Spin Transfer Torque: A Multiscale Picture

Yunkun Xie, Ivan Rungger, Kamaram Munira, Maria Stamenova, Stefano Sanvito and Avik W. Ghosh, Nanomagnetic and Spintronic Devices for Energy-Efficient Memory and Computing , Chapter 4 (2016).
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We present a multi-scale analysis of spin transfer torque (STT) in magnetic tunnel junctions that connect atomistic bandstructure models with quantum transport all the way to circuit-level error rates. We start with quasi-analytical Simmons models for oxide tunneling, modified for contact magnetization. This is then extended to “first principles” DFT studies that capture detailed material chemistry such as orbital symmetry across interfaces. The DFT is then coupled with Non-Equilibrium Green’s Function (NEGF) to evaluate STT in layered structures. We show that the computation is considerably simplified by ignoring self-consistency in the voltage drop across oxides, which proves to be a minor effect. We use our machinery to explain symmetry spin filtering across MgO, an escalation of the tunnel magneto-resistance (TMR) and its dilution in presence of vacancies. We analytically and numerically explain the origin of asymmetry in STT between parallel to antiparallel (P to AP) and AP to P, as arising from the asymmetry in energy of the spin polarized electrons added to or removed from the soft magnet. Finally, we discuss the physics of write-error rates in presence of stochastic thermal kicks. This is done by analytical and numerical solutions to a macro-spin Fokker-Planck model across various parameter ranges. We illustrate the integrated approach, from material embodiment to device and circuit performance metrics, for a variety of systems.