  Engineering of ferroelectric domain structures enables direct control over
the switching dynamics and is crucial for tuning the functional properties of
ferroelectrics for various applications, ranging from capacitors to future
nanoelectronics. Here, we investigate domain formation in poly- and single
crystalline improper ferroelectric DyMnO3. We show that a non-uniform
grain-size distribution in the polycrystals facilitates the coexistence of
multi-scale domains, varying by up to one order of magnitude in size. This
unusual domain structure originates from an inverted domain-size/grain-size
dependence that is intrinsic to the hexagonal manganite polycrystals, expanding
previous studies towards non-uniform grain-size distributions. Our results
demonstrate that the micrometer-sized grains in DyMnO3 represent individual
ferroelectric units with a characteristic domain structure, giving a new
dimension to domain engineering in ferroelectric polycrystals with non-uniform
microstructures.
