Dependence of the tunneling magnetoresistance on an inserted nonmagnetic layer

When a crystalline nonmagnetic (NM) spacer is inserted between a magnetic layer and a tunnel barrier in magnetic tunnel junctions (MTJs), the tunneling magnetoresistance (TMR) oscillates and decays as a function of the NM spacer thickness. An envelope-function theory is adopted to express the electronic states of the MTJ, and the dependence of the TMR on the spacer is theoretically investigated. The TMR is obtained from an numerically exact calculation and from an analytical model proposed previously, and the two results are shown to be in good agreement.