Validity of the Julliere model of spin-dependent tunneling

TLDR: In this article, the authors consider spin-dependent tunneling between two ferromagnets separated by a simple step barrier, and examine four models for the magnetoconductance ratio of free electrons tunneling through a barrier.

Abstract: We consider spin-dependent tunneling between two ferromagnets separated by a simple step barrier, and examine four models for the magnetoconductance ratio $\ensuremath{\Delta}G/G:$ A model due to Julliere which characterizes the magnetoconductance solely in terms of the tunneling spin polarization, a model due to Slonczewski which provides an approximate expression for the magnetoconductance of free electrons tunneling through a barrier, the exact expression for the magnetoconductance of free electrons tunneling through a barrier, and the numerical calculation of the magnetoconductance of band electrons in iron tunneling through a barrier. We find that the Julliere model does not accurately describe the magnetoconductance of free electrons tunneling through a barrier. Although Slonczewski's model provides a good approximation to the exact expression for free electrons in the limit of thick barriers, we find that the tunneling of band electrons shows features that are not described well by any free electron picture and which reflect the details of the band structure of iron at the Fermi energy.