Experimental and theoretical determination of the anisotropic anomalous scattering tensor at the Mn K edge in LaMnO$_{3}$

A resonant x-ray scattering (RXS) study of (h 0 0), (0 k 0) and (0 0 l) forbidden reflections (h, k, l odd) at the Mn K- edge of LaMnO$_{3 }$was performed between 10 and 300 K. We observed strong resonant peaks at the three reflections. The azimuth angle dependence of all these reflections showed a characteristic sine evolution of $\pi $-period. The energy dependence of the intensity for (h 0 0) and (0 k 0) reflections was identical while different structures were observed for (0 0 l) reflections. We did not observe any change either on the resonance intensity or on the line shape when crossing the N\'{e}el temperature T$_{N}\sim $ 140 K. The energy, azimuth angle and polarization dependences of the three reflections are originated by off-diagonal terms of the scattering tensor. The theoretical analysis show that the principal axes of the anomalous scattering tensor depends on the photon energy. Moreover, resonant scattering in LaMnO3 is not a probe of d-orbital ordering.