# Currents, torques, and polarization factors in magnetic tunnel junctions

## 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 sin θ 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 F/I interface regions. In this model, the spin-(σ) dependence of a basis-state weighting factor proportional to the sum over general state index p of (∫∫dydzΨp,σ) 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. ©2005 The American Physical Society.