Charge-ordered state satisfying the Anderson condition in ${\mathrm{LiRh}}_2{\mathrm{O}}_4$ arising from local dimer order

We report on the charge-ordered structure of $\mathrm{Li}{\mathrm{Rh}}_2{\mathrm{O}}_4$ arising below the metal-insulator transition at 170 K. Structural studies using synchrotron x rays have revealed that the charge-ordered states of ${\mathrm{Rh}}^{3+}$ and ${\mathrm{Rh}}^{4+}$ with dimerization are realized in the low-temperature phase below 170 K. Although the low-temperature ground state resembles that of $\mathrm{Cu}{\mathrm{Ir}}_2{\mathrm{S}}_4$, a charge-ordering pattern satisfying the Anderson condition is realized in $\mathrm{Li}{\mathrm{Rh}}_2{\mathrm{O}}_4$. Based on structural information such as the short-range order of dimers appearing above the transition temperature and the weakening of the correlation between rhodium one-dimensional chains appearing in the crystal structure, we argue that the Coulomb interaction plays an important role in determining the charge-ordering patterns.

Figure 1

(a) PXRD patterns obtained at 235 K, 190 K, and 150 K. The inset shows temperature-dependent lattice parameters. (b) The unit cell and crystal axis in each temperature region with the $xy, yz$, and $zx$ chains consisting of Rh. (c) FWHM of some peaks colored in panel (a). The inset shows relationship between the $xy$ chains and the crystal planes corresponding to the colored indices.

Figure 2

(a) Rietveld analysis for 115 K data using the space group $A{2}_{1}22$. The reliability factor $S$ ($=R_{wp}/R_e$) is the ratio of the residual sum of squares, $R_{wp}$, to the smallest statistically expected $R_{wp}, R_e$. The peaks originating from the frost are refined together. Inset shows magnified view. The mixture of wide and sharp peaks makes it difficult to fit the peaks well, especially in the highlights. (b) Rh dimers revealed by Rietveld analysis. (c), (d) Results of fitting the reduced $G(r$) data with the models for (e) no displacement of Rh and (b) displacement, respectively. The tick marks indicate the Rh-Rh distance component. (f) Enlarged view around $r\left(\text{Å}\right)\sim 3.0$. (g) Simulated contribution calculated using the (b) model.

Figure 3

Charge-ordered pattern with dimerization in LT phase, drawn in a similar fashion to the presentation in Ref. [39], and the Rh-Rh distances obtained from the analysis in Fig. 2.

Figure 4

(a)–(c) Results of fitting reduced $G(r$) data with tetragonal model (d), orthorhombic model without atomic displacement of Rh, and orthorhombic model with atomic displacement of Rh for dimerization, respectively. (e) Enlarged view around $r\sim 3.0$ for (a)–(c).