Jahn-Teller Effect and Superexchange in Half-Doped Manganites

We investigate the stability of the charge exchange (CE) phase within a microscopic model which describes a single plane as in La$_{0.5}$Sr$_{1.5}$MnO$_4$. The model includes Coulomb interactions (on-site and intersite), the Jahn-Teller term and the superexchange interactions due to $e_g$ and $t_{2g}$ electrons. By investigating the phase diagram at T=0 in mean-field approximation we conclude that the superexchange interactions can stabilize the CE phase, but only if they are stronger than estimated from spectroscopy.