Study of Correlation Effects in the High Formal Oxidation State Compound   Sr$_2$CoO$_4$
  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. 
K.-W. Lee and W. E. Pickett