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Oscillatory tunneling magnetoresistance (TMR) as a function of spacerthickness is investigated theoretically for a magnetic tunnel junction with anonmagnetic layer inserted between the tunnel barrier and the ferromagneticlayer. TMR is characterized in an analytical form, that is expressed with thetransmission and reflection amplitudes of single interfaces at the Fermi level,and by the extremal wavevectors. Electronic structures with multiple bands aretaken into account in the derivation characterizing the TMR, and the proposedanalytical expression can be directly applied to real junctions. Based on ourmodel, the features of TMR dependence on spacer thickness are discussed,including selection rules for the oscillation period. Numerical calculationsare performed using an envelope-function theory for several cases, and we showthat our model is in good agreement with the exact result.

Oscillatory tunneling magnetoresistance in magnetic tunnel junctions with inserted nonmagnetic layer