5 Figure 6: (Color online) Transmission T ( k$_{|}$$_{|}$ , E$_{F}$ ) for the P (bottom row) and AP (top row) magnetic configuration within two-dimensional Brillouin zones for Fe(001)/ x (Co)/6(MgO)/ x (Co)/Fe(001) MTJs, x = 0 , . . . , 6 ML (from left to the right). The panels on the right hand side are for Co(001)/6(MgO)/Co(001) MTJs with infinite bcc Co leads. The Brillouin zones cover the range between − π/a and π/a . this model is able to reproduce the principal experimental TMR characteristics $^{24}$. For a detailed analysis of the ef- fect of structural imperfections, however, one has to rely on more sophisticated computational approaches, like the coherent potential approximation or a supercell method. nority transmission maps in Fig. 4 exhibit slight varia- tions which are in anti-phase to the majority transmission modulations, the corresponding RA products in Fig. 5 reveal no signatures of such an even-odd characteristic. The weak thickness dependence can be understood with help of the complex bandstructure in Fig. 3. From first- principles investigations on Fe/MgO/Fe it is known 40,41 that Δ$_{5}$ states are the main carrier within the minor- ity transport channel. Due to the Δ$_{5}$ real band at the Fermi energy it is very likely that these Bloch states just propagate undamped through the Cr interlayer. The minority RA is therefore marginally affected by the Cr spacer and gives contributions which are similar to those of Fe/MgO/Fe MTJs. In this section we discuss the effects of Co interlay- ers embedded into Fe(001)/MgO/Fe(001) MTJs on the electronic transport. With respect to previous theoreti- cal investigations of MgO barriers with bcc Co leads 25 we specifically studied the thickness dependence of ultrathin Co interlayers which are inserted at both Fe/MgO inter- faces. Since Co grows epitaxially only up to few ML on a bcc substrate, the Co thicknesses d$_{Co}$ are restricted to x ≤ 6 ML. The monolayer separations are taken identical to the case of Cr interlayers. Substituting all Fe atoms with Co atoms the effect of semi-infinite bcc Co leads is studied in addition. In contrast to the above finding, the pronounced modu- lations within the AP transmission maps in Fig. 4 — with maxima (minima) at odd (even) x — lead to an even-odd oscillation of the corresponding RA . Due to the spin- filter effect of the Cr interface layer RA AP is in anti-phase to RA P $_{maj}$. This behavior results in TMR ratios which exhibit 2 ML oscillations with periodic changes of the sign. The amplitudes of the TMR ratios, are with about 7000 % and 9000 % at x = 0 ML and 2 ML, considerably larger than for the other thicknesses, with values between about − 100 % and +100 %. This even-odd oscillation of the TMR ratio as a function of the Cr thickness has been observed experimentally 24 but with a phase shift of 1 ML. In more recent experiments 44 it has been found that this phase shift depends on whether the Cr interlayer is grown after or before growth of the MgO barrier. However, a large maximum of the TMR ratio for small Cr thicknesses does not show up in both growth conditions. Instead, an exponential decay of the optimistic TMR ratio for in- creasing x is reported $^{24}$. Since variations of the Cr layer thickness cannot be ruled out in experiment, we assume a model with resistors in parallel connection to mimic Cr- thickness fluctuations. The resistance of the mean thick- ness x is weighted by w , the contributions from x − 1 and x + 1 are weighted by (100 % − w ) / 2, respectively. With already large central weights of w = 96 % and w = 90 % The elsewhere published conductances and TMR ratios 42 are inserted into Fig. 7 as red boxes. In accor- dance with the findings for bcc Co leads $^{25}$, we identify specific Co thicknesses ( x = 3 ML and 5 ML) that ex- First, we recall previously reported conductances and TMR ratios in MTJs with equal thickness variations of both Co interlayers $^{42}$. The corresponding k$_{|}$$_{|}$ -resolved transmissions versus x are shown in Fig. 6 for both mag- netic configurations (P, AP). The shapes of the trans- mission maps for P configuration (bottom row) are — beside the case of the semi-infinite Co leads — very sim- ilar. In contrast to this weak dependence, one observes a rise and a decline of the transmission probabilities in the central regions of the Brillouin zones for the AP con- figuration for small x (top row). The maximum shows up at x = 2 ML. Based on these observations it is rea- sonable to expect a relatively constant behavior of the P conductance and a maximum at x = 2 ML for the AP conductance. B. Fe(001)/ x(Co)/ 6(MgO)/ x(Co)/ Fe(001)