## 3 Results and Discussion
### Interface Electronic Properties  
In order to analyze the electronic properties of interface layer atoms, the densities of state (DOS) of the two outermost layer atoms in Heusler alloy Ti\({}_{2}\)CoAl and the first interface layer atom in MgO for 10 potential terminations were analyzed in the Ti\({}_{2}\)CoAl/MgO supercell. Figure 2 shows that the atom-resolved DOS at the middle layer was extremely close to the feature of the bulk. In all 10 terminations, we could find that the spin-down gap in the bulk had been destroyed. In TiAl-Mg and AlAl-O termination, the spin-down gap narrowed down compared with the middle layers. In the rest of the eight terminations, some peaks from interface/subinterface Co or Ti atoms appeared in the spin-down gap and crossed the Fermi level. For the interface/subinterface Al atom, a slight spin polarization was observed at the Fermi level. In all 10 terminations, all interface Mg and O atoms suffered an extremely small spin polarization at the Fermi level, thereby indicating that the interface alloy-Mg and alloy-O bonding was not strong enough to contribute to the electronic properties at the Fermi level. Unfortunately, unexpected interface states appeared at the Fermi level and destroyed the \"ideal\" half-metallicity observed in the bulk. Meanwhile, the interface states in the AlAl-Mg, TiTi-Mg, TiCo-Mg and TiTi-O terminations had entirely filled the spin-metallic gaps in the spin-down channel at the Fermi level. By contrast, in the CoCo-Mg and CoCo-O terminations, the electronic structure was very similar to the behavior of the middle layer atoms. Evidence of high spin polarization has been previously reported in the CoCo termination of the Ti\({}_{2}\)CoAl(100) surface system [34]. In the TiAl-Mg and AlAl-O terminations, the half-metallic gap suffered minimal destruction, and the DOSs were in accordance with that of the middle layer atoms. We deduced that a high spin polarization might be reserved in these terminations. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Termination** & **Layers** & **Ti** & **Co** & **Al** & **O** & **Mg** \\ \hline bulk & & 0.94 (1.68) & \(-\)0.48 & \(-\)0.14 & 0.00 & 0.00 \\ \hline TiAl & (100) surface & 1.08 & \(-\)0.36 & \(-\)0.18 & 0.00 & 0.00 \\ \hline TiCo & (100) surface & 1.70 & \(-\)0.20 &  
Given the significance of interface polarization in MTJs, we examined the interface spin polarizations in various terminations, especially for the several interface layers in contact with the MgO slab. Table 3 summarizes the spin polarization \(P\), spin-up state density \(N_{\uparrow}\), and spin-down state density \(N_{\downarrow}\) at the Fermi level. The contributions from the interface and subinterface layers in Ti\({}_{2}\)CoAl (labeled I-type) and from the three interface layers with the addition of the first interface layer in MgO (labeled II-type) were also analyzed. Surprisingly, the lowest value was less than 1% in three interface layers for the TiTi-Mg terminations for the TiCo-Mg, TiAl-Mg, and AlAl-Mg terminations. However, for the first two interface layers in the Ti\({}_{2}\)CoAl slab, the \(P\) value was the largest. According to the Julliere formula, we could deduce that the TMR value was not larger than 150% in the Ti\({}_{2}\)CoAl/MgO(100) heterojunction at low temperature. Figure 2: _Cont._