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We report a first-principles study of SrFeO$_2$, an infinite-layer oxide withFe atoms in a perfect square-planar coordination down to essentially 0 K. Ourresults reveal this striking behavior relies on the double occupation of the3$d_{z^2}$ orbitals of high-spin Fe$^{2+}$. Such an electronic state resultsfrom the hybridization of iron's 3$d_{z^2}$ and 4$s$ orbitals, which enables alarge reduction of the intra-atomic exchange splitting of the $z^2$ electrons.The generality of the phenomenon is discussed.

Understanding the Unique Structural and Electronic Properties of SrFeO2