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A series of layered perovskites Sr$_2$$M$O$_4$ ($M$=Ti, V, Cr, and Mn) isstudied by $ab $ $initio$ calculations within generalized gradientapproximation (GGA) and GGA+$U$ schemes. The total energies in differentmagnetic configurations, including the nonmagnetic, ferromagnetic, the layeredantiferromagnetic with alternating ferromagnetic plane and the staggeredin-plane antiferromagnetic (AFM-II) order, are calculated. It is found thatSr$_2$TiO$_4$ is always a nonmagnetic band insulator. For Sr$_2$MnO$_4$, bothGGA and GGA+$U$ calculations show that the insulating AFM-II state has thelowest total energy among all the considered configurations. For $M$=V and Cr,the GGA is not enough to give out the insulating AFM-II states and includingthe on-site electron-electron correlation effect $U$ is necessary andefficient. The AFM-II state will have the lowest total energy in both caseswhen $U$ is larger than a critical value. Further, the optical conductivityspectra are calculated and compared with the experimental measurements to showhow well the ground state is described within the GGA or GGA+$U$. The resultsindicate that $U$ is overestimated in Sr$_2$VO$_4$ and Sr$_2$CrO$_4$. To makeup such a deficiency of GGA+$U$, the contributions from proper changes in theligand field, acting cooperatively with $U$, are discussed and shown to beefficient in Sr$_2$CrO$_4$.Comment: Final version published on Phys. Rev. B, 19 pages, 8 figures, 2  table

physical review. b, condensed matter and materials physics

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Electronic structure and optical properties of layered perovskitesSr2MO4(M=Ti…