Figure 4.

Band structure and layer resolved density of states (DOS) for the octahedral and tetrahedral layers of LSMO brownmillerite (a–d) ABO_2.5 with ferromagnetic coupling in the octahedral layers and G-type antiferromagnetism in the tetrahedral layers, and (e–h) ABO_2.67 with A-type antiferromagnetism in the octahedral layers and C-type antiferromagnetism in the tetrahedral layers. For the bands, the k _x and k _y k _y are parallel to the layers, while the k _z is normal to the layers. The bands and DOS are further projected onto spherical harmonics. The bands where the projection on the Mn: $d_{x^2-y^2}$ and Mn: $d_{z^2}$ orbitals on each k-point exceeds 33% are coloured according to the legend; the rest of the points are coloured grey. (b,c), and (f,g) show the projection on the different octahedral layers for ABO_2.5 and ABO_2.67 respectively (DOS oct layer), while (d) and (h) shows the sum of both tetrahedral layers (DOS tet layer).