provides ∼ 0.18 µ$_{B}$ at the O1 site. The total magnetic moment per formula unit for both the solutions is found to be ∼ 3 µ$_{B}$ /fu representative of S = 3/2 spin state. In- terestingly, the energy of the S1 is ∼ 234 meV less than that of the S2 indicating that the S1 corresponds to the true ground state of the system. Present work clearly shows the importance of U in stabilizing a half-metallic state which turns out to be the lowest energy state of the system. Thus, the ground state of Sr$_{2}$CoO$_{4}$ is found to be half-metallic with S = 3/2 spin configuration. Our half-metallic ground state is quite different from that obtained in earlier work. 5 The half-metallic solution of Lee et al . gives S = 1/2 spin configuration. This so- lution corresponds to almost occupied d$_{xz}$ $^{↓}$/ d$_{yz}$ ↓ states and half-filled d$_{xy}$ ↓ state whereas our S1 corresponds to the opposite situation where d$_{xz}$ $^{↓}$/ d$_{yz}$ ↓ states are almost vacant and d$_{xy}$ ↓ state is filled. Here it is worth mention- ing that we have also included the generalized gradient approximation in the calculations whereas Lee et al . have only considered the local density approximation (LDA). This may give an impression that the different formula- tions of the exchange correlation functional can be the reason for the difference between our results and that of the Lee et al . To address this issue we have also carried out detailed calculations using spin polarized LDA+ U method. The results obtained from these calculations are found to be almost the same as those obtained by GGA+ U . This indicates that the existence of two solu- tions has nothing to do with the approximations involved in treating different exchange correlation functional and solely related to the orbital polarization. The total and partial densities of states correspond to the half-metallic solution are shown in Fig. 5. The large spin polarization is evident from the total den- sity of states plotted in Fig. 5(a). The lowest occupied band shows the signature of van Hove singularity aris- ing from the e$_{g}$ symmetric states as evident from Fig. 5 (c). The d$_{xy}$ orbital is fully occupied and a gap of ∼ 1 eV is created between it and the unoccupied d$_{xz}$ / d$_{yz}$ or- bitals in the down-spin channel. In the up-spin channel only e$_{g}$ sector provides the conducting electrons with a dominating contribution from the d$_{z}$ $^{2}$− r 2 electrons. The d$_{x}$ $^{2}$− y 2 symmetric PDOS in the vicinity of the E$_{F}$ is al- most flat suggesting that the temperature dependent be- haviour of the compound should be decided by d$_{z}$ $^{2}$− r 2 electrons. Fig. 5(b) shows a huge exchange splitting ( ∼ 7.5 eV) for the degenerate d$_{xz}$ / d$_{yz}$ orbitals. This result also suggests that the Coulomb correlation in the pres- ence of strong hybridization between Co 3 d and O 2 p orbitals along with a tetragonal distortion makes full oc- cupation of nondegenerate d$_{xy}$ orbital energetically more favorable. This may be considered as a signature of a ferrodistortive Jahn-Teller ordering. In order to study the detailed nature of magnetic inter- actions we have calculated the Heisenberg exchange pa- rameters J$_{0}$$_{i}$ between the Co atoms using FLEUR code, 22 where 0 and i stand for the central atom and coordina- tion shell index, respectively. The Co atom sitting at the Table 2: The Heisenberg exchange parameters ( J$_{0}$$_{i}$ ) up to fourth nearest neighbours (coordination shells) ob- tained by ferromagnetic GGA calculations using FLEUR origin is considered as the central atom, Fig. 1. The values of J$_{0}$$_{i}$ up to 4 th nearest neighbours (coordination shells) are shown in Table 2. It is evident from the table that the first and third nearest neighbour interactions are ferromagnetic whereas second and fourth nearest neigh- bour interactions are antiferromagnetic in nature. The value of J$_{01}$ is found to be 19.06 meV which is about 15 times larger than the values of neighbouring interactions. This suggests that the effective magnetic interaction in Sr$_{2}$CoO$_{4}$ is ferromagnetic in nature, which is in accor- dance with the experimentally observed ferromagnetic ground state. 3 Under the mean-field approximation we calculated the Curie temperature ( T$_{C}$ ) of ∼ 887 K, which is roughly 3.5 times larger than the experimentally mea- sured value. Such discrepancy between the experimental and calculated T$_{C}$ is not surprising as the overestimation of T$_{C}$ under mean-field approximation is well known in the literature. 23–25 FIG. 5: (Color online) The density of states corresponds to the ferromagnetic half-metallic solution obtained from GGA+ U ( U = 4 eV and J = 0.4 eV) calculation. (a) to- tal density of states (TDOS), (b) d xz /d yz (thin lines) and d xy (thick lines) states, and (c) d$_{x}$ $^{2}$$_{−}$y2 (thin lines) and d$_{z}$ $^{2}$$_{−}$r2 (thick lines) states. In (d) partial density of p symmetric states for planar oxygen (O1) and apical oxygen (O2) are represented by thin and thick lines, respectively. -8 -6 -4 -2 0 2 4 -1 0 1 PDOS(statese V $_{-1}$ atom-1 ) (d) O1 2 p O2 2 p PDOS (states eV $_{-1}$ atom-1 ) Energy (eV) -1 0 1 (c) Co  e$_{g}$ d$_{x}$ $^{2}$-y2 d$_{z}$ $^{2}$-r2 Co  t$_{2g}$ -2 0 2 (b) d$_{xz}$ / d$_{yz}$ d$_{xy}$ DOS (states eV $_{-1}$ fu-1 ) -5 0 5 (a) TDOS 5