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