Strongly momentum-dependent screening dynamics in La${}_{0.5}$Sr${}_{1.5}$MnO${}_4$ observed with resonant inelastic x-ray scattering

We report strongly momentum-dependent short-ranged charge screening dynamics in CE-type charge, orbital, and spin ordered La${}_{0.5}$Sr${}_{1.5}$MnO${}_4$, based on Mn $K$-edge resonant inelastic x-ray scattering data. Through a comparison with theoretical calculations, we show that the observed momentum dependence reflects highly localized, nearest-neighbor screening of the transient local charge perturbation in this compound with an excitonlike screening cloud, rather than delocalized screening. The size of the screening cloud is estimated to be about 0.4–0.5 interatomic distances.

Figure 1

(a) RIXS spectra at three Q points. (b) The Q points surveyed in the $(H,H,L)$ plane. The radius of the dot is proportional to the integrated intensity of the 2 eV peaks. $\theta$ and $2\theta$ are the incident and detector angles. (c) RIXS spectra for the Q points along the $2\theta ={68}^{\circ }$ line, with the elastic intensity subtracted. The gray shaded region is the energy window used in calculating the integrated intensity of the feature.

Figure 2

(a) Contour plot of RIXS intensity calculated for the electron hopping parameter $t_0=0.9$ eV, after averaging over twin domains. (b) The integrated RIXS intensity of the 2 eV peak relative to the $(-0.03,-0.03)$ point, plotted with respect to the in-plane momentum transfer along the $(H,H)$ direction. Symbols represent experimental data. Lines represent theoretical results for different values of $t_0$. Both experimental data and theoretical results are normalized for comparison.

Figure 3

(a) and (b): Screening configuration in real space for $t_0=0.9$ and 1.5 eV, respectively. The top left half corresponds to the case with the core hole at a Mn${}^{3+}$ site, while the bottom right it is at a Mn${}^{4+}$ site. The volumes of the red and blue spheres are proportional to the electron and hole numbers. The large red spheres at Mn${}^{4+}$ core-hole sites represent about 0.9 electrons. (c) and (d): Integrated RIXS intensity plotted in the $(H,K,0)$ plane of reciprocal space for $t_0=0.9$ and 1.5 eV, respectively. Red and blue represent the maximum and minimum intensities, respectively.

Figure 4

The excited hole number normalized by the excited electron number at the core-hole site, plotted in semilogarithmic scale with respect to the distance from the core-hole site along the zigzag chain.