Using the method of scattering matrix, we investigated the quantum coherent transport in ferromagnet/insulating barrier/semiconductor/insulating barrier/ferromagnet (FM/I/SM/I/FM) magnetic double tunnel junctions. When the mean free path of the tunneling electrons(lp) is comparable to the thickness of the middle semiconductor(L), the tunneling magneto-resistance(TMR) shows quantum oscillations with the variation of the L. At the inflection point of the oscillations the cut-off vector will appear if lp is much longer than L. The analysis reveals that it is the mismatch of the electron momentum in ferromagnet and semiconductor layer that leads to the appearance of the cut-off vector. The decay of oscillation amplitude caused by phase loss restrains the occurrence of the cut-off vector. We arrive at the conclusion that the value of TMR is the square of the value of spin injection efficiency(SIE) η1 in a single junction; and the value of TMR is also the square of the value of SIE η2 in double junctions(parallel configuration)if L is much longer than lp. For this reason, the value of SIE in a single junction or double junctions can be obtained by measuring the value of TMR of double junctions. Numerical calculations indicate that the ratio TMR/η22 will also show quantum oscillations with the variation of the L if the L is comparable to the lp.
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