Asymmetric binary nanocrystals (BNCs), comprising one c-axis elongated anatase TiO2 section and one γ-Fe2O3 spherical domain attached together, are synthesized by heterogeneous nucleation of iron oxide onto the longitudinal facets of TiO2 nanorods in a ternary surfactant mixture. The topologically controlled composition of the BNCs is ascertained by a combination of powder X-ray diffraction, Raman and Mössbauer spectroscopy, high-angle annular dark-field imaging, and high-resolution transmission electron microscopy lattice fringe mapping, while their size-dependent magnetic behavior is demonstrated by ac susceptibility measurements. The heteroepitaxial growth proceeds through a mechanism never observed before for colloidal nanoheterostructures:  the two domains share a restricted and locally curved junction region, which accommodates efficiently the interfacial strain and retards the formation …