Currents, Torques, and Polarization Factors in Magnetic Tunnel Junctions

TL;DR

This paper applies Bardeen's tunneling theory to magnetic tunnel junctions with atomic disorder, revealing relationships between magneto-conduction, voltage-driven pseudo-torque, and polarization factors, including their dependence on voltage and thickness.

Contribution

It introduces an ideal middle model incorporating atomic disorder and derives new formulas for polarization factors and torque behavior under various conditions.

Findings

Torque varies as sin theta at constant voltage.

Voltage-driven torque is proportional to polarization factors when well-defined.

Significant voltage asymmetry affects torque even with reduced magnetoconductance.

Abstract

Application of Bardeen's tunneling theory to magnetic tunnel junctions having a general degree of atomic disorder reveals the close relationship between magneto-conduction and voltage-driven pseudo-torque, as well as the thickness dependence of tunnel-polarization factors. Among the results: 1) The torque generally varies as sin theta at constant applied voltage. 2) Whenever polarization factors are well defined, the voltage-driven torque on each moment is uniquely proportional to the polarization factor of the other magnet. 3) At finite applied voltage, this relation predicts significant voltage-asymmetry in the torque. For one sign of voltage the torque remains substantial even when the magnetoconductance is greatly diminished. 4) A broadly defined junction model, called ideal middle, allows for atomic disorder within the magnets and F/I interface regions. In this model, the spin dependence of a state-weighting factor proportional to the sum over general state index of evaluated within the (e.g. vacuum) barrier generalizes the local state density in previous theories of the tunnel-polarization factor. 5) 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 auto-correllation scales.