Spin, charge, and orbital ordering in Mn perovskite oxides studied by model Hartree-Fock calculations

The spin, charge, and orbital ordering in $R_{0.5}{A}_{0.5}$MnO${}_3$ and $R_{0.5}{A}_{1.5}$MnO${}_4$ $(R$=rare earth, $A$=Sr, Ca) has been studied by means of unrestricted Hartree-Fock calculations on the multiband $p-d$ model. Since the superexchange interaction between the Mn${}^{3+}$ and Mn${}^{4+}$ sites depends on which type of $e_g$ orbital is occupied at the Mn${}^{3+}$ site, antiferromagnetic states such as $A$ type and $\mathrm{CE}$ type favor a specific orbital ordering. It is shown that the Jahn-Teller distortion consistent with the orbital ordering plays an essential role in stabilizing the experimentally observed antiferromagnetic states.