Observation of orbital ordering and Jahn-Teller distortions supporting the Wigner-crystal model in highly doped ${\mathrm{Bi}}_{1-x}{\mathrm{Ca}}_x\mathrm{Mn}{\mathrm{O}}_3$

We report on the experimental characterization of orbital ordering and the associated lattice distortions in highly doped ${\mathrm{Bi}}_{1-x}{\mathrm{Ca}}_x\mathrm{Mn}{\mathrm{O}}_3$. Resonant x-ray diffraction was used at the $\mathrm{Mn}L$-edge for the direct observation of the ordered localized states, and at the $\mathrm{Mn}K$-edge for the sensitivity to the distortions of the manganese-oxygen octahedra. The orbital ordering on Mn atoms was directly observed at $x=0.69$; the analysis and the numerical simulations of the $K$-edge spectra allow us to characterize the pattern of the distorted octahedra at $x=\frac{4}{5}$. These observations support the Wigner-crystal-type model at both dopings; the bi-stripe model is ruled out at $x=0.69$.

Figure 1

$L_{\mathit{II}∕\mathit{III}}$-edge resonant x-ray diffraction spectra of the $\left(0\delta 0\right)$ reflection $(\delta =0.31)$ for ${\mathrm{Bi}}_{0.31}{\mathrm{Ca}}_{0.69}\mathrm{Mn}{\mathrm{O}}_3$, at $T=200\mathrm{K}$ taken with two polarizations of the incident photon, $\pi$ and $\sigma$ (without absorption correction). Inset, longitudinal $Q$-scan.

Figure 2

Scattering geometry for the $L$-edge experiment. The crystallographic directions of the sample are indicated following the $Pbnm$ settings.

Figure 3

$K$-edge resonant x-ray diffraction spectra of the $(02+\delta 0)$ reflection for various doped manganites in their orbital ordered phase (without self-absorption correction). Similarities in the spectra indicate the presence and the same specific arrangement of Jahn-Teller distorted octahedra. The slight shift (about $2\mathrm{eV}$) in the resonance is due to various interatomic distances and differing energy calibrations on the beamline.

Figure 4

$K$-edge resonant x-ray diffraction spectra for ${\mathrm{Bi}}_{0.2}{\mathrm{Ca}}_{0.8}\mathrm{Mn}{\mathrm{O}}_3$ in the orbital ordered phase $\left(8.5\mathrm{K}\right)$, $\delta \sim 0.20$ (without absorption correction).

Figure 5

(Color online) Model of a crystallographic structure for the orbital order phase at $x=0.8$ doping. The arrows indicate the direction of the displacements from the undistorted structure. The displacement pattern is the same as in the structure proposed for ${\mathrm{La}}_{0.33}{\mathrm{Ca}}_{0.66}\mathrm{Mn}{\mathrm{O}}_3$. The small circles represent planar oxygen atoms. Larger circles are Mn atoms; shaded circles are the Jahn-Teller Mn atoms; the labels corresponds to the atoms listed in Table . Squares represent the cations.

Figure 6

Calculation of the resonant spectra presented in Fig. 4 using the structure for ${\mathrm{Bi}}_{0.2}{\mathrm{Ca}}_{0.8}\mathrm{Mn}{\mathrm{O}}_3$ presented in Table and the FDMNES code (Ref. 17). The intensities are normalized to the maximum intensity calculated for the (116) reflection. Straight lines are the intensities with self-absorption correction (Ref. 30), to be compared with Fig. 4; dashed lines are the normalized intensities without the absorption correction.

Figure 7

Illustration of the sensitivity of the resonant spectra to displacements of oxygen atoms. The calculations are performed for the same positions as in Table , except for the oxygens $\mathrm{O}p1$ and $\mathrm{O}p2$ which undergo the same displacements as $\mathrm{O}p3$, $\mathrm{O}p4$ and $\mathrm{O}p5$. The positions are (0.765, 0.05, 0.035) for $\mathrm{O}p1$ and (0.265, 0.05, $-0.035$) for $\mathrm{O}p2$, with the effect of reducing the distortion of the Jahn-Teller octahedra. Remarkably, only on-resonance scattering of $2\delta$ superstructure reflections is affected, in intensity and in energy line shape.