Duality of topological defects in hexagonal manganites.

We show that the spontaneous symmetry breaking in multiferroic hexagonal manganites can be chemically manipulated to yield two complementary ground states: the well-known ferroelectric P6(3)cm and an antipolar P3c phase. Both symmetry breakings yield topologically protected vortex defects, with the antipolar vortices dual to those of the ferroelectric. This duality stems from the existence of 12 possible angles of MnO5 tilting, and broad strain-free walls with low energy spontaneously emerge through an intermediate P3c1 state, providing a complete unified symmetry description.