Origin of the Orbital Ordering in LaMnO${}_3$

We use the temperature of the structural phase transition to determine the Jahn-Teller (JT) coupling constant in the model derived for LaMnO${}_3$ which includes both the superexchange between S=2 spins and the JT effect. We also investigate the dependence of the exchange constants on the value of the on-site Coulomb element $U$, and on the orbital ordering.