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 Mn^{3+} ions dominates the magnetic symmetry at 10 K < T < T_N with Mn^3+ order according to the Gamma_4 representation triggering 4f ordering according to the same representation on the Er^{3+}(4b) site. Below 10 K the magnetic order is governed by 4f exchange interactions of Er^{3+} ions on the 2a site. The magnetic Er^{3+}(2a) order according to the representation Gamma_2 induces a magnetic reorientation (Gamma_4 --> Gamma_2) at the Er^{3+}(4b) and the Mn^{3+} sites. Our findings highlight the fundamentally different roles the Mn^{3+}, R^{3+}(2a), and R^{3+}(4b) magnetism play in establishing the magnetic phase diagram of the hexagonal RMnO3 system.