Revisiting La_0.5Sr_1.5MnO₄ lattice distortion and charge ordering with multi-beam resonant diffraction

Sinusoidal wave type distortions of La_0.5Sr_1.5MnO₄ in the low-temperature orthorhombic phase were observed using multi-beam resonant X-ray diffraction (MRXD) with (7/4 7/4 0) fractional primary diffraction. Two four-beam diffractions with opposite asymmetry were measured at 6.5545 keV and compared with the curves simulated by the dynamical X-ray diffraction theory. This approach provides the possibility of resolving the distortion modes which are perpendicular to the momentum transfer by a single azimuthal scan. The paper also demonstrates the sensitivity of MRXD profiles versus incident X-ray energy in the vicinity of the Mn K edge to the charge disproportion between the two manganese sites, reconfirming the small charge disproportion feature.