Orbital ordering and superexchange in manganite oxides

The magnetic couplings in insulating ${\mathrm{LaMnO}}_{3}$, ${\mathrm{CaMnO}}_{3}$, and the planar analogs ${\mathrm{La}}_{\mathrm{n}+1}$${\mathrm{Mn}}_{\mathrm{n}}$${\mathrm{O}}_{3\mathrm{n}+1}$ are estimated using standard superexchange arguments. The orbital ordering observed in ${\mathrm{LaMnO}}_{3}$ is found to lead to the observed magnetic exchange constants if the effective Mn on-site interaction ${\mathrm{U}}_{\mathrm{Mn}}$ is larger than the charge transfer energy. Differences between the pseudocubic and the planar materials are accounted for. The effect of doping is discussed.