  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. 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 period of oscillation in
the TMR ratio and its asymptotic value for thick nonmagnetic spacer.
