  While double perovskites A2BB'O6, if ordered, usually form a rock-salt-type
structure with a checkerboard B/B' ordering, it is surprising that Ca2FeMnO6
has alternate FeO2 and MnO2 layers in its perovskite structure. Here we
demonstrate, using density functional calculations, that this unusual layered
ordering facilitates, and is largely helped by, the Fe3+-Fe5+ charge
disproportionation (CD) of the formal Fe4+ ions, which would otherwise be
frustrated in the common rock salt structure. To further verify the important
role of the CD for stabilization of this layered ordering, we carry out a
comparative study for the isostructural Ca2TiMnO6 which has a simple Ti4+-Mn4+
state free of the CD. Our calculations indicate that Ca2TiMnO6 instead prefers
the standard rock salt structure to the layered one. Thus our study shows a
nontrivial interplay between the CD and the type of ion ordering, and proves
that the CD is strongly involved in stabilizing the unusual layered order of
Ca2FeMnO6.
