Localized and Delocalized Excitons: Resonant Inelastic X-Ray Scattering in ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{NiO}}_4$ and ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$

The dynamics of doped charge in an antiferromagnetic lattice is central to the description of the insulator-metal transition that occurs on doping the parent high $T_c$ compounds. In this work we use high resolution resonant inelastic x-ray scattering to investigate the dynamics of the charge-transfer exciton by measuring its energy dispersion in two prototype compounds, ${\mathrm{La}}_2{\mathrm{CuO}}_4$ and ${\mathrm{La}}_2{\mathrm{NiO}}_4$. We show that this behavior is radically different in the cuprate with respect to a system known to exhibit strong polaronic behavior, namely, the nickelate: the exciton is mobile in the cuprate while it is well localized in the nickelate. Using a simple Wannier-Mott model we can estimate the total hole plus electron effective mass in the cuprate to be $3.5\pm 0.3m_e$ which would exclude strong localization in the undoped cuprate.

Figure 1

Total fluorescence yield Cu-$K$ edge absorption in (a) ${\mathrm{La}}_2{\mathrm{CuO}}_4$ (photon polarization at 15° from $c$ axis and (b) ${\mathrm{La}}_2{\mathrm{NiO}}_4$ (polarization parallel to $c$ axis).

Figure 2

(a) RIXS dispersion in ${\mathrm{La}}_2{\mathrm{CuO}}_4$ along the $[100/010]$ direction. The spectra have been shifted vertically, the baseline is indicated for each spectrum. Solid line: 3 point smoothed guide for the eye; dotted line: BZ edge spectrum; open circles label crystal field excitations. (b) Differences between smoothed spectra at various points in the BZ and the BZ edge spectrum from (a). (c) Dispersion of the exciton as determined from our data (solid circles) and as determined by Kim et al. [5] (triangles).

Figure 3

(a) RIXS dispersion in ${\mathrm{La}}_2{\mathrm{NiO}}_4$ along the $[100/010]$ direction. The spectra have been shifted vertically, the baseline is indicated for each spectrum. Solid line: three-point smoothed guide for the eye; dotted line: BZ edge spectrum; open circles label crystal field excitations. (b) Differences between smoothed spectra at various points in the BZ and the BZ edge spectrum from (a). (c) Dispersion of the exciton as determined from our data.

Figure 4

(a) RIXS spectra of ${\mathrm{La}}_{1.93}{\mathrm{Sr}}_{0.07}{\mathrm{CuO}}_4$ (open triangles) and ${\mathrm{La}}_2{\mathrm{CuO}}_4$ (solid circles) at the BZ center. (b) RIXS spectra of ${\mathrm{La}}_{1.9}{\mathrm{Sr}}_{0.1}{\mathrm{NiO}}_4\times 2$ (open triangles) and ${\mathrm{La}}_2{\mathrm{NiO}}_4$ (solid circles). Here, spectra have been summed over the BZ to increase statistics. Solid lines: three-point smoothed guides for the eye. (c) Schematics of formation of twin spin zero Cu sites in the ${\mathrm{CuO}}_2$ planes. The bigger central sphere represents Cu while the surrounding smaller spheres represent O atoms on a ${\mathrm{CuO}}_2$ plaquette. Charge transfer results in an exciton and a Cu $3d^{10}$ spin zero configuration on the left while the hole spins form a spin zero Z-R singlet on the right.