Quantum oscillation of magnetoresistance in tunneling junctions with a nonmagnetic spacer

We make a theoretical study of the quantum oscillations of the tunneling magnetoresistance (TMR) as a function of the spacer layer thickness. Such oscillations were recently observed in tunneling junctions with a nonmagnetic metallic spacer at the barrier-electrode interface. We calculate the TMR ratio for disordered tunneling junctions containing a spacer at which quantum well states are formed. A single-orbital tight-binding model, the linear response theory, and the coherent potential approximation are used for the calculation. As a function of the spacer thickness, calculated TMR ratio shows damped oscillation around zero with a single period given by the Fermi wave vector of the spacer, which is consistent with observed results. It is shown that momentum selection due to the insulating barrier and conduction via quantum well states in the spacer, mediated by diffusive scattering caused by disorder, are essential features required to explain the observed oscillation in the TMR ratio. We further show that calculated results can be reproduced by the stationary phase approximation, which implies that obtained results hold qualitatively in more realistic band models.