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We report on first-principles calculations of spin-transfer torque (STT) inepitaxial magnetic tunnel junctions (MTJs) based on ferrimagnetic tetragonalMn$_3$Ga electrodes, both as analyzer in an Fe/MgO stack, and also in ananalogous stack with a second Mn$_3$Ga electrode (instead of Fe) as polarizer.Solving the ballistic transport problem (NEGF + DFT) for the nonequilibriumspin density in a scattering region extended to over 7.6 nm into the Mn$_3$Gaelectrode, we find long-range spatial oscillations of the STT decaying on alength scale of a few tens of angstroms, both in the linear response regime andfor finite bias. The oscillatory behavior of the STT in Mn$_3$Ga is robustagainst variations in the stack geometry and the applied bias voltage, whichmay affect the phase and the amplitude of the spatial oscillation, but the wavenumber is only responsive to variations in the longitudinal lattice constant ofMn$_3$Ga (for fixed in-plane geometry) without being commensurate with thelattice. Our interpretation of the long-range STT oscillations is based on thebulk electronic structure of Mn$_3$Ga, taking also into account thespin-filtering properties of the MgO barrier. Comparison to a fullyMn$_3$Ga-based stack shows similar STT oscillations, but a significantenhancement of both the TMR effect at the Fermi level and the STT at theinterface, due to resonant tunneling for the mirror-symmetric junction withthinner barrier (three monoatomic layers). From the calculated energydependence of the spin-polarized transmissions at 0 V, we anticipate asymmetricor symmetric TMR as a function of the applied bias voltage for the Fe-based andthe all-Mn$_3$Ga stacks, respectively, which also both exhibit a sign changebelow 1 V. In the latter (symmetric) case we expect a TMR peak at zero, whichis larger for the thinner barriers because of a spin-polarized resonanttunneling contribution.

Spin transfer torque in Mn$_3$Ga-based ferrimagnetic tunnel junctions from first principles