Origin of infrared peaks in the optical conductivity of ytterbium compounds

We have calculated optical conductivity $\left[\sigma \left(\omega \right)\right]$ spectra of ytterbium compounds (${\text{YbAl}}_3$, ${\text{YbAl}}_2$, ${\text{YbCu}}_2{\text{Si}}_2$, ${\text{YbNi}}_2{\text{Ge}}_2$, ${\text{YbInCu}}_4$, ${\text{YbRh}}_2{\text{Si}}_2$, ${\text{YbIr}}_2{\text{Si}}_2$, and ${\text{YbB}}_{12}$) based on the direct interband transition derived from first-principle band calculation and compared the results with the experimentally obtained $\sigma \left(\omega \right)$ spectra. The spectral feature of a peak in the middle-infrared (IR) region (mid-IR peak) and a shoulder structure in the far-infrared region (far-IR shoulder) in the experimental $\sigma \left(\omega \right)$ spectra can be described by the band calculation with a common renormalization factor. This result indicates that the infrared spectra of Yb compounds originate from the interband transition from the $\text{Yb}4f$ state but that the $\text{Yb}4f$ state shifts to the Fermi level with strong electron correlation.

Figure 1

(Color online) Calculated optical conductivity $\left[\sigma \left(\omega \right)\right]$ spectra compared with experimental spectra of ${\text{YbAl}}_3$ (Ref. 30), ${\text{YbAl}}_2$ (Ref. 8), ${\text{YbCu}}_2{\text{Si}}_2$ (Ref. 8), ${\text{YbNi}}_2{\text{Ge}}_2$ (Ref. 8), ${\text{YbInCu}}_4$ (Ref. 31), ${\text{YbRh}}_2{\text{Si}}_2$ (Ref. 32), ${\text{YbIr}}_2{\text{Si}}_2$ (Ref. 33), and ${\text{YbB}}_{12}$ (Ref. 34). The $\sigma \left(\omega \right)$ spectra of ${\text{YbCu}}_2{\text{Si}}_2$, ${\text{YbNi}}_2{\text{Ge}}_2$, ${\text{YbRh}}_2{\text{Si}}_2$, and ${\text{YbIr}}_2{\text{Si}}_2$ were calculated along the $a$ axis, in the same way as the experimental spectra. The horizontal scales of the experimental and calculated spectra are located at the top and bottom, respectively. Note that the horizontal scale of the calculated $\sigma \left(\omega \right)$ spectra is reduced by a factor of 0.42 $\left(=0.5/1.2\right)$ compared with that of the experimental spectra. The vertical scales of the calculated and experimental $\sigma \left(\omega \right)$ spectra are identical except in the case of ${\text{YbInCu}}_4$, in which the experimental spectrum is three times as large as the calculated spectrum. The mid-IR peaks and far-IR shoulders of the experimental and calculated spectra are marked by open triangles and open circles, respectively.

Figure 2

(Color online) Experimental energies $\left(\hslash {\omega }_{expt}\right)$ of the mid-IR peaks and far-IR shoulders as a function of the corresponding calculated energies $\left(\hslash {\omega }_{calc}\right)$ of Yb compounds (solid circles). The error bars show the width of the peak top in both the experimental and calculated spectra. The dashed line indicates $\hslash {\omega }_{expt}=0.42\times \hslash {\omega }_{calc}$, which is the reducing ratio of the photon energy in Fig. 1