Order parameter saturation in LaAlO₃

High-resolution x-ray rocking diffraction has been used to measure the spontaneous strain associated with the cubic-rhombohedral phase transition in LaAlO₃ in the range 10 K ≤ T ≤ 750 K. The data are consistent with a second-order Landau-like model at high temperatures, with T_C = 834(2) K. At lower temperatures, the strain data display order parameter saturation, related to the quantum saturation of the phonon modes. Comparison of the saturation temperature for the spontaneous strain (θ_S = 95 K) with the saturation temperatures for independent measurements of the rotation (θ_S = 260 K) and distortion (θ_S = 150 K) of the AlO₆ octahedra indicates that the phase transition consists of two coupled processes, and that the coupling does not have the same effect in the classical and quantum saturation limits.