Incompatible magnetic order in multiferroic hexagonal ${\text{DyMnO}}_3$

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 $3d\text{−}4f$ coupling in the $\text{h-}R{\text{MnO}}_3$ system ($R=\text{Sc}$, Y, In, Dy–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.

Figure 1

Spectral, polarization, and temperature dependence of SHG in $\text{h-}R{\text{MnO}}_3$ compounds. A “0” indicates zero SHG intensity. [(a) and (b)] SHG spectra of ${\text{h-HoMnO}}_3$ measured in (a) transmission and (b) reflection with a femtosecond laser. (c) SHG spectra of ${\text{h-DyMnO}}_3$ measured in reflection with a femtosecond laser. (d) Temperature dependence of the signal in (c).

Figure 2

Temperature dependence of the (101) and (100) reflections of ${\text{h-DyMnO}}_3$ measured in a cooling run on the sample from Fig. 1. The dashed line marks the offset due to crystallographic contributions.

Figure 3

Phase diagram of the magnetic ${\text{Mn}}^{3+}$ order in ${\text{h-DyMnO}}_3$ in a magnetic field along $z$. [(a) and (b)] Sketch of the SHG contributions in the course of the spin reorientation toward the (a) $P{6}_3\underset{̱}{cm}$ and (b) $P{6}_{3}cm$ phases. (c) Exemplary field dependence of the SHG signal at 32 K in a field-increasing run. (d) Phase diagram derived from data as in (c). Temperature-increasing and -decreasing runs yield the boundaries on the right- and left-hand side of the gray area, respectively. The boundary values correspond to observation of 50% of the SHG yield of the $P{\underset{̱}{6}}_3\underset{̱}{c}m$ phase.