Orbital Structure and Magnetic Ordering in Layered Manganites: Universal Correlation and Its Mechanism

Correlation between orbital structure and magnetic ordering in bilayered 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. A mechanism of the correlation between orbital and magnetism is investigated based on the theoretical model with the two $e_g$ orbitals under strong electron correlation.