Resonant x-ray scattering at the forbidden reflections in Mn³⁺ perovskites REMnO₃ (RE:La and Tb)

We here report a combined experimental and theoretical resonant x-ray scattering study in two isomorphous compounds, LaMnO₃ and TbMnO ₃. The two samples show an orthorhombic Pbnm structure with four Mn³⁺ atoms at equivalent positions. The Mn sites have a local inversion symmetry and they are surrounded by nearly tetragonal-distorted oxygen octahedron. The tetragonal distortion is larger in TbMnO₃ than in LaMnO₃. Resonances were measured at the Mn K-edge of the (h,0,0), (0,k,0) and (0,0,1) (h,k,1=3,5) reflections. All the reflections show a resonance only in the σ-π' polarization channel. The observed resonant intensities exhibit a sin²φ dependence on the azimuth angle φ. The (h,0,0) and (0,k,0) reflections have identical energy dependence but markedly different than the (0,0,1) reflections. Differences in the energy line shape and width of these resonant reflections between La and Tb samples are explained in terms of the different tetragonal distortion and the different ionic radius of the rare-earth. The origin of the two types of reflections (related to two different nonzero non-diagonal elements of the scattering tensor) is explained within the multiple scattering theory considering long-range order of structural distortions in a cluster up to 63 atoms without invoking any d-orbital order.