  Transition metal oxides hold great potential for the development of new
device paradigms because of the field-tunable functionalities driven by their
strong electronic correlations, combined with their earth abundance and
environmental friendliness. Recently, the interfaces between transition-metal
oxides have revealed striking phenomena such as insulator-metal transitions,
magnetism, magnetoresistance, and superconductivity. Such oxide interfaces are
usually produced by sophisticated layer-by-layer growth techniques, which can
yield high quality, epitaxial interfaces with almost monolayer control of
atomic positions. The resulting interfaces, however, are fixed in space by the
arrangement of the atoms. Here we demonstrate a route to overcoming this
geometric limitation. We show that the electrical conductance at the
interfacial ferroelectric domain walls in hexagonal ErMnO3 is a continuous
function of the domain wall orientation, with a range of an order of magnitude.
We explain the observed behaviour using first-principles density functional and
phenomenological theories, and relate it to the unexpected stability of
head-to-head and tail-to-tail domain walls in ErMnO3 and related hexagonal
manganites. Since the domain wall orientation in ferroelectrics is tunable
using modest external electric fields, our finding opens a degree of freedom
that is not accessible to spatially fixed interfaces.
