  Using density functional calculations, we find that the newly synthesized
Ca$_2$FeOsO$_6$ has the high-spin Fe$^{3+}$ ($3d^5$)-Os$^{5+}$ ($5d^3$) state.
The octahedral Os$^{5+}$ ion has a large intrinsic exchange splitting, and its
$t_{2g\uparrow}^3$ configuration makes the spin-orbit coupling ineffective.
Moreover, there is a strong antiferromagnetic (AF) coupling between the
neighboring Fe$^{3+}$ ($S$ = 5/2) and Os$^{5+}$ ($S$ = -3/2), but the AF
couplings within both the fcc Fe$^{3+}$ and Os$^{5+}$ sublattices are one order
of magnitude weaker. Therefore, a magnetic frustration is suppressed and a
stable ferrimagnetic (FiM) ground state appears. This FiM order is due to the
virtual hopping of the $t_{2g}$ electrons from Os$^{5+}$ ($t_{2g\downarrow}^3$)
to Fe$^{3+}$ ($t_{2g\uparrow}^3e_{g\uparrow}^2$). However, if the experimental
bended Fe$^{3+}$-O$^{2-}$-Os$^{5+}$ exchange path gets straight, the $e_g$
hopping from Fe$^{3+}$ ($t_{2g\uparrow}^3e_{g\uparrow}^2$) to Os$^{5+}$
($t_{2g\uparrow}^3$) would be facilitated and then a ferromagnetic (FM)
coupling would occur.
