Probing orbital fluctuations in $R$VO${}_3$ ($R$ $=$ Y, Gd, or Ce) by ellipsometry

We study optical excitations across the Mott gap in the multiorbital Mott-Hubbard insulators $R$VO${}_3$. The multipeak structure observed in the optical conductivity can be described consistently in terms of the different $3d^3$ multiplets or upper Hubbard bands. The spectral weight is very sensitive to nearest-neighbor spin-spin and orbital-orbital correlations and thus shows a pronounced dependence on both temperature and polarization. Comparison with theoretical predictions based on either rigid orbital order or strong orbital fluctuations clearly rules out that orbital fluctuations are strong in $R$VO${}_3$. Both the line shape and the temperature dependence give clear evidence for the importance of excitonic effects.

Figure 1

(a) Optical conductivity ${\sigma }_1^a\left(\omega \right)$ of YVO${}_3$. (b)–(d) ${\sigma }_1^c\left(\omega \right)$ of YVO${}_3$, GdVO${}_3$, and CeVO${}_3$, respectively. Temperature labels refer to the dashed lines. The absorption bands are labeled as peaks A ($\approx$2 eV), B ($\approx$$2.5$ eV), C (3.0–3.6 eV), and D (3.8–4.4 eV). (e) $G$-type OO with $C$-type SO. (f) $C$-type OO with $G$-type SO. In both, (e) and (f), the vertical axis corresponds to the $c$ axis. (g) Sketch of $t_{2g}^2$ and $t_{2g}^3$ multiplets.

Figure 2

Sum of the spectral weights of peaks A and B in ${\sigma }_1^c$. Inset: Theoretical results for $N_{\mathrm{eff}}\left(T\right)$ of the lowest Mott-Hubbard excitation (${}^4{A}_2$ multiplet) in ${\sigma }_1^c$ for strong orbital fluctuations (blue, $T_N=T_{\mathrm{OO}}$) and rigid orbital order [red, $T_{\mathrm{OO}}=\infty$, i.e., only the reduction of the spin part to 2/3 is taken into account (see Refs. 10 and 11)].

Figure 3

Ratio of the spectral weights of peaks A and B in ${\sigma }_1^c$, normalized to the value at 300 K.