Relationship between orbital structure and lattice distortions in Jahn-Teller systems

We show that the usual approach directly relating the orbital occupation of Jahn-Teller ions to the displacements of neighboring ligands may be misleading. For the correct identification of orbital structure, it is necessary to take self-consistently into account the electron-lattice interaction, kinetic energy of charge carriers, and crystal-field effects. We demonstrate it on the example of the CE phase of the single-layer manganite La${}_{0.5}$Sr${}_{1.5}$MnO${}_{4}$, in which the type of orbital ordering strongly deviates from that which one would deduce from the local lattice distortions.