  We show that, contrary to common belief, the depolarizing electric field
generated by bound charges at thin-film surfaces can have a substantial impact
on the domain structure of an improper ferroelectric with topological defects.
In hexagonal-manganite thin films, we observe in phase-field simulations that
through the action of the depolarizing field, (i) the average magnitude of the
polarization density decreases, (ii) the local magnitude of the polarization
density decreases with increasing distance from the domain walls, and (iii)
there is a significant alteration of the domain-size distribution, which is
visualized with the pair-correlation function. We conclude that, in general, it
is not appropriate to ignore the effects of the depolarizing field for thin
film ferroelectrics.
