Optical study of the electronic structure and correlation effects in K${}_{0.49}$RhO${}_2$

We study the optical properties of the layered rhodium oxide K${}_{0.49}$RhO${}_2$, which is isostructural to the thermoelectric material Na${}_x$CoO${}_2$. The optical conductivity shows broad interband transition peaks as well as a low-energy Drude-like upturn, reminiscent of the optical spectra of Na${}_x$CoO${}_2$. We find that the peaks clearly shift to higher energies with respect to those of Na${}_x$CoO${}_2$, indicating a larger crystal-field splitting between $e_g$ and $t_{2g}$ bands in K${}_{0.49}$RhO${}_2$. The Drude weights suggest that the effective mass of K${}_{0.49}$RhO${}_2$ is almost two times smaller than that of Na${}_x$CoO${}_2$. These differences in electronic structures and correlation effects between Na${}_x$CoO${}_2$ and K${}_{0.49}$RhO${}_2$ are discussed in terms of the difference between Co 3$d$ and Rh 4$d$ orbitals.

Figure 1

Temperature dependence of the $ab$-plane resistivity ${\rho }_{ab}$ of K${}_{0.49}$RhO${}_2$ single crystal. Inset illustrates the crystal structure of K${}_x$RhO${}_2$.

Figure 2

Reflectivity spectrum of K${}_{0.49}$RhO${}_2$ single crystal measured at room temperature with polarization parallel to the $ab$ planes. Inset shows the reflectivity spectrum in high-energy region.

Figure 3

Optical conductivity ${\sigma }_1\left(\omega \right)$ of (a) K${}_{0.49}$RhO${}_2$ obtained from the Kramers-Kronig transformation of the reflectivity spectrum and (b) Na${}_x$CoO${}_2$ taken from previous reports.[18, 20] The dc conductivity ${\sigma }_1(\omega \to 0)$ is plotted by the circle for K${}_{0.49}$RhO${}_2$. The peak locations in K${}_{0.49}$RhO${}_2$ (Na${}_x$CoO${}_2$) spectra are labeled by ${\alpha }^{\prime }$ ($\alpha$), ${\beta }^{\prime }$ ($\beta$), and ${\gamma }^{\prime }$ ($\gamma$), which correspond to the O $2p$-$e_g$, $t_{2g}$-$e_g$, and $t_{2g}$-$t_{2g}$ transitions, respectively, as illustrated in schematic energy diagrams for (c) Na${}_x$CoO${}_2$ and (d) K${}_{0.49}$RhO${}_2$.

Figure 4

Comparison of the effective carrier number in K${}_{0.49}$RhO${}_2$ and Na${}_{0.5}$CoO${}_2$ at room temperature. The data of Na${}_{0.5}$CoO${}_2$ is taken from Ref.20.