  Sr$_{2}$NiIrO$_{6}$ would be a ferromagnetic (FM) insulator in terms of the
common superexchange mechanism between the first nearest neighboring (1NN)
magnetic ions Ni$^{2+}$ ($t_{2g}^{6}e_{g}^{2}$) and Ir$^{6+}$ ($t_{2g}^{3}$).
However, the observed antiferromagnetic (AF) order questions this viewpoint. In
this work, we present first-principles calculations and find that while the 1NN
Ni$^{2+}$-Ir$^{6+}$ exchange is indeed FM, the 2NN and 3NN couplings in the fcc
Ir (and Ni) sublattice are AF. Moreover, the 2NN AF Ir-Ir coupling turns out to
be even stronger than the 1NN FM Ni-Ir coupling, thus giving rise to a magnetic
frustration. Sr$_{2}$NiIrO$_{6}$ hence becomes a distorted low-temperature
antiferromagnet. Naturally, a very similar magnetic property in
Sr$_{2}$ZnIrO$_{6}$ can be explained by the frustrated AF coupling in the fcc
Ir$^{6+}$ sublattice. This work highlights the long-range magnetic interaction
of the delocalized $5d$ electrons, and also addresses why the spin-orbit
coupling is ineffective here.
