E -type noncollinear magnetic ordering in multiferroic o−LuMnO3

Multiferroic orthorhombic $o\ensuremath{-}{\mathrm{LuMnO}}_{3}$ exhibits large ferroelectric polarization induced by an $E$-type magnetic order. Recently, the $E$-type magnetic phase in ${\mathrm{LuMnO}}_{3}$ was proposed to feature magnetic moments tilted away from the collinear ordering. We employed neutron diffraction to determine the symmetry of the magnetic order in $o\ensuremath{-}{\mathrm{LuMnO}}_{3}$. We observed that below ${T}_{N}=39$ K, the ${\mathrm{Mn}}^{3+}$ spins order into an incommensurate amplitude-modulated phase that obeys the Pbnm crystal symmetry and is paraelectric. The incommensurate phase locks into a commensurate phase at ${T}_{C}=35.5$ K described by a fully antiferromagnetic and noncollinear $E$-type order. This noncollinear $E$-type ordering breaks the spatial inversion symmetry and induces a spontaneous polarization at ${T}_{C}$. At $T=2$ K, an appreciably large electric polarization was observed similar to that of other orthorhombic manganites featuring $E$-type magnetic order. We also present a Pbnm symmetry-allowed Dzyaloshinskii-Moriya interaction that explains the noncollinear $E$-type order in the commensurate phase. These results are in qualitative agreement with the type of distortions from collinear $E$-type antiferromagnetic order found using Monte Carlo simulation for rare-earth manganites [M. Mochizuki et al., Phys. Rev. B 84, 144409 (2011)].