Direct observation of orbital ordering in La$_{0.5}$Sr$_{1.5}$MnO$_4$ using soft x-ray diffraction
We report the first direct resonant soft x-ray scattering observations of orbital ordering. We have studied the low temperature phase of La$_{0.5}$Sr$_{1.5}$MnO$_4$, a compound that displays charge and orbital ordering. Previous claims of orbital ordering in such materials have relied on observations at the Manganese $K$ edge. These claims have been questioned in several theoretical studies. Instead we have employed resonant soft x-ray scattering at the manganese $L_{III}$ and $L_{II}$ edges which probes the orbital ordering directly. Energy scans at constant wavevector are compared to theoretical predictions and suggest that at all temperatures there are two separate contributions to the scattering, direct orbital ordering and strong cooperative Jahn - Teller distortions of the Mn$^{3+}$ ions.