  A promising mechanism for achieving colossal dielectric constants is to use
insulating internal barrier layers, which typically form during synthesis and
then remain in the material. It has recently been shown that insulating domain
walls in ferroelectrics can act as such barriers. One advantage domain walls
have, in comparison to stationary interfaces, is that they can be moved,
offering the potential of post-synthesis control of the dielectric constant.
However, to date, direct imaging of how changes in domain wall pattern cause a
change in dielectric constant within a single sample has not been realized. In
this work, we demonstrate that changing the domain wall density allows the
engineering of the dielectric constant in hexagonal-ErMnO3 single crystals. The
changes of the domain wall density are quantified via microscopy techniques,
while the dielectric constant is determined via macroscopic dielectric
spectroscopy measurements. The observed changes in the dielectric constant are
quantitatively consistent with the observed variation in domain wall density,
implying that the insulating domain walls behave as 'ideal' capacitors
connected in series. Our approach to engineer the domain wall density can be
readily extended to other control methods, e.g., electric fields or mechanical
stresses, providing a novel degree of flexibility to in-situ tune the
dielectric constant.
