Spin-Lattice Coupling and Frustrated Magnetism in Fe-doped Hexagonal LuMnO3

Strong spin-lattice coupling and prominent frustration effects observed in the 50$\mathrm{\%}$ Fe-doped frustrated hexagonal ($h$)LuMnO${}_3$ are reported. A N'{e}el transition at $T_{\mathrm{N}}\approx$ 112~K and a possible spin re-orientation transition at $T_{\mathrm{S}\mathrm{R}}\approx$ 55~K are observed in the magnetization data. From neutron powder diffraction data, the nuclear structure at and below 300~K was refined in polar $P{6}_{3}cm$ space group. While the magnetic structure of LuMnO${}_3$ belongs to the ${\mathrm{\Gamma }}_4$ ($P{6}_3^{\mathrm{\prime }}{c}^{\mathrm{\prime }}m$) representation, that of LuFe${}_{0.5}$Mn${}_{0.5}$O${}_3$ belongs to ${\mathrm{\Gamma }}_1$ ($P{6}_{3}cm$) which is supported by the strong intensity for the $(\mathbf{100})$ reflection and also judging by the presence of spin-lattice coupling. The refined atomic positions for Lu and Mn/Fe indicate significant atomic displacements at $T_{\mathrm{N}}$ and $T_{\mathrm{S}\mathrm{R}}$ which confirms strong spin-lattice coupling. Our results complement the discovery of room temperature multiferroicity in thin films of $h$LuFeO${}_3$ and would give impetus to study LuFe${}_{1-x}$Mn${}_x$O${}_3$ systems as potential multiferroics where electric polarization is linked to giant atomic displacements.