  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.
