3 Figure 3: (Color) Complex bandstructure of bulk bcc Cr in the commensurate AFM (c-afm) phase along [001] for k$_{|}$$_{|}$ = 0. The real part of k$_{⊥}$ and the exponential decay rate κ (imag- inary part of k$_{⊥}$ ) are shown in panels (b) and (a, c), respec- tively. The color code of the bands indicates the irreducible representations of the point group 4 mm of the associated Bloch states. The green circles at the Fermi energy mark the complex Δ$_{1}$-band of second kind, to k$_{⊥}$ = (0 . 922 , 0 . 503) π / a , which governs the transmission of majority electrons at ¯ Γ (cf. Fig. 1a). Figure 2: (Color online) Fermi surface cross sections in the (100) plane of commensurate AFM Cr (c-afm). The nesting vectors along [001] (arrows) are shown in an extended zone scheme and are listed in Table I. Table I: Nesting vectors of commensurate AFM (c-afm) Cr along [001], as given in Fig. 2, are characterized by their os- cillation periods (in ML). c-afm L’ L” S A B C D’ D” λ [ML] 11.03 9.21 2.12 2.82 3.62 7.21 13.26 6.96 date the underlying mechanism of these oscillations. To strengthen the discussion we focus in the following on the transmissions at ¯ Γ. The oscillation period can be estimated by fitting co- sine functions to the deviation of T P $_{maj}$( k$_{|}$$_{|}$ = 0) from the averaged exponential decay (black diamonds in Fig. 1b). The fit with a period of 2 ML (blue) reproduces only the peak positions but deviates significantly in amplitude. A second fit, with 2 . 17 ML period (red), hits the data best. The 2 ML oscillation can be explained by the local magnetic structure of the layer-wise antiferromagnetic (LAFM) Cr interlayers (Fig. 1c). The magnetic mo- ments of the Cr layers at the Cr/MgO interface is siz- ably enhanced due to the nonmagnetic MgO film. As a consequence of these partially uncompensated magnetic moments, the Cr interface layers act as spin filters for the tunnel currents. Hence, the latter are increased (de- creased) if the magnetic moments within the Cr interface layers are parallel (anti-parallel) to the magnetization of the opposite Fe electrode. Due to the LAFM growth of the Cr interlayer the tunnel current characteristics should exhibit signatures of 2 ML oscillations. The maxima of these oscillations should arise for P (AP) magnetic config- urations of the Fe leads at even (odd) multiples of the Cr interlayer thickness x . This behaviour was already found for LAFM Mn interlayers in Fe(001)/ x (Mn)/Vac/Fe(001) MTJs $^{36}$. However, the mismatch in Fig. 1b appears like an undersampling which cannot be satisfactorily ex- plained by means of the spin filter effect. The better match of the other oscillation period with 2 . 17 ML points to another effect which additionally influences the elec- tronic transport. other wavelengths than the 2 ML. Firstly, one could think of spin-density waves within the Cr interlayers. Spin-density waves are found for Cr bulk systems 37 and are related to nesting vectors of the Fermi surface. Nest- ing vectors that come into question are shown in Fig. 2 for a cross section of the Fermi surface in the (100) plane. The corresponding wavelengths of these vectors along the [001] direction (i. e. in transport and growth direction) are given in Table I. The only vector that exhibits a wavelength which is comparable to that of the transmis- sion (2 . 17 ML) is S, with an oscillation period of 2 . 12 ML. However, since we are interested in the oscillatory onset at k$_{|}$$_{|}$ = 0, the vector S cannot explain our findings be- cause it is offset from ¯ Γ. The oscillatory exponential decay of T P $_{maj}$( k$_{|}$$_{|}$ = 0) is explained most promisingly in terms of the complex bandstructure 38 of the Cr interlayers. Since a (continu- ous) dispersion relation is not defined for thin films, due to lack of translational invariance, we refer to the com- plex bandstructure of bulk Cr along [001]. The latter is decomposed with respect to the irreducible representa- There are two possible mechanisms that may explain