Local structural evidence for strong electronic correlations in spinel LiRh${}_2$O${}_4$

The local structure of the spinel LiRh${}_2$O${}_4$ has been studied using atomic-pair distribution function analysis of powder x-ray diffraction data. This measurement is sensitive to the presence of short Rh-Rh bonds that form due to dimerization of Rh${}^{4+}$ ions on the pyrochlore sublattice, independent of the existence of long-range order. We show that structural dimers exist in the low-temperature phase, as previously supposed, with a bond shortening of $\Delta r\sim 0.15$ Å. The dimers persist up to 350 K, well above the insulator-metal transition, with $\Delta r$ decreasing in magnitude on warming. Such behavior is inconsistent with the Fermi-surface nesting-driven Peierls transition model. Instead, we argue that LiRh${}_2$O${}_4$ should properly be described as a strongly correlated system.

Figure 1

(a) Structural motif of Rh-pyrochlore sublattice. Red atoms denote single Rh${}_4$ tetrahedron. Red, blue, and green colored bonds differentiate independent chain directions. (b) Two-dimensional sketch of different charge distributions in $d_{xy}$ (red) and $d_{yz}$ (blue) orbitals of the $t_{2g}$ manifold with charge filling represented by color intensity: (i) homogeneous, (ii) subband disproportionated (band Jahn-Teller effect), and (iii) CDW. Arrows denote disproportionation of charge.

Figure 2

(a) Temperature dependence of LiRh${}_2$O${}_4$ resistivity (red) and magnetic susceptibility (blue). (b) Lattice parameters determined from Le Bail fit of the x-ray data. Vertical dashed lines denote structural phase transitions at 170 K (blue) and 225 K (red).

Figure 3

Comparison of experimental PDFs at 240 K (red) and 160 K (blue) for (a) LiRh${}_2$O${}_4$ and (b) CuIr${}_2$S${}_4$. Difference curves (green) are offset for clarity. Dotted lines indicate $r$ position of short (dimerized) and long (undimerized) peaks. $\Delta r$, defined as half the distance between the long and short bonds, is used as a measure of the distortion associated with dimerization.

Figure 4

(a) Plot of temperature evolution of LiRh${}_2$O${}_4$ RDF in the 1.5–3.5 Å range. Inset displays differential RDF near the dimer peak obtained by subtracting a reference RDF at 500 K with black lines at 170 K (solid line), and 225 K (dashed line) denoting differential RDFs at phase-transition temperatures. (b),(c) Results of differential RDF analysis: (b) distortion, $\Delta r$, (c) integrated intensity of short-bond peak normalized to its low-$T$ value, representing the dimer fraction. Black arrow indicates observed break in slope at 350 K. Horizonal dotted line, drawn at zero, is a guide to the eye. Vertical dashed lines indicate phase-transition temperatures.

Figure 5

(a) Best fit (red line) to LiRh${}_2$O${}_4$ PDF (blue circles) at 200 K in the 1.5–20 Å range using $I{4}_1/amd$ model. Difference curve (green) is offset for clarity. Shaded area denotes poorly fit region. (b) Refinement residual, $R_w$, for the entire temperature range. Black dotted line is a linear fit to the high-temperature tail. Inset shows expanded view in the 200–500 K range, with observed break in slope at 350 K indicated by arrow. (c) Temperature dependence of the isotropic atomic displacement parameter (ADP), $U_{\mathrm{iso}}$, of Rh obtained from the fits. Black dashed line represents a fit of the Debye model to the high-temperature tail. (d) Differential ADP, $\Delta U_{\mathrm{iso}}$, obtained from data shown in (c) by subtracting the Debye model values from the refined ADPs at all temperatures. Vertical dashed lines in (b)–(d) denote phase transitions.

Figure 6

(a) Gaussian fit (red) to 80 K LiRh${}_2$O${}_4$ PDF (blue circles) in the 1.5–3.5 Å range. Difference curve (green) is offset for clarity. Inset shows fit components. (b) Temperature evolution of the difference curve shown in (a). Arrows in (a) and (b) indicate the short-bond peak which is unaccounted for in the two-Gaussian model. Crystallographic phases are color coded (LTO blue, ITT green, HTC red), while the black profiles mark the phase transitions.

Figure 7

(a) Renormalized-temperature dependence of the specific heat for LiRh${}_2$O${}_4$ (red circles) and CuIr${}_2$S${}_4$ (black squares), compared with the Debye model (green line). (b) $\Delta C$, the contribution to the specific heat coming from the phase transitions for LiRh${}_2$O${}_4$ (red line) and CuIr${}_2$S${}_4$ (black line). (c) $\Delta C/T$. (d) The corresponding entropy, $\Delta S\left(T\right)={\int }_0^T\Delta C/TdT$.

Figure 8

(a) LiRh${}_2$O${}_4$charge distribution model based on band Jahn-Teller scenario: (i) homogeneous charge distribution, (ii) subband charge disproportionation, and (iii) CDW. (b) Alternative model based on experimental observations made in this work, with CDW existing in all three phases. As in Fig. 1b, color intensity corresponds to the average amount of charge, while arrows denote charge disproportionation.