  The research on topological phenomena in ferroelectric materials has
revolutionized the way we understand polar order. Intriguing examples are polar
skyrmions, vortex/anti-vortex structures and ferroelectric incommensurabilties,
which promote emergent physical properties ranging from
electric-field-controllable chirality to negative capacitance effects. Here, we
study the impact of topologically protected vortices on the domain formation in
improper ferroelectric ErMnO3 polycrystals, demonstrating inverted domain
scaling behavior compared to classical ferroelectrics. We observe that as the
grain size increases, smaller domains are formed, which we relate to the
interaction of the topological vortices with local strain fields. The inversion
of the domain scaling behavior has far-reaching implications, providing
fundamentally new opportunities for topology-based domain engineering and the
tuning of the electromechanical and dielectric performance of ferroelectrics in
general.
