Structural properties in $R{\mathrm{Fe}}_2{\mathrm{O}}_4$ compounds ($R=\mathrm{Tm}$, 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 (∼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.

Figure 1

(a) DSC measurements (heating runs) for powder samples of $R{\mathrm{Fe}}_2{\mathrm{O}}_4$ ($R$ = Lu, Yb, and Tm). (b) Electrical resistivity (natural logarithm) vs temperature for the $R{\mathrm{Fe}}_2{\mathrm{O}}_4$ ($R$ = Lu, Yb, and Tm) samples. Inset: Temperature dependence of −$d$ ln(ρ)/dT (sign changed for the sake of comparison). The vertical lines indicate the temperature of the anomalies detected in DSC curves ($T_{\mathrm{CO}}$). (c) Temperature dependence of magnetization for ${\mathrm{LuFe}}_2{\mathrm{O}}_4$ (circles), ${\mathrm{YbFe}}_2{\mathrm{O}}_4$ (triangles), and ${\mathrm{TmFe}}_2{\mathrm{O}}_4$ (squares). Open and filled symbols correspond to ZFC and FC conditions respectively. The external magnetic field was 100 Oe.

Figure 2

Left: Details of the x-ray patterns for ${\mathrm{TmFe}}_2{\mathrm{O}}_4$ at 80 and 400 K. The former has been shifted upward for the sake of comparison. Right: Hexagonal unit cell volume of $R{\mathrm{Fe}}_2{\mathrm{O}}_4$ compounds.

Figure 3

Temperature dependence of lattice parameters for ${\mathrm{YbFe}}_2{\mathrm{O}}_4$ (filled symbols) and ${\mathrm{TmFe}}_2{\mathrm{O}}_4$ (open symbols). Dashed lines indicate the temperature peak in DSC curves [see Fig. 1].

Figure 4

(a) Temperature dependence of $R$-O2 bond lengths and BVS for ${\mathrm{TmFe}}_2{\mathrm{O}}_4$ (a) and ${\mathrm{YbFe}}_2{\mathrm{O}}_4$ (b). The lines are guides for the eyes. Interatomic distances in the ${\mathrm{FeO}}_5$ bipyramids for ${\mathrm{TmFe}}_2{\mathrm{O}}_4$ (c) and ${\mathrm{YbFe}}_2{\mathrm{O}}_4$ (d).

Figure 5

Selected regions of ${\mathrm{LuFe}}_2{\mathrm{O}}_4$ x-ray patterns. Comparison of patterns collected at 400 and 260 K showing (a) the occurrence of superstructure peaks and (b) the splitting of main peaks. (c) Comparison of patterns taken at 260 and 80 K showing additional splitting of peaks at lower temperatures.

Figure 6

Crystal structure of monoclinic (left) and triclinic (right) structures for ${\mathrm{LuFe}}_2{\mathrm{O}}_4$. The Fe positions within bipyramids are indicated by arrows, while big (red) and small (blue) balls stands for Lu and O atoms, respectively. Insets: (left) Relationship between the parent rhombohedral cell (hexagonal setting) and the monoclinic distorted cell; (right) relationship between the parent $C$-centered monoclinic cell and the primitive triclinic cell.

Figure 7

Rietveld refinement of ${\mathrm{LuFe}}_2{\mathrm{O}}_4$ at (a) 300 and (b) 80 K. Points and continuous line refer to experimental and calculated patterns, respectively. The difference is plotted at the bottom with the allowed reflections.

Figure 8

Temperature dependence of the lattice parameters in the monoclinic setting of two ${\mathrm{LuFe}}_2{\mathrm{O}}_4$ specimens. Filled symbols correspond to the first specimen with high resolution measurements performed at selected temperatures. Open symbols correspond to the second specimen with data acquired (every 5 min) in a heating ramp of 0.5 K ${\min }^{-1}$.

Figure 9

Temperature dependence of BVS for (a) Lu and (b) Fe atoms in ${\mathrm{LuFe}}_2{\mathrm{O}}_4$. (c) Temperature dependence of BVS for Fe in the three $R{\mathrm{Fe}}_2{\mathrm{O}}_4$ compounds. The data for Lu-based sample below $T_{\mathrm{CO}}$ correspond to the average values.