Relation between $c$-$f$ hybridization and magnetic ordering in CeRu$_2$Al$_{10}$: An optical conductivity study of Ce(Ru$_{1-x}$Rh$_x$)$_2$Al$_{10}$ ($x\leq0.05$)

A Kondo semiconductor CeRu$_2$Al$_{10}$ with an orthorhombic crystal structure shows an unusual antiferromagnetic ordering at rather high temperature $T_0$ of 27.3 K, which is lower than the Kondo temperature $T_{\rm K}\sim$ 60 K. In optical conductivity [$σ(ω)$] spectra that directly reflect electronic structure, the $c$-$f$ 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. With increasing $x$ to 0.05 in Ce(Ru$_{1-x}$Rh$_x$)$_2$Al$_{10}$, the $T_0$ decreases slightly from 27.3 K to 24 K, but the direction of the magnetic moment changes from the $c$ axis to the $a$ axis. Thereby, the $c$-$f$ hybridization gap in the $σ(ω)$ 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 of the magnetic moment direction originates from the decreasing of the $c$-$f$ hybridization intensity. The magnetic ordering temperature $T_0$ is not directly related to the $c$-$f$ hybridization but is related to the charge excitation at 20 meV observed along the $b$ axis.

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