Orbital ordering in La0.5Sr1.5MnO4 studied by model Hartree-Fock calculation

We have investigated orbital ordering in the half-doped manganite La0.5Sr1.5MnO4, which displays spin, charge, and orbital ordering, by means of unrestricted Hartree-Fock calculations on the multiband p-d model. From a recent experiment, it has become clear that La0.5Sr1.5MnO4 exhibits a cross-type (z2-x2/y2-z2) orbital ordering rather than the widely believed rod-type (3x2-r2/3y2-r2) orbital ordering. The calculation reveals that cross-type (z2-x2/y2-z2) orbital ordering results from an effect of in-plane distortion as well as from the relatively long out-of-plane Mn-O distance. For the "Mn4+" site, it is shown that the elongation along the c axis of the MnO6 octahedra leads to an anisotropic charge distribution rather than the isotropic one.