Optical study of charge instability in CeRu${}_2$Al${}_{10}$ in comparison with CeOs${}_2$Al${}_{10}$ and CeFe${}_2$Al${}_{10}$

The anisotropic electronic structure responsible for the antiferromagnetic transition in CeRu${}_2$Al${}_{10}$ at the unusually high temperature of $T_0=28$ K was studied using optical conductivity spectra, Ce $3d$ x-ray photoemission spectra, and band calculation. It was found that the electronic structure in the $ac$ plane is that of a Kondo semiconductor, whereas that along the $b$ axis has a nesting below 32 K (slightly higher than $T_0$). These characteristics are the same as those of CeOs${}_2$Al${}_{10}$ [S. Kimura et al., Phys. Rev. Lett. 106, 056404 (2011)]. The $c$-$f$ hybridization intensities between the conduction and $4f$ electrons of CeRu${}_2$Al${}_{10}$ and CeOs${}_2$Al${}_{10}$ are weaker than that of CeFe${}_2$Al${}_{10}$, showing no magnetic ordering. These results suggest that the electronic structure with one-dimensional weak $c$-$f$ hybridization along the $b$ axis combined with two-dimensional strong hybridization in the $ac$ plane causes charge-density wave (CDW) instability, and the CDW state then induces magnetic ordering.

Figure 1

Crystal structure of Ce$M_2$Al${}_{10}$ ($M=\text{Fe}$, Ru, Os). Eight unit cells marked by lines are depicted.

Figure 2

Low-energy portion of the temperature-dependent polarized reflectivity [$R\left(\omega \right)$] spectra of CeRu${}_2$Al${}_{10}$ along the three principal axes. (Inset) The entire reflectivity spectra at 10 K along the $a$ axis (solid lines), $b$ axis (dashed lines), and $c$ axis (dotted lines).

Figure 3

Temperature-dependent polarized optical conductivity [$\sigma \left(\omega \right)$] spectra of CeRu${}_2$Al${}_{10}$ in the photon energy $\hslash \omega$ region below 70 meV. Each of the lines is shifted by $1.5\times {10}^3{\Omega }^{-1}{\mathrm{cm}}^{-1}$ for clarity.

Figure 4

Optical conductivity [$\sigma \left(\omega \right)$] spectra of Ce$M_2$Al${}_{10}$ ($M=\text{Fe}$, Ru, Os) along the $a$ axis (upper) and $c$ axis (lower) in the $\hslash \omega$ range below 80 meV at $T=10$ K. The downward arrows indicate the absorption structures in the $c$-$f$ hybridization gaps.

Figure 5

Ce $3d$ XPS spectra of Ce$M_2$Al${}_{10}$ ($M=\text{Fe}$, Os, Ru) at 10 K. The energies of the $f^0$, $f^1$, and $f^2$ final states of the $3d_{3/2}$ and $3d_{5/2}$ core levels are marked by vertical lines. The subtraction spectra obtained by subtracting CeRu${}_2$Al${}_{10}$ from CeFe${}_2$Al${}_{10}$ and CeOs${}_2$Al${}_{10}$ are also plotted as $I_{\mathrm{Fe}}-I_{\mathrm{Ru}}$ and $I_{\mathrm{Os}}-I_{\mathrm{Ru}}$, respectively.

Figure 6

(a) Total density of states (DOS) of Ce$M_2$Al${}_{10}$ ($M=\text{Os}$, Ru, Fe) and partial DOS of the Ce $f$ (dashed lines) and $Md$ (dotted lines) states near the Fermi level at an energy of 0 eV. The shallowest peaks in the valence bands of CeRu${}_2$Al${}_{10}$ and CeOs${}_2$Al${}_{10}$ are denoted by downward arrows. (b) Total DOS of Ce$M_2$Al${}_{10}$ in the wide energy range. Each of the lines is shifted by 50 eV${}^{-1}$ for clarity.

Figure 7

(a) Temperature-dependent optical conductivity [$\sigma \left(\omega \right)$] spectrum of CeRu${}_2$Al${}_{10}$ in $E\parallel b$. Each of the lines is shifted by $2\times {10}^3{\Omega }^{-1}{\mathrm{cm}}^{-1}$ for clarity. The cross-hatched areas are shoulder structures caused by band nesting due to CDW formation. (b) Effective electron number ($N_{\mathrm{eff}}$) of the shoulder structures shown in (a) plotted as a function of temperature. The $N_{\mathrm{eff}}$ of CeOs${}_2$Al${}_{10}$ is also plotted. The solid lines indicate the square of the order parameter $\Delta \left(T\right)$ of the BCS theory. The critical temperature $T^{*}$ of $\Delta \left(T\right)$ was set at 32 K for CeRu${}_2$Al${}_{10}$ and 37.5 K for CeOs${}_2$Al${}_{10}$. The vertical dot-dashed lines indicate the antiferromagnetic ordering temperature $T_0$ of CeRu${}_2$Al${}_{10}$ and CeOs${}_2$Al${}_{10}$.