## 1 Introduction  
The current-perpendicular-to-plane spin valve (CPP-SV) is regarded as one of the most significant spintronics devices, and has great potential for spin transfer torque devices in spin random access memory and ultra-high-speed reading in magnetic read heads of hard disk drivers [1; 2; 3; 4]. The generation and detection of highly polarized spin current is one of the foremost challenges of a CPP-SV. Half metallic Heusler alloys (HMHA) usually have a high Curie temperature (T\({}_{\text{C}}\)) and their lattice constants are close to Ag and Cu. In addition, one spin band (majority spin) of HMHA exhibits metallic behavior, while the other spin band (minority spin) displays semiconductor behavior, and such a band structure could generate a high spin polarized current. Therefore, HMHA has been explored as an electrode of CPP-SV to achieve a high magnetoresistance (MR) ratio [5; 6; 7; 8; 9; 10; 11]. [PERSON] et al. reported a large MR ratio of 74.8% at room temperature (RT) in CPP-SV using Co\({}_{2}\)MnGa\({}_{0.25}\)Ge\({}_{0.75}\)[12]. [PERSON] et al. demonstrated an MR ratio of 58% at RT and 184% at 30 K in Co\({}_{2}\)Fe\({}_{0.4}\)Mn\({}_{0.6}\)Si/ AgCPP-SV [13]. Moreover, a number of CPP-SVs employing a Heusler alloy as the spin injector, such as Co\({}_{2}\)MnSi/Ag, Co\({}_{2}\)FeAl\({}_{0.5}\)Si\({}_{0.5}\)/Ag, and Co\({}_{2}\)FeGa\({}_{0.5}\)Ge\({}_{0.5}\)/Ag, also obtained high MR ratios [14; 15]. More recently, the Hg\({}_{2}\)CuTi type Heusler alloy Mn\({}_{2}\)CoAl has been demonstrated to be one of the spin gapless semiconductors (SGS) from theoretical calculation combined with experimental work [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. The minority spin band of Mn\({}_{2}\)CoAl has an energy gap around the Fermi level, while the top of the valence band and the bottom of the conduction band touch at the Fermi level (see Figure 1). The special band structure allows the holes and electrons to be spin polarized simultaneously. Mn\({}_{2}\)CoAl has attracted much attention and it is considered to possess great potential for spintronics. Since the MR ratio of spin valves based on a Heusler alloy severely depends on its interface properties, and in order to explore outstanding candidates for CPP-SV, we study the interface magnetism, electronic structure, and spin transport properties of Mn\({}_{2}\)CoAl/Ag/Mn\({}_{2}\)CoAl CPP-SV.  
There are two ideal terminations along the (0 0 1) direction in a Heusler alloy Mn\({}_{2}\)CoAl: MnCo and MnAl. Besides, there are two ways to connect a Heusler alloy with an Ag spacer, one of which is where atoms from the Heusler alloy sit on top of Ag atoms, which is noted as MnCoT and MnAlT. The other way is where atoms from the Heusler alloy locate in the bridge site between Ag atoms, which is noted as MnCoB and MnAlB. In addition, according to previous works, a pure Mn-modified artificial termination could improve the spin polarization [27; 28], so MnMn terminations are also considered. When interface Co atoms in MnCoT and MnCoB are replaced by Mn atoms, MnMnT and MnMnB1 are built, respectively. Similarly, when interface Al atoms in MnAlT and MnAlB are substituted with Mn atoms, MnMnT2 and MnMnB2 are built, respectively. Various interface structures of Mn\({}_{2}\)CoAl/Ag/Mn\({}_{2}\)CoAl CPP-SV are exhibited in Figure 2.