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Ab initio comparison of spin-transport properties in MgO-spaced ferrimagnetic tunnel junctions based on Mn$_3$Ga and Mn$_3$Al

We report on first-principles spin-polarised quantum transport calculations (from NEGF+DFT) in MgO-spaced magnetic tunnel junctions (MTJs) based on two different Mn-based Heusler ferrimagnetic metals, namely Mn$_3$Al and Mn$_3$Ga in their tetragonal DO$_{22}$ phase. The former is a fully compensated half-metallic ferrimagnet, while the latter is a low-moment high-spin-polarisation ferrimagnet, both with a small lattice mismatch from MgO. In identical symmetric and asymmetric interface reconstructions across a 3-monolayer thick MgO barrier for both ferrimagets, the linear response (low-voltage) spin-transfer torque (STT) and tunneling magneto-resistance (TMR) effects are evaluated. A larger staggered in-plane STT is found in the Mn$_3$Ga case, while the STT in Mn$_3$Al vanishes quickly away from the interface (similarly to STT in ferromagnetic MTJs). The roles are reversed for the TMR, which is practically 100\% in the half-metallic Mn$_3$Al-based MTJs (using the conservative definition) as opposed to 60\% in the Mn$_3$Ga case. The weak dependence on the exact interface reconstruction would suggest Mn$_3$Ga-Mn$_3$Al solid solutions as a possible route towards optimal trade-off of STT and TMR in the low-bias, low-temperature transport regime.