  Electronic reconstruction at the polar interface LaMnO$_3$/SrMnO$_3$
(LMO/SMO) (100) resulting from the polar catastrophe is studied from a model
Hamiltonian that includes the double and super exchange interactions, the
Madelung potential, and the Jahn-Teller coupling terms relevant for the
manganites. We show that the polar catastrophe, originating from the
alternately charged LMO layers and neutral SMO layers, is quenched by the
accumulation of an extra half electron per cell in the interface region as in
the case of the LaAlO$_3$/SrTiO$_3$ interface. In addition, the Mn e$_g$
electrons leak out from the LMO side to the SMO side, the extent of the leakage
being controlled by the interfacial potential barrier and the substrate induced
epitaxial strain. The leaked electrons mediate a Zener double exchange, making
the layers adjacent to the interface ferromagnetic, while the two bulk
materials away from the interface retain their original type A or G
antiferromagnetic structures. A half-metallic conduction band results at the
interface, sandwiched by the two insulating bulks. We have also studied how the
electron leakage and consequently the magnetic ordering are affected by the
substrate induced epitaxial strain. Comparisons are made with the results of
the density-functional calculations for the (LMO)$_6$/(SMO)$_4$ superlattice.
