Microscopy of the magnetoelectric coupling in hexagonal manganites: multiferroic domains and emergent topological defects*

When studying magnetoelectric coupling effects in materials with simultaneous magnetic and electric order, the so-called multiferroics, fundamental understanding of the cross coupling between ferroic orders at the level of domains and domain walls is paramount. Domains and domain walls reflect the different interdependence of magnetic and electric order in multiferroics. For example in type-II multiferroics, domain patterns are one-to-one coupled whereas in type-I, magnetic and electric domain configurations can be different and their coupling no longer mandatory. We show in experiment and theory, that multiferroics with separately emerging magnetic and electric order (type-I) can exhibit a strong bulk coupling. We show, taking h-ErMnO3 as an example, that a strong bulk coupling between ferroelectric and antiferromagnetic orders is realized even though the linear magnetoelectric effect is symmetry forbidden. We show that the structural distortions that lead to the ferroelectric polarization break the balance of the competing superexchange contributions leading to this hidden, yet strong phenomenon. The non-rigidity of this bulk coupling leads to uncommon types of magnetoelectric domain walls and vortex-like singularities.