Orbital structure and magnetic ordering in layered manganites: Universal correlation and its mechanism

Correlation between orbital structure and magnetic ordering in layered manganites is examined. A level separation between the ${3d}_{{3z}^2-r^2}$ and ${3d}_{x^2-y^2}$ orbitals in a Mn ion is calculated in the ionic model for a large number of the compounds. It is found that the relative stability of the orbitals dominates the magnetic transition temperatures as well as the magnetic structures at zero temperature. A mechanism of the correlation between orbital and magnetism is explained by a theory based on the model with the two $e_g$ orbitals under strong electron correlation.