Cooperative Jahn-Teller Effect on the Magnetic Structure of Manganese Oxides

The magnetic structure of LaMnO$_3$ is investigated on three-dimensional clusters of MnO$_6$ octahedra by using a combination of relaxation and Monte Carlo techniques. It is found that the cooperative Jahn-Teller phonons lead to the stabilization of A-type antiferromagnetic and C-type orbital structures in the physically relevant region of parameter space for LaMnO$_3$ with small corrections due to tilting effects. The results suggest that strong Coulomb interactions are not necessary for a qualitative description of undoped manganites. In fact, it is shown that the present result is not essentially changed even if the Coulomb interaction is explicitly included.