Orbital ordering in paramagnetic LaMnO3 and KCuF3

Ab initio studies of the stability of orbital ordering, its coupling to magnetic structure and its possible origins (electron-phonon and/or electron-electron interactions) are reported for two perovskite systems, ${\mathrm{LaMnO}}_{3}$ and ${\mathrm{KCuF}}_{3}.$ We present an average spin state calculational scheme that allowed us to treat a paramagnetic state and to succesfully describe the experimental magnetic or orbital phase diagram of both ${\mathrm{LaMnO}}_{3}$ and ${\mathrm{KCuF}}_{3}$ in crystal structures when the Jahn-Teller distortions are neglected. Hence, we conclude that the orbital ordering in both compounds is purely electronic in origin.