Electronic structures and optical properties of layered perovskites Sr_2MO_4 (M=Ti, V, Cr, and Mn): An ab initio study

A series of layered perovskites Sr${}_2$$M$O${}_4$ ($M$=Ti, V, Cr, and Mn) is studied by $ab$ $initio$ calculations within generalized gradient approximation (GGA) and GGA+$U$ schemes. The total energies in different magnetic configurations, including the nonmagnetic, ferromagnetic, the layered antiferromagnetic with alternating ferromagnetic plane and the staggered in-plane antiferromagnetic (AFM-II) order, are calculated. It is found that Sr${}_2$TiO${}_4$ is always a nonmagnetic band insulator. For Sr${}_2$MnO${}_4$, both GGA and GGA+$U$ calculations show that the insulating AFM-II state has the lowest 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 including the on-site electron-electron correlation effect $U$ is necessary and efficient. The AFM-II state will have the lowest total energy in both cases when $U$ is larger than a critical value. Further, the optical conductivity spectra are calculated and compared with the experimental measurements to show how well the ground state is described within the GGA or GGA+$U$. The results indicate that $U$ is overestimated in Sr${}_2$VO${}_4$ and Sr${}_2$CrO${}_4$. To make up such a deficiency of GGA+$U$, the contributions from proper changes in the ligand field, acting cooperatively with $U$, are discussed and shown to be efficient in Sr${}_2$CrO${}_4$.