is in line with the experimentally observed magnetic easy axis. 3 This value of magnetocrystalline anisotropy energy (MAE) is ∼ 2.1 meV/Co more than that obtained by Lee et al . 5 Based on the magnetization data of Ref. [3], Lee et al . have given a rough estimate of ∼ 1.5 meV/Co for the MAE. This value is about three times larger than that of the Lee et al . and about half of our value. The inclusion of SOC keeps the spin magnetic moments almost intact and induces 0.1 µ$_{B}$ orbital magnetic moment at the Co site. The above GGA calculations provide the good repre- sentation of experimentally observed electronic and mag- netic properties of the system including magnetocrys- talline anisotropy. However, the on-site Coulomb inter- action parameter U has been found to be important in understanding the detailed electronic and magnetic prop- erties of the 3 d transition metals oxies. 12 Therefore, it would be interesting to see the effect of U on electronic and magnetic states of the compound under GGA+ U . In this approximation U and J are used as parameters. The values of U and J required to reproduce the elec- tronic structure of a compound are sensitive to the ap- proximations used in the calculations. 13,14 Moreover, it is well known that the GGA+ U calculations often converge to the local minima depending on the starting electronic configurations used. 15–17 In the light of these facts we have varied U from 3 to 5 eV and fixed the value of J to 0.4 eV as estimated for the e$_{g}$ electrons. To know the exact ground state we have also used different starting configurations for the Co 3 d electrons. This range of U is found to provide the good representation of the exper- imentally observed electronic and magnetic properties of different Co based systems. 13,18–21 Based on symmetry consideration we used 10 differ- ent starting electronic configurations for the Co atom in the calculations. For these configurations only two kind of FM solutions S1 and S2 are found to exist. The S1 and S2 give half-metallic and metallic states, respec- tively. The difference in the electronic structure of Co in both the solutions can be found from Fig. 4, where we have plotted the Co 3 d PDOS calculated for U = 4 eV. The half-metallicity with a gap of about 1 eV in the down-spin channel is evident for the S1. The S2 shows metallic state with a large t$_{2}$$_{g}$ symmetric states around the E$_{F}$ in the down-spin channel. In the up-spin channel both the solutions provide similar PDOS of e$_{g}$ character in the vicinity of E$_{F}$ . The comparison of Co 3 d PDOS obtained from the S2 and FM GGA solutions indicates that S2 is originating from the FM GGA solution. The S1 solution is quite different and it has origin to the orbital polarization. The PDOS closer to E$_{F}$ along with occupancies of the Co 3 d orbitals listed in Table 1 can be used to charac- terize both the solutions. Numbers written in normal and italics are corresponding to the S1 and S2, respec- tively. The t$_{2}$$_{g}$ ↑ states are fully occupied in both the solutions. The main difference between the two solutions arises from the t$_{2}$$_{g}$ ↓ sector. In the S1 and S2, d$_{xy}$ ↓ state can be considered as fully occupied and unoccupied, re- spectively. The contribution of d$_{xz}$ $^{↓}$/ d$_{yz}$ ↓ state below the E$_{F}$ is small ( ∼ 0.17 electron) and can be considered as fully unoccupied in the S1, which gives rise to the half-metallic state. However, d$_{xz}$ $^{↓}$/ d$_{yz}$ ↓ state is roughly half-filled ( ∼ 0.6) in the S2 and mainly responsible for the metallic state. Thus, we can represent the S1 and S2 by d$_{xy}$ ↓ 1 and d$_{xz}$ ↓ 1 / $^{2}$/ d$_{yz}$ ↓ 1 / 2 electronic configurations, respectively. Both the solutions give roughly same magnetic mo- ment ( ∼ 2.7 µ$_{B}$ ) for the Co. The S1 induces magnetic moment of ∼ 0.08 µ$_{B}$ at the O2 site whereas the S2 d$_{xz}$ / d$_{yz}$ d$_{xy}$ d$_{x}$ $^{2}$− y 2 d$_{z}$ $^{2}$− r 2 Total d Up 0.95, 0.94 0.94, 0.95 0.84, 0.90 0.88, 0.82 4.56, 4.55 Down 0.17, 0.61 0.92, 0.14 0.22, 0.25 0.36, 0.25 1.84, 1.86 Up - Down 0.78, 0.33 0.02, 0.81 0.62, 0.65 0.52, 0.57 2.72, 2.69 Table 1: Electronic occupancies of different Co 3 d or- bitals along with the total number of d electrons for both the spin channels obtained from ferromagnetic GGA+ U ( U = 4 eV and J = 0.4 eV) calculations corresponding to two self consistent solutions represented by S1 (normal) and S2 (italics). FIG. 4: (Color online) The partial density of Co 3 d symmet- ric states obtained from ferromagnetic GGA+ U ( U = 4 eV and J = 0.4 eV) calculations corresponding to two conversed solutions represented by S1 and S2. t 2 g and e g orbitals are denoted by solid and dashed lines, respectively. -8 -6 -4 -2 0 2 4 -2 -1 0 1 2 S1  Energy (eV) t$_{2g}$ e$_{g}$ Down Up P D OS (states eV -1  atom -1 ) -8 -6 -4 -2 0 2 4 S2 Down Up t$_{2g}$ e$_{g}$  Energy (eV) 4