Orbital Order, Stripe Phases and Mott Transition in a Planar Model for Manganites

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 for $0.25\le x\le 0.45$. Motivated thereby, we study the OO states in a planar model for bilayer manganites using DMFT and finite-size diagonalisation methods. We derive the correct OO ground states observed in manganites for $x=0,1\mathrm{/}2,2\mathrm{/}3,3\mathrm{/}4$ in exact agreement with observations, including the charge-orbital-magnetic ordered stripe phases for $x>1\mathrm{/}2$. These OO states are {\it exactly} shown to be associated with an ``alloy’’ ordering of the $d_{3x^2-r^2}\mathrm{/}{d}_{3y^2-r^2}$ orbitals on each $M{n}^{3+}$ site.