Resonant magnetic scattering of multiferroic HoMnO$_{3}$

The multiferroic material HoMnO$_{3 }$displays electrical polarization below the Curie temperature $T_{C}$ = 875 K and antiferromagnetic Mn$^{3+}$ ordering at N\'{e}el temperature, $T_{N}$~= 75 K. The ferroelectric phase possesses hexagonal P6$_{3}$cm symmetry with polarization $P_{c}$~=~5.6~$\mu $C~cm$^{-2}$ along the hexagonal $c$ axis. In order to shed further light on the magnetic order in this compound, element specific X-ray resonant magnetic scattering was performed at the Ho $L_{III}$ absorption edge. Resonance enhancement was observed in both quadrupole and dipole channels below 40 K. Measurement of ($0 0 l)$ and $(h 0 l) $( $l$ odd) reflections have resolved contradictions present in the literature regarding the magnetic order of Ho$^{3+}$ moments. From 40 K down to 6 K, Ho$^{3+ }$ moments order according to magnetic space group P6$_{3}^{\mbox{'}}$cm$^{\mbox{'}}$ with different values for the ordered moment on the Wyckoff sites 2a and 4b. According to this space group, Ho moments are ferromagnetically correlated in the \textbf{a-b} plane and antiferromagnetically correlated in the \textbf{c}-direction. The coincidence of the transition temperature (40 K) for Ho$^{3+ }$moment ordering, spin rotation for Mn$^{3+}$ moments, and sharp anomaly in dielectric constant indicates that the interplay between ferroelectricity and magnetism is strongly related to the Ho magnetic order.