2 analyses $^{30,31}$. This structure has been used in pre- vious theoretical studies $^{16,32}$. In detail, a super- cell geometry with six MgO layers sandwiched by 20 Fe layers was used to compute self-consistently the atomic potentials. The insertion of x magnetic in- terlayers in planar Fe(001)/ x (Cr)/6(MgO)/Fe(001) and Fe(001)/ x (Co)/6(MgO)/ x (Co)/Fe(001) junctions was achieved by replacing x Fe monolayers (ML) at the Fe/MgO interfaces by x Cr or Co layers. This procedure implies that Cr and Co atoms occupy the same positions as the replaced Fe atoms; worded differently, the inter- layers follow the bcc structure of the Fe(001) leads. Due to the broken translational invariance in transport direction ( z , i. e. [001]) and the in-plane translational in- variance, the eigenstates of the electrodes are labeled by in-plane wave vectors k$_{|}$$_{|}$ = ( k$_{x}$, k$_{y}$ ). The point group of the two-dimensional lattice is 4 mm . The ballistic conductance C per unit cell area A$_{□}$ is computed for zero bias voltage in terms of transmis- sion probabilities (Landauer-B¨ uttiker approach $^{33}$) at the Fermi energy E$_{F}$ , The transmission probability T ( k$_{|}$$_{|}$ , E$_{F}$ ) is obtained by means of a Green function approach $^{34}$. The integration over the two-dimensional Brillouin zone (2BZ) requires typically about 90 000 k$_{|}$$_{|}$ . The use of special k$_{|}$$_{|}$ points 35 reduces that number to 1 / 8. The resistance area product as normalized quantity, is used to compare the theoretical with experimental data. The optimistic TMR ratio is obtained from the RAs which are computed for the parallel (P) and the anti- parallel (AP) alignment of the two Fe(001) lead magne- tizations, For the normalized TMR ratio the denominator is re- placed by RA $^{AP}$+ RA $^{P}$. Since interfaces determine con- siderably the transport properties, transmittance maps which display T ( k$_{|}$$_{|}$ , E$_{F}$ ) versus k$_{|}$$_{|}$ need to be interpreted by means of the local electronic structure, rather than by the electronic structures of the bulk electrodes. The for- mer is obtained from the layer-resolved Bloch spectral density (SD) of atom a in layer l . G + $_{al}$( E, k$_{|}$$_{|}$ ) is the site-diagonal Green function of that site. The trace involves integration over the ASA sphere and summation over spin-angular quan- tum numbers. It turns out that an oscillatory modulation of T P maj shows up for all k$_{|}$$_{|}$ within the 2BZ. These oscillations are also present in the conductance C which is an inte- gral over the transmission probabilities, eq. (1); hence, there is no destructive interference which would lead to (complete) cancellation. Thus, it is essential to eluci- We start with the tunneling behavior of Bloch states at ¯ Γ ( k$_{|}$$_{|}$ = 0). The associated transmission probabilities for x = 0 , . . . , 7 are plotted in Fig. 1a. Both the minor- ity spin contribution for P and the AP contribution stay almost constant, whereas the majority spin contribution of P decays exponentially with an oscillatory modula- tion. Its decay rate is estimated by an exponential fit, exp( − 2 κx ) with κ = 0 . 75 (green line in Fig. 1a). In the following we present results of the thickness de- pendence of both the conductances and the TMR ratios for ultra-thin Cr interlayers which are embedded at a sin- gle interface in Fe(001)/ x (Cr)/6(MgO)/Fe(001) MTJs. The Cr thickness d$_{Cr}$ is varied in steps of monolayers (ML), x = 0 , . . . , 7 with d$_{Cr}$$_{,}$$_{1ML}$ = 2 . 35 ˚ A, d$_{Cr}$$_{,}$$_{2ML}$ = 4 . 04 ˚ A and d$_{Cr}$$_{,x}$$_{ML}$ = d$_{Cr}$$_{,}$$_{2ML}$ + x · 1 . 69 ˚ A. N$_{al}$ ( E, k$_{|}$$_{|}$ ) = − 1 π ImTr G + $_{al}$( E, k$_{|}$$_{|}$ ) , (4) TMR = RA AP − RA P RA P . (3) RA = 1 C , (2) C = e 2 h ∫ 2BZ T ( k$_{|}$$_{|}$ , E$_{F}$ ) d k$_{|}$$_{|}$ . (1) Figure 1: (Color) (a) Dependence of spin-resolved P (ma- jority, minority) and AP transmissions on a logarithmic scale versus Cr thickness x for Bloch states at k$_{|}$$_{|}$ = 0 in Fe(001)/ x (Cr)/6(MgO)/Fe(001) MTJs, x = 0 , . . . , 7. The green line is a fitted exponential to the majority transmis- sion. The deviation of the majority transmission from this fit is shown in panel (b). These data are fitted by cosine functions (fixed at x = 1) with 2 ML (blue) and 2.17 ML (red) periods. (c) Magnetic profiles of MTJs with Cr layer thicknesses x = 0 , . . . , 7 ML. The green area highlights the magnetic moments of the Cr layers. III. RESULTS A. Cr interlayer in Fe(001)/MgO/Fe(001)