Mott-Hubbard exciton in the optical conductivity of ${\text{YTiO}}_3$ and ${\text{SmTiO}}_3$

In the Mott-Hubbard insulators ${\text{YTiO}}_3$ and ${\text{SmTiO}}_3$ we study optical excitations from the lower to the upper Hubbard band, $|d^1{d}^1⟩\to |d^0{d}^2⟩$. The multipeak structure observed in the optical conductivity reflects the multiplet structure of the upper Hubbard band in a multiorbital system. Absorption bands at 2.55 and 4.15 eV in the ferromagnet ${\text{YTiO}}_3$ correspond to final states with a triplet $d^2$ configuration, whereas a peak at 3.7 eV in the antiferromagnet ${\text{SmTiO}}_3$ is attributed to a singlet $d^2$ final state. A strongly temperature-dependent peak at 1.95 eV in ${\text{YTiO}}_3$ and 1.8 eV in ${\text{SmTiO}}_3$ is interpreted in terms of a Hubbard exciton, i.e., a charge-neutral (quasi-) bound state of a hole in the lower Hubbard band and a double occupancy in the upper one. The binding to such a Hubbard exciton may arise both due to Coulomb attraction between nearest-neighbor sites and due to a lowering of the kinetic energy in a system with magnetic and/or orbital correlations. Furthermore, we observe anomalies of the spectral weight in the vicinity of the magnetic ordering transitions, both in ${\text{YTiO}}_3$ and ${\text{SmTiO}}_3$. In the $G$-type antiferromagnet ${\text{SmTiO}}_3$, the sign of the change of the spectral weight at $T_N$ depends on the polarization. This demonstrates that the temperature dependence of the spectral weight is not dominated by the spin-spin correlations, but rather reflects small changes of the orbital occupation.

Figure 1

(Color online) Optical conductivity of ${\text{YTiO}}_3$ at 15 K. Inset: sketch of the optical excitations from the LHB and the oxygen $2p$ band into the UHB in case of a single, half-filled orbital at the transition-metal site.

Figure 2

(Color online) Optical conductivity of ${\text{YTiO}}_3$ in the vicinity of the onset of excitations across the gap. Good agreement is observed between our ellipsometry data and results determined from the combination of transmittance and reflectance measurements (Ref. 51).

Figure 3

(Color online) Optical conductivity of ${\text{YTiO}}_3$ below the onset of charge-transfer excitations, i.e., in the range of the lowest excitations from the lower to the upper Hubbard band. Peak B is attributed to the lowest multiplet, whereas peak A is identified as an excitonic resonance. Peak C reflects the lowest excitation to an $e_g$ orbital.

Figure 4

(Color online) Optical conductivity of ${\text{SmTiO}}_3$.

Figure 5

(Color online) Left: Calculated energies for a $|d^1{d}^1⟩\to |d^0{d}^2⟩$ excitation with different $d^2$ final states in a cubic crystal field (Ref. 57). The Slater integrals were chosen as $F^0=3.60\text{eV}$, $F^2=6.75\text{eV}$, and $F^4=4.55\text{eV}$, corresponding to $U=4.5\text{eV}$ (Ref. 56) and $J_H\approx 0.6\text{eV}$. For $10Dq=0$ the ionic multiplet structure is obtained. For $10Dq\approx 1.5–1.9\text{eV}$ (gray area) the energy of 4.15 eV for peak C is well described by excitations into the ${{}^{3}T}_2$ state. Right: sketch of the orbital occupation in the strong crystal-field limit for the ${{}^{3}T}_1$ triplet (red), the ${{}^{1}T}_2$ and ${}^{1}E$ singlets (green), and the ${{}^{3}T}_2$ triplet (blue).

Figure 6

(Color online) Top: Leading edge of the optical conductivity ${\sigma }_1^b\left(\omega \right)$ of ${\text{SmTiO}}_3$. Bottom: Temperature dependence of ${\sigma }_1^b\left(\omega =1.85\text{eV}\right)$ (crosses, left axis) and of the leading edge ${\omega }_e$, which we define by ${\sigma }_1^b\left({\omega }_e\right)=350{\left(\Omega \text{cm}\right)}^{-1}$ (full symbols, right axis). Open symbols show ${\tilde{\omega }}_e$ corrected for the change of the spectral weight, i.e., ${\sigma }_1^b\left({\tilde{\omega }}_e\right)=c\cdot 350{\left(\Omega \text{cm}\right)}^{-1}$ with $c={\sigma }_1^b\left(1.85\text{eV},T\right)/{\sigma }_1^b\left(1.85\text{eV},60\text{K}\right)$.

Figure 7

(Color online) Sketch of the suggested formation and propagation of a Hubbard exciton (dashed line). We consider two types of orbitals (circles and squares, e.g., $d_{xy}$ and $d_{xz}$) per site, where hopping is zero between orbitals of different type (crossed out arrows). Full (open) symbols denote occupied (empty) orbitals. (a) Ground state with antiferro-orbital order. (b) Creation of a hole and a double occupancy on sites 2 and 3, respectively. (c)–(f) Propagation of the double occupancy, the hole, or of an exciton (see main text for more details).

Figure 8

Temperature dependence of the effective carrier concentration $N_{\text{eff}}$ [see Eq. (1)] of ${\text{YTiO}}_3$ for ${\omega }_{\text{c}1}=1.6\text{eV}$ and ${\omega }_{\text{c}2}=2.6\text{eV}$ (left) and for ${\omega }_{\text{c}1}=2.6\text{eV}$ and ${\omega }_{\text{c}2}=3.9\text{eV}$ (right).

Figure 9

Temperature dependence of the effective carrier concentration $N_{\text{eff}}$ [see Eq. (1)] of ${\text{SmTiO}}_3$ for ${\omega }_{\text{c}1}=0.75\text{eV}$ and ${\omega }_{\text{c}2}=3.1\text{eV}$ (left) and for ${\omega }_{\text{c}1}=3.1\text{eV}$ and ${\omega }_{\text{c}2}=4.3\text{eV}$ (right).

Figure 10

(Color online) Comparison of the optical conductivity for the $b$ axis of ${\text{YTiO}}_3$ with spectra reported by Kovaleva et al. (Ref. 52), which were determined from either the $ab$ or the $bc$ surface of a freshly polished sample, or from the $ab$ surface of a sample measured after 1.5 years.