Determination of the Mechanism for Resonant Scattering in ${\mathrm{LaMnO}}_3$

The resonant multiple Bragg x-ray diffraction is used to study the forbidden $(10\overline{4})$ reflection in ${\mathrm{LaMnO}}_3$. Using the interference between the three-beam scattering and resonant scattering we can determine the phase of the resonant scattering. This phase is shown to be consistent with a model in which the resonant scattering is caused by the influence of the Mn-O bond length distortion rather than directly by the orbital ordering on the Mn $4p$ band structure.

Figure 1

An artistic concept, according to Ref. 2, of the orbital ordering and JT distortion in the (001) Mn-O plane of ${\mathrm{LaMnO}}_3$.

Figure 2

The $(1,0,\overline{4})$ interference profiles for (a) the $(\overline{1},\overline{2},0)$ and (b) the $(4,\overline{2},\overline{4})$ simultaneous reflections.

Figure 3

Real and imaginary part of the trace of the Mn form factor calculated in local-density approximation with 3 eV core-hole lifetime (left panel). The $x$ and $y$ diagonal components of $\Delta f_{Mn}$ are plotted for $B$ sites in a cubic coordinate system with the $x$ and $y$ axes pointing along the long and short Mn-O bonds in the $ab$ plane, respectively (right panel).

Figure 4

Three-beam interference profile calculated for the $(\overline{1},\overline{2},0)$ (left panel) and the $(4,\overline{2},\overline{4})$ (right panel) simultaneous reflections with the energy of the incident $\mathrm{\text{photons}}=6.554\mathrm{keV}$.