A-type Antiferromagnetic and C-type Orbital-Ordered State in LaMnO${}_3$ Using Cooperative Jahn-Teller Phonons

The effect of Jahn-Teller phonons on the magnetic and orbital structure of LaMnO${}_3$ is investigated using a combination of relaxation and Monte Carlo techniques on three-dimensional clusters of MnO${}_6$ octahedra. In the physically relevant region of parameter space for LaMnO${}_3$, and after including small corrections due to tilting effects, the A-type antiferromagnetic and C-type orbital structures were stabilized, in agreement with experiments.