Abstract: Although crystals with perovskite structure have been intensively investigated, there is up to now no clear explanation of why some of them do not remain cubic at low temperature. In particular, the mechanisms of the octahedral tilting in the perovskites have usually been discussed in terms of empirical models based on ion sizes. Here, we show that this important phenomenon is always controlled by changes in covalent bonding through the mixing of occupied and unoccupied orbitals as described by the pseudo-Jahn?Teller effect. These claims are supported by ab initio calculations for the highly ionic perovskite family KMF3 (M is Ca2+ or a 3d transition metal). In particular, it is found that the tilting angle in these compounds depends linearly on the electron population of the ?-bonding t2g orbital of the transition metal. This observation is explained using a pseudo-Jahn?Teller model and by studying the calculated electron density of these crystals for different magnetic states.

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