  The Mott insulating perovskite KCuF3 is considered the archetype of an
orbitally-ordered system. By using the LDA+dynamical mean-field theory (DMFT)
method, we investigate the mechanism for orbital-ordering (OO) in this
material. We show that the purely electronic Kugel-Khomskii super-exchange
mechanism (KK) alone leads to a remarkably large transition temperature of T_KK
about 350 K. However, orbital-order is experimentally believed to persist to at
least 800 K. Thus Jahn-Teller distortions are essential for stabilizing
orbital-order at such high temperatures.
