Resonant X-Ray Scattering from Orbital Ordering in ${\mathrm{LaMnO}}_3$

Dipole resonant x-ray scattering from ordered Mn $3d$ orbitals in $\mathrm{LaMn}{\mathrm{O}}_3$ has been observed near the Mn $K$-absorption edge. The polarization of the scattered photons is rotated from $\sigma$ to ${\pi }^{\prime }$ and the azimuthal angle dependence shows a characteristic twofold symmetry. A theory for the resonant scattering mechanism has been developed by considering the splitting of the Mn $4p$ levels due to the Mn $3d$ orbital ordering. The order parameter of the orbital ordering decreases above the Néel temperature ( $T_N=140\mathrm{}\mathrm{K}$) and disappears at $T_O=780\mathrm{}\mathrm{K}$, concomitant with a structural phase transition.