Abstract
Understanding orbital ordered (OO) Mott insulating states lies at the heart of a consistent resolution of the colossal magneto-resistance (CMR) observed in manganites, where its melting induces a low-$T$ insulator-metal transition upon hole doping for $0.25 \le x\le 0.45$. Motivated thereby, we study the OO states in a planar model for bilayer manganites using dynamical-mean-field-theory (DMFT) and finite-size diagonalisation methods. We derive the OO ground states in manganites, for $x=0,\frac{1}{2},\frac{2}{3},\frac{3}{4}$ in agreement with observations, including the charge-orbital-magnetic ordered stripe phases for $x>\frac{1}{2}$. These OO states are shown to be associated with an alloy ordering of the $d_{3x^{2}-r^{2}}/d_{3y^{2}-r^{2}}$ orbitals on each $Mn^{3+}$ site.
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