surface spin polarizations were predicted in only the CoCo and AlAl terminations [34]. To obtain direct evidence of inverse Heusler MTJs, we extended our research to Ti\({}_{2}\)CoAl heterojunctions. Given its popular use as a binary semiconductor and its well-matching structure with that of Heusler alloys, MgO was selected as the seeding layer in Ti\({}_{2}\)CoAl MTJ. Therefore, the Ti\({}_{2}\)CoAl(100)/MgO interfaces were further examined in this work. Given the fact that interface atomic disorder can significantly change the spin polarization of Heusler MTJs [14], apart from the standard epitaxial Heusler terminated surfaces cleaved along the Miller indices (100) crystal direction (i.e., TiCo and TiAl terminations), the modified artificial terminations that cape the pure atoms (i.e., TTi, CoCo, and AlAl terminations) were also examined to extensively search for possible films with a high spin polarization.