Spin transfer torque in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Mn</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mi>Ga</mml:mi></mml:mrow></mml:math>-based ferrimagnetic tunnel junctions from first principles

Abstract

We report on first-principles calculations of spin-transfer torque (STT) in epitaxial magnetic tunnel junctions (MTJs) based on ferrimagnetic tetragonal ${\mathrm{Mn}}_{3}\mathrm{Ga}$ electrodes, both as analyzer in a Fe/MgO stack, and also in an analogous stack with a second ${\mathrm{Mn}}_{3}\mathrm{Ga}$ electrode (instead of Fe) as polarizer. Solving the ballistic transport problem ($\mathrm{NEGF}+\mathrm{DFT}$) for the nonequilibrium spin density in a scattering region extended to over 7.6 nm into the ${\mathrm{Mn}}_{3}\mathrm{Ga}$ electrode, we find long-range spatial oscillations of the STT decaying on a length scale of a few tens of angstroms, both in the linear response regime and for finite bias. The oscillatory behavior of the STT in ${\mathrm{Mn}}_{3}\mathrm{Ga}$ is robust against variations in the stack geometry (e.g., the barrier thickness and the interface spacing) and the applied bias voltage, which may affect the phase and the amplitude of the spacial oscillation, but the high (carrier) frequency mode is only responsive to variations in the longitudinal lattice constant of ${\mathrm{Mn}}_{3}\mathrm{Ga}$ (for fixed in-plane geometry) without being commensurate with the lattice. Our interpretation of the long-range STT oscillations is based on the bulk electronic structure of ${\mathrm{Mn}}_{3}\mathrm{Ga}$, taking also into account the spin-filtering properties of the MgO barrier. Comparison to a fully ${\mathrm{Mn}}_{3}\mathrm{Ga}$-based stack shows similar STT oscillations, but a significant enhancement of both the TMR effect at the Fermi level and the STT at the interface, due to resonant tunneling for the mirror-symmetric junction with thinner barrier (three monoatomic layers). From the calculated energy dependence of the spin-polarized transmissions at 0 V, we anticipate asymmetric or symmetric TMR as a function of the applied bias voltage for the Fe-based and the all-${\mathrm{Mn}}_{3}\mathrm{Ga}$ stacks, respectively, which also both exhibit a sign change below $\ifmmode\pm\else\textpm\fi{}1\phantom{\rule{4pt}{0ex}}\mathrm{V}$. In the latter, symmetric, case we expect a TMR peak at zero, which is larger for the thinner barriers because of a spin-polarized resonant tunneling contribution.

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