Structural properties in RFe2O4 compounds (R = Tm, Yb, and Lu)

We report a complete characterization of the crystal structure between 400 and 80 K for $R{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ ($R$ = Rm, Yb, and Lu) compounds using high resolution x-ray synchrotron powder diffraction. The three samples have a hexagonal structure (space group $R\overline{3}m$) characterized by a sequence of double layers of mixed valence iron and oxygen atoms forming two-dimensional triangular layers separated by a single $R$-O layer along the $c$ axis. This structure is stable down to 80 K for ${\mathrm{TmFe}}_{2}{\mathrm{O}}_{4}$ and ${\mathrm{YbFe}}_{2}{\mathrm{O}}_{4}$ though a sudden expansion in the $c$ axis is observed at around 300 K coupled to a variation in the electrical properties. However, ${\mathrm{LuFe}}_{2}{\mathrm{O}}_{4}$ exhibits two structural transitions upon cooling. The splitting of some reflections and the occurrence of superstructure peaks below 320 K reveal a structural phase transition. The unit cell is monoclinic (space group $C2/m$), and there are four nonequivalent Fe sites with a maximum charge disproportionation of 0.5 $e$. The hexagonal to monoclinic transition is characterized by a sudden expansion of the $c$ axis on cooling, and it seems to be driven by the condensation of ${\mathrm{Y}}_{2}$ modes. At lower temperatures (\ensuremath{\sim}170 K) additional splitting of several peaks indicate that the unit cell is no longer monoclinic but triclinic (space group $P\overline{1}$). This transition is characterized by a contraction of the monoclinic $ab$ plane, while the $c$ axis remains almost unchanged. There are six nonequivalent Fe sites in the triclinic cell, and the charge disproportionation magnitude is little affected.