Oscillatory dependence of tunneling magnetoresistance on barrier thickness in magnetic tunnel junctions

TL;DR

This paper presents a theoretical analysis of how tunneling conductance and magnetoresistance oscillate with barrier thickness in magnetic tunnel junctions, revealing classical interference effects rather than quantum confinement as the cause.

Contribution

The authors derive an analytical formula incorporating complex band structure effects and validate it with numerical models, highlighting the oscillatory behavior of TMR.

Findings

TMR exhibits significant oscillations with barrier thickness.

Oscillations are due to classical interference, not quantum confinement.

Analytical formula matches numerical results.

Abstract

The dependence of tunneling conductance and tunneling magnetoresistance (TMR) on barrier thickness in magnetic tunnel junctions is theoretically investigated. The complex band structure of the insulator is taken into account, and an analytical formula for tunneling conductance and TMR is derived. Numerical calculations using a tight-binding model validate the analytical formula. The complex nature of insulator's band structure leads to significant oscillations in tunneling conductance and TMR as functions of barrier thickness. It is demonstrated that these TMR oscillations are not caused by quantum confinement within the barrier, but are instead analogous to classical two-slit optical interference.