  We report a first-principles study of SrFeO$_2$, an infinite-layer oxide with
Fe atoms in a perfect square-planar coordination down to essentially 0 K. Our
results reveal this striking behavior relies on the double occupation of the
3$d_{z^2}$ orbitals of high-spin Fe$^{2+}$. Such an electronic state results
from the hybridization of iron's 3$d_{z^2}$ and 4$s$ orbitals, which enables a
large reduction of the intra-atomic exchange splitting of the $z^2$ electrons.
The generality of the phenomenon is discussed.
