Low-temperature orbital ordering and dynamical frustration of spins in KCuF$_3$: Experimental*

We present new Raman and x-ray scattering evidence for the existence of a structural phase transition at 50 K in KCuF$_3$. Phonon modes associated with the F-ions in CuF$_{6}$ octahedra soften with decreasing temperature down to 50 K, at which temperature there is a splitting of the E$_g$ phonon. Above T$_{N}$ = 40 K, diffuse resonant magnetic scattering from critical fluctuations was observed at the Cu L$_{3}$ edge. Below T$_{N}$, orbital reflections seen by 8.8 keV x-ray scattering exhibit diffuse scattering that is hysteretic with temperature, indicating glassy orbital disorder. The phase behavior of KCuF$_{3}$ above T$_{N}$ is dominated by coupled orbital/lattice fluctuations that are likely associated with dynamical rotations of the CuF$_{6}$ octahedra. A model with interactions between orbital, spin and lattice degrees of freedom explain these observations.