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

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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 < Tₙ with Mn³+ order according to the Gamma₄ 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 Gamma₂ induces a magnetic reorientation (Gamma₄ --> Gamma₂) at the Er³⁺(4b) and the Mn³⁺ sites. Our findings highlight the fundamentally different roles the Mn³⁺, R³⁺(2a), and R³⁺(4b) magnetism play in establishing the magnetic phase diagram of the hexagonal RMnO3 system.