Orbital ordering in striped phases of La$_{1-x}$Ca$_x$MnO$_3$: GGA+U versus GGA results

We have investigated the orbital ordering in La$_{1-x}$Ca$_x$MnO$_3$, with x=2/3 and 1/2, within the generalized gradient approximation (GGA) of density functional theory and within the GGA plus onsite Coulomb interaction (GGA+U) approach. The calculations were performed using the pseudopotential plane-waves scheme and include structural relaxation. In the half-doped case, similar results are obtained for the orbital and atomic structure within the two approaches, with structural properties consistent with experiment. For the two-third-doped system, instead, the results differ between the two approaches. Only the GGA+U yields an insulating striped phase with structural properties in agreement with experiment. Our results show the importance of the cooperative effects of the Jahn-Teller distortion, strain modulation, and electronic localization in stabilizing the orbital-ordered striped phases, and provide new insight into the atomic-scale structure of the orbital order in La$_{1/3}$Ca$_{2/3}$MnO$_3$.