  A general consideration is presented for the magnetic interaction at an
interface between a perovskite manganite and other transition metal 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.
