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In strongly correlated oxides, heterointerfaces, manipulating the interaction, frustration, and discontinuity of lattice, charge, orbital, and spin degrees of freedom, generate new possibilities for next generation devices. In this study, existing oxide heterostructures are examined and local conduction at the BiFeO3-CoFe2O4 vertical interface is found. In such hetero-nanostructures the interface cannot only be the medium for the coupling between phases, but also a new state of the matter. This study demonstrates a novel concept on for oxide interface design and opens an alternative pathway for the exploration of diverse functionalities in complex oxide interfaces.