  Two recent reports confirm that the newly synthesized Sr$_2$CoO$_4$ (formal
oxidation state Co$^{4+}$) shows a high Curie temperature (~ 250 K), but they
report different moments of 1.8 $\mu_B$ and 1 $\mu_B$ per Co. Using both
commonly used functionals in the correlated band approach (LDA+U) as well as
the local density approximation (LDA),the combined effects of correlation and
hybridization with O 2p states are calculated and analyzed. Sr$_2$CoO$_2$ is
already ferromagnetic within LDA (M=1.95 $\mu_B$). Increasing U from zero, the
two LDA+U schemes affect the moment oppositely out to a critical value
$U_c$=2.5 eV, at which point they transform discontinuously from different
states to the same large U state. Fixing U at $U_c$, fixed spin moment
calculations show similar behavior out to a minimum at 1$\mu_B$ (a half
metallic state), beyond which the fully-localized-limit scheme jumps to a state
with energy minimum very near 2$\mu_B$ very close to the LDA moment). Although
the energy minima occur very near integer values of the moment/Co (1$\mu_B,
2$\mu_B$), the strong 3d-2p mixing and resulting 3d orbital occupations seem to
preclude any meaningful S=1/2 or S=1 assignment to the Co ion.
