Modified Double Exchange Model with Novel Spin and Orbital Coupling: Phase Diagram of The Manganites

From a general model of the Mn oxides R_{1-x}A_{x}MnO_3, we derive an effective Hamiltonian in the low-energy subspace using the projection operator method, in which a novel coupling between the spin and orbital degrees of freedom is included. A phase diagram for temperature T versus doping concentration x is computed by means of Monte Carlo simulation. Our result is consistent with experimental observations in the Mn oxides with relatively wide conduction band, such as Pr_{1-x}Sr_{x} MnO_{3} and La_{1-x}Sr_{x}MnO_{3}. According to the obtained orbital ordering, we also predict that the motion of charge carriers transforms from three-dimensional to two-dimensional as x is increased beyond a critical value.