Currents, torques, and polarization factors in magnetic tunnel junctions

TLDR

The authors employ Bardeen’s transfer‑Hamiltonian method together with an ideal‑middle junction model that incorporates atomic disorder in the magnets and interfaces, thereby generalizing the spin‑dependent weighting factor used to compute tunnel‑polarization. The results show that magnetoconduction is tightly coupled to voltage‑driven pseudotorque, which follows a sin θ dependence, is proportional to the opposing magnet’s polarization factor, displays pronounced voltage asymmetry, can remain large even when conductance is suppressed, and that tunnel‑polarization factors remain valid to first order in inverse thickness with algebraic corrections expressed through lateral autocorrelation scales.

Abstract

Bardeen's transfer-Hamiltonian method is applied to magnetic tunnel junctions having a general degree of atomic disorder. The results reveal a close relationship between magnetoconduction and voltage-driven pseudotorque, and also provide a means of predicting the thickness dependence of tunnel-polarization factors. Among the results: (i) The torque generally varies with moment direction as $\mathrm{sin}\phantom{\rule{0.2em}{0ex}}\ensuremath{\theta}$ at constant applied voltage. (ii) Whenever polarization factors are well defined, the voltage-driven torque on each moment is uniquely proportional to the polarization factor of the other magnet. (iii) At finite applied voltage, this relation implies significant voltage-asymmetry in the torque. For one sign of voltage the torque remains substantial even if the magnetoconductance is greatly diminished. (iv) A broadly defined junction model, called ideal middle, allows for atomic disorder within the magnets and $\mathrm{F}\∕\mathrm{I}$ interface regions. In this model, the spin-$(\ensuremath{\sigma})$ dependence of a basis-state weighting factor proportional to the sum over general state index $p$ of ${(\ensuremath{\int}\ensuremath{\int}dydz{\ensuremath{\Psi}}_{p,\ensuremath{\sigma}})}^{2}$ evaluated within the (e.g., vacuum) barrier generalizes the local state density in previous theories of the tunnel-polarization factor. (v) For small applied voltage, tunnel-polarization factors remain legitimate up to first order in the inverse thickness of the ideal middle. An algebraic formula describes the first-order corrections to polarization factors in terms of newly defined lateral autocorrellation scales.