Incompatible Magnetic Order in Multiferroic Hexagonal DyMnO3

Magnetic order of the manganese and rare-earth lattices according to different symmetry representations is observed in multiferroic hexagonal (h-) ${\text{DyMnO}}_{3}$ by optical second-harmonic generation and neutron diffraction. The incompatibility reveals that the $3d\text{\ensuremath{-}}4f$ coupling in the $\text{h-}R{\text{MnO}}_{3}$ system ($R=\text{Sc}$, Y, In, Dy\char21{}Lu) is less rigid than commonly expected. Instead, a triggered magnetic phase transition is introduced that constitutes a framework for magnetic and magnetoelectric coupling effects in the $\text{h-}R{\text{MnO}}_{3}$ system.