  We present a detailed mean-field study to address the fundamental discrepancy
in the ground state magnetization of $\mathrm{Sr_{2}CoO_{4}}$ (SCO). In
contrast to the ferromagnetic metallic ground state obtained from density
functional theory (DFT), DFT+$U$ gives three ferromagnetic solutions converging
to integer moment values (1, 2 \& 3 $\mu_B$/f.u) over a range of $U$.
Interestingly, two of the solutions are found to exhibit half-metallicity with
correspondingly $S$=1/2 and S=3/2 spin states. The half-metallic ferromagnetic
state with $S$=3/2 is found to be the ground state solution for SCO. Co atoms
show a large deviation from the formal +4 oxidation state indicating the
presence of strong covalency effects. Our results suggest a plausible metal to
half-metal phase transition around $U$($J$)=4.4(1.16) eV. The Fermi surface
study shows gradual collapse in states leading to half-metallicity suggesting
\textit{\textbf{k}}-dependence of effective $U$ around the critical region.
Surprisingly, in the presence of spin-orbit coupling (SOC), unexpectedly large
orbital moment ($L_{z}$=0.6) is noted in SCO putting it among the class of 3$d$
based transition metal compounds exhibiting pronounced orbital magnetization.
The calculations give large magnetocrystalline anisotropy energy (MAE) of
$\sim$48 meV. Large values of orbital magnetic moment contribution and MAE, in
the presence of strong correlation effects, provide a better interpretation of
experimental magnetization observed in SCO.
