Relation between $c\text{−}f$ hybridization and magnetic ordering in ${\mathrm{CeRu}}_2{\mathrm{Al}}_{10}$: An optical conductivity study of $\mathrm{Ce}\left({\mathrm{Ru}}_{1-x}{\mathrm{Rh}}_x\right){}_2{\mathrm{Al}}_{10} \left(x\le 0.05\right)$

A Kondo semiconductor ${\mathrm{CeRu}}_2{\mathrm{Al}}_{10}$ with an orthorhombic crystal structure shows unusual antiferromagnetic ordering at a rather high temperature $T_0$ of 27.3 K, which is lower than the Kondo temperature $T_{\mathrm{K}}\sim 60$ K. In optical conductivity [$\sigma \left(\omega \right)$] spectra that directly reflect the electronic structure, a $c\text{−}f$ hybridization gap between the conduction and $4f$ states is observed at around 40 meV along the three principal axes. However, an additional peak at around 20 meV appears only along the $b$ axis. By increasing $x$ to 0.05 in $\mathrm{Ce}{\left({\mathrm{Ru}}_{1-x}{\mathrm{Rh}}_x\right)}_2{\mathrm{Al}}_{10}$, the $T_0$ decreases slightly from 27.3 to 24 K, but the direction of the magnetic moment changes from the $c$ axis to the $a$ axis. Thereby, the $c\text{−}f$ hybridization gap in the $\sigma \left(\omega \right)$ spectra is strongly suppressed, but the intensity of the 20 meV peak remains as strong as for $x=0$. These results suggest that the change in the magnetic moment direction originates from a decrease in the $c\text{−}f$ hybridization intensity. The magnetic ordering temperature $T_0$ is not directly related to $c\text{−}f$ hybridization but is related to the charge excitation at 20 meV observed along the $b$ axis.

Figure 1

Temperature-dependent reflectivity [$R\left(\omega \right)$] spectra of $\mathrm{Ce}({\mathrm{Ru}}_{1-x}{\mathrm{Rh}}_x){}_2{\mathrm{Al}}_{10}$ ($x=0$, 0.03, 0.05) along all principal axes. The $R\left(\omega \right)$ spectra of $x=0$ are referred from Ref. [16].

Figure 2

(a) Temperature-dependent optical conductivity [$\sigma \left(\omega \right)$] spectra of $\mathrm{Ce}{\left({\mathrm{Ru}}_{1-x}{\mathrm{Rh}}_x\right)}_2{\mathrm{Al}}_{10}$ ($x=0$, 0.03, 0.05) along all principal axes in the photon energy region below 300 meV. (b) The centers of gravity [$\langle \hslash \omega \rangle$] of the $\sigma \left(\omega \right)$ spectra are plotted as a function of temperature.

Figure 3

Temperature-dependent optical conductivity [$\sigma \left(\omega \right)$] spectra of $\mathrm{Ce}{\left({\mathrm{Ru}}_{1-x}{\mathrm{Rh}}_x\right)}_2{\mathrm{Al}}_{10}$ ($x=0$, 0.03, 0.05) along all principal axes in the photon energy range below 65 meV. Vertical arrows indicate the optical transitions across the $c\text{−}f$ hybridization gap.

Figure 4

(a) $\sigma \left(\omega \right)$ spectra along the $b$ axis at 10 K and the fitted lines of one Drude and three Lorentz functions. The three Lorentz functions are assumed as a peak appearing below $\sim T_0$, the interband transition (IB) in the $c\text{−}f$ hybridization gap, and a higher interband transition from the lower energy side. (b) Obtained effective electron numbers of the Drude, ${\mathrm{\Delta }}_0$, and ${\mathrm{\Delta }}_{c\text{−}f}$ components and the magnetic ordering temperature $T_0$ as a function of the Rh substitution $x$. Note that, at $x=0.03$, two magnetic ordering temperatures at 23.5 and 25.5 K reported in Ref. [18] are plotted.