  We use density functional calculations to investigate the accommodation and
migration of oxygen vacancies in bulk hexagonal YMnO$_3$, and to study
interactions between neutral ferroelectric domain walls and oxygen vacancies.
Our calculations show that oxygen vacancies in bulk YMnO$_3$ are more stable in
the Mn-O layers than in the Y-O layers. Migration barriers of the planar oxygen
vacancies are high compared to oxygen vacancies in perovskites, and to
previously reported values for oxygen interstitials in h-YMnO$_3$. The
calculated polarization decreases linearly with vacancy concentration, while
the out-of-plane lattice parameter expands in agreement with previous
experiments. In contrast with ferroelectric perovskites, oxygen vacancies are
found to be more stable in bulk than at domain walls. The tendency of oxygen
vacancies to segregate away from neutral domain walls is explained by
unfavorable Y-O bond lengths caused by the local strain field at the domain
walls.
