  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.
