Origin of the Antiferroorbital Ordering in LaMnO3and Other Related Compounds

In order to get a realistic view of the origin of the antiferroorbital (AFO) order in LaMnO 3 , MnF 3 and KCuF 3 , both the cooperative Jahn–Teller effect (CJTE) and the orbital-dependent exchange interaction (OEI) are taken into account for the d γ electron–lattice system in compounds with the perovskite-type structure. The phonon-mediated orbital interaction in the CJTE and the d γ electron-mediated one in the OEI are treated by use of the mean-field approximation with preserving the symmetry of the crystal, and are joined to give an effective Hamiltonian. It is stressed that the CJTE favors any of the FO and AFO orders, while the OEI does only the AFO order. The present theory is consistent with the observed fact that the AFO order is characterized by an arrangement of alternate mixed orbitals of d x 2 - y 2 and d 3 z 2 - r 2 , the AFO phase survives even at sufficiently high temperatures in the paramagnetic phase, and the AFO order is always accompanied by the ferrodistortion and the antiferrodistortion.