Mutual induction of magnetic 3d and 4f order in multiferroic hexagonal ErMnO3

The complex interplay between the 3d and 4f moments in hexagonal ErMnO3 is investigated by magnetization, optical second harmonic generation, and neutron-diffraction measurements. We revise the phase diagram and provide a microscopic model for the emergent spin structures, with a special focus on the intermediary phase transitions. Our measurements reveal that the 3d exchange between Mn3+ ions dominates the magnetic symmetry at 10 K < T < T-N with Mn3+ order according to the Gamma(4) representation triggering 4f ordering according to the same representation on the Er3+(4b) site. Below 10 K the magnetic order is governed by 4f exchange interactions of Er3+ ions on the 2a site. The magnetic Er3+(2a) order according to the representation Gamma(2) induces a magnetic reorientation (Gamma(4) -> Gamma(2)) at the Er3+(4b) and the Mn3+ sites. Our findings highlight the fundamentally different roles that Mn3+, R3+(2a), and R3+(4b) magnetism play in establishing the magnetic phase diagram of the hexagonal RMnO3 system.