Low-energy optical excitation in rare-earth hexaborides

Reflectivity spectra of trivalent rare-earth hexaborides (R${\mathrm{B}}_6$; R=La, Ce, Pr, Nd, Gd, Tb, Dy, Ho, and Y) and mixed-valent ${\mathrm{SmB}}_6$ have been measured in the photon energy region from 1 meV to 40 eV at 300 and 9 K. We discuss the absorption structure due to conduction electrons. Even in ${\mathrm{LaB}}_6$ and ${\mathrm{YB}}_6$, which have no 4f electrons, the optical conductivity spectra were not fitted by a simple Drude model and a frequency-dependent relaxation time was observed. This was attributed to the electron-phonon and electron-electron scattering. In R${\mathrm{B}}_6$ with 4f electrons, a common absorption structure was observed at the energy position of about 0.6 eV. The intensity was found to be almost proportional to the 4f spin angular momentum. From the f-sum rule, the absorption was found to be due to the conduction electrons. The origin was assigned to be due to the transition or to the relevant exciton absorption from the saddle points of ${\mathrm{\Sigma }}_1$ at the neck point to the saddle points of ${\mathrm{\Gamma }}_{12}$ and ${\mathrm{\Gamma }}_{25}$ assisted by the scattering of the intra-atomic 5d-4f Coulomb exchange interaction, in particular enhanced in the heavy R${\mathrm{B}}_6$ compounds by the lattice instability. In ${\mathrm{SmB}}_6$, the absorption that was seen in trivalent R${\mathrm{B}}_6$’s was also observed in addition to absorptions from 4f states of ${\mathrm{Sm}}^{2+}$ to 5d states and from 5d to 4f in ${\mathrm{Sm}}^{3+}$. This is thought to mean that the Fermi level of ${\mathrm{SmB}}_6$ is located at the same energy position in the band structure as that of the trivalent R${\mathrm{B}}_6$.