Ref. 25, are not reproduced. Previous investigations of Fe/MgO/Fe systems have shown that conductances de- pend strongly on details of the calculations, in particular on the atomic positions in the interface region. Thus, one is lead to attribute the above mentioned discrepancy to computational details. 

Since increased TMR ratios are not obtained by sym- metric MTJs, we studied the effect of asymmetric MTJs, with one interlayer thickness fixed to 5 ML, in addition. The fixed thickness of 5 ML is chosen with respect to the largest TMR ratio in symmetric MTJs (Fig. 7). Both the RA products and the TMR ratios of the asymmet- ric junctions do not differ significantly from those of the symmetric junctions (Fig. 8). For both kinds of MTJs, the TMR ratio follows the characteristics of RA AP be- cause RA P is almost constant. The presence of the min- imum at x = 2 ML additionally substantiates that the Δ$_{5}$-minority interface resonances, which cause the drop of RA $^{AP}$, are marginally affected by symmetry breaking of an ideal MTJ. 

In summary, the computed conductances and TMR ra- tios exhibit the oscillatory decays for thickness variations of ultrathin Cr interlayers, which have been found in ex- periment. The analysis of the associated transmission probabilities reveals that the tunneling of Bloch states is affected by the interplay of two mechanisms. On the 

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## IV. CONCLUSION 

one hand a spin-filter effect which is induced by the en- hanced magnetic moments of the Cr interface layers and on the other hand the presence of complex bands which are formed within the Cr interlayers. The oscillations are therefore mixtures of 2 ML oscillations of magnetic ori- gin and superpositions of the individual modulations of the tunneling Bloch states, which can be traced back to the corresponding complex wave vectors. Our results fur- ther indicate that spin-density waves are of minor impor- tance for understanding of electronic transport through Fe/MgO/Fe MTJs with ultrathin Cr interlayers. 

The embedding of Co interlayers at both interfaces does not lead to an increase of the TMR ratios with re- spect to Fe/MgO/Fe MTJs. Please note that the refer- ence values for x = 0 (i.e. no Co interlayer) have been calculated under the assumption of ideal interface struc- tures and are therefore probably considerably overesti- mated. Thus, we suggest to include the effects of imper- fect interfaces, which are unavoidable in real samples, in a future investigation. 

Helpful discussions with S. Yuasa, R. Matsumoto, and N. F. Hinsche are gratefully acknowledged. This work is supported by the Sonderforschungsbereich 762, Func- tionality of Oxidic Interfaces. P. B. is supported by the International Max Planck Research School for Science and Technology of Nanostructures. 

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## Acknowledgments 

