Exciton Doublet in the Mott-Hubbard Insulator ${\mathrm{LiCuVO}}_4$ Identified by Spectral Ellipsometry

Spectroscopic ellipsometry was used to study the dielectric function of ${\mathrm{LiCuVO}}_4$, a compound comprised of chains of edge-sharing ${\mathrm{CuO}}_4$ plaquettes, in the spectral range 0.75–6.5 eV at temperatures 7–300 K. For photon polarization along the chains, the data reveal a weak but well-resolved two-peak structure centered at 2.15 and 2.95 eV whose spectral weight is strongly enhanced upon cooling near the magnetic ordering temperature. We identify these features as an exciton doublet in the Mott-Hubbard gap that emerges as a consequence of the Coulomb interaction between electrons on nearest and next-nearest-neighbor sites along the chains. Our results and methodology can be used to address the role of the long-range Coulomb repulsion for compounds with doped copper-oxide chains and planes.

Figure 1

Real ${\epsilon }_1(\omega )$ and imaginary ${\epsilon }_2(\omega )$ parts of the dielectric function of ${\mathrm{LiCuVO}}_4$ at 7, 100, and 300 K for polarizations (a) $E\parallel a$, (b) $E\parallel b$ and (c) $E\parallel c$. Blue and red arrows mark the $T$-dependent features discussed in the text.

Figure 2

(a), (b) $T$-difference spectra $\Delta {\sigma }_1(T,\omega )={\sigma }_1(T_1,\omega )-{\sigma }_1(T_2,\omega )$ (red) and $\Delta {\epsilon }_1(T,\omega )={\epsilon }_1(T_1,\omega )-{\epsilon }_1(T_2,\omega )$ (black) of ${\mathrm{LiCuVO}}_4$ for polarizations (a) perpendicular to and (b) along the chains. Successive $\Delta {\sigma }_1(T,\omega )$ and $\Delta {\epsilon }_1(T,\omega )$ spectra are shifted by $130{\Omega }^{-1}{\mathrm{cm}}^{-1}$ and 0.26 for clarity [23]. (c),(d) $T$ dependence of ${\sigma }_1$ and ${\epsilon }_1$ measured at 3.8, 4.21, and 4.45 eV for polarization perpendicular to the chains and at 2.65, 3.0, and 3.45 eV for polarization along the chains, as marked by vertical lines in (a) and (b), respectively.

Figure 3

(a) SW changes $\Delta N_{\mathrm{eff}}(\omega )=N_{\mathrm{eff}}(\omega ,50\mathrm{K})-N_{\mathrm{eff}}(\omega ,7\mathrm{K})$ in ${\mathrm{LiCuVO}}_4$ for polarizations along (open squares) and perpendicular (open circles) to the chains. (b) ${\epsilon }_2$ spectrum for polarizations along and perpendicular to the chains derived from experiment at 7 K and calculated from the $pd$-Hamiltonian as described in text. The optical bands above 5 eV listed in Table S1 of 23 were subtracted.

Figure 4

(a) Mott-Hubbard exciton formed by $d^9{L}_h$ and $d^{10}$ states generated by NN ($t_1$) or NNN ($t_2$) hopping. (b) $T$-difference spectra of ${\epsilon }_2(\omega )$ near 2.9 eV for polarization along the chains, background corrected due to the temperature variation of the high-energy optical bands [23]. (c) $T$ dependence of SW of exciton bands at 2.15 and 2.95 eV. Inset: ${\sigma }_1(\omega )$ and density of states $D(\omega )$ of the UHB calculated with Eq. (1) at $T=0$ and $U=3.75$, $V=1.6$, $t_1=0.08$, and $t_2=0.1\mathrm{eV}$.