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 BiFeO(3)-CoFe(2)O(4) 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.

Heterointerfaces between complex oxides have sparked considerable interest due to their fascinating physical properties and their offering of new possibilities for next-generation electronic devices. The key to realize practical applications is the control through external stimuli. In this study, we take the self-assembled BiFeO3-CoFe2O4 tubular interface as a model system to demonstrate the nonvolatile electric control of the local conduction at the complex oxide tubular interface. The fundamental mechanism behind this modulation was explored based on static and dynamic conductive atomic force microscopies. We found the movement of oxygen vacancies in the BiFeO3-CoFe2O4 heterostructure is the key to drive this intriguing behavior. This study delivers a possibility in developing next-generation electronic devices.

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Abstract. Let X be a complex hyperelliptic curve of genus two equipped with the canonical metric ds 2 . We study mean field equations on complex hyperelliptic curves and show that the Gaussian curvature function of (X, ds 2 ) determines an explicit solution to a mean field equation.

Abstract. We analyze Weierstrass cycles and tautological rings in moduli spaces of smooth algebraic curves and in moduli spaces of integral algebraic curves with embedded disks with special attention to moduli spaces of curves having genus ≤ 6. In particular, we show that our general formula gives a good estimate for the dimension of Weierstrass cycles for low genera.