Novel mechanism for displacive distortions in perovskites: On the orbital ordering transition in KCuF$_3$

The Mott insulating perovskite KCuF$_3$ is considered the paradigmatic system with long-ranged orbital order and a cooperative Jahn-Teller distortion of the Cu-F octahedra. However, recent experiments have revealed that the JT-like distortions persist and even grow as temperature is increased. We show that neither superexchange nor Jahn-Teller can accurately describe this behavior---even qualitatively. Supported by GGA+U and model calculations, we explain this anomalous result in terms of a volume-driven lattice instability of purely ionic origin. We examine the effect of ionic size on this mechanism through the related systems KCu$_{1-x}$Mg$_x$F$_3$, KCrF$_3$, and ACuF$_3$. As a non-electronic effect, this instability should allow for octahedral distortions even in closed-shell systems with cubic ground states, and we propose design guidelines for the realization of this high-temperature broken-symmetry phase experimentally.