Abstract
A general consideration is presented for the magnetic interaction at an interface
between a perovskite manganite and other transition-metal (TM) oxides.
The latter is specified by the electron number $n$ in the $d_{3z^2-r^2}$ level as $(d_{3z^2-r^2})^n$.
Based on the molecular orbitals formed at the interface and the generalized Hund's rule,
the sign of the magnetic interaction is rather uniquely determined.
The exception is when the $d_{3z^2-r^2}$ orbital is stabilized in the interfacial manganite layer
neighboring to a $(d_{3z^2-r^2})^1$ or $(d_{3z^2-r^2})^2$ system.
In this case, the magnetic interaction is sensitive to the occupancy of the Mn $d_{3z^2-r2}$ orbital.
It is also shown that the magnetic interaction between the interfacial Mn layer and the bulk region can be changed.
Manganite-based heterostructures thus show a rich magnetic behavior.
We also present how to generalize the argument including $t_{2g}$ orbitals.
