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We investigate the origin of the orbital ordering in the paramagnetic phaseof KCrF$_3$. All previous studies described structural parameters of theparamagnetic phase using a magnetic ordering in the compound. Our simulationsof real paramagnetic KCrF$_3$ were performed within an approach combiningdensity functional theory and dynamical mean field theory (DFT+DMFT). As aresult, it was found that the experimentally observed cooperative Jahn-Tellereffect is successfully described in a lattice relaxation calculation forstructure without any long-range magnetic ordering. It is established that theexistence of the orbital ordering even in undistorted perovskite structureclearly confirms the electronic origin of the orbital ordering in KCrF$_3$.

Correlations induced orbital ordering and cooperative Jahn-Teller distortion in the paramagnetic insulator KCrF$_3$