Soft-Phonon Response Function: Inelastic Neutron Scattering from LaA1<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

Abstract

High-resolution inelastic-neutron-scattering measurements have been performed at the cubic-rhombohedral ($\mathrm{Pm}3\mathrm{m}\ensuremath{\rightarrow}\mathrm{R}\overline{3}\mathrm{c}$) phase transitions in a low-mosaic flux-grown single crystal of LaA1${\mathrm{O}}_{3}$. The transition occurred at (489 \ifmmode\pm\else\textpm\fi{} 2) \ifmmode^\circ\else\textdegree\fi{}C, somewhat lower than reported for Verneuil-grown samples. The scattering from the soft ${R}_{25}$ mode at the corner of the Brillouin zone in the cubic phase exhibits the central component up to 610 \ifmmode^\circ\else\textdegree\fi{}C. In addition, phonon sidebands centered around $\ifmmode\pm\else\textpm\fi{}{\ensuremath{\omega}}_{\ensuremath{\infty}}$ are observed which are overdamped below 550 \ifmmode^\circ\else\textdegree\fi{}C. The observed intensities are well described by a model which relates the central component to the phonon sidebands through an anharmonic coupling parameter $\ensuremath{\delta}(T)$, as recently reported by Shapiro et al. for SrTi${\mathrm{O}}_{3}$. ${\ensuremath{\omega}}_{\ensuremath{\infty}}^{2}(T)$ is found to deviate from the mean-field behavior near the transition temperature and ${\ensuremath{\delta}}^{2}(T)$ is found to be nearly constant. A comparison is made between LaA1${\mathrm{O}}_{3}$, SrTi${\mathrm{O}}_{3}$, and KMn${\mathrm{F}}_{3}$ with respect to these parameters as well as the anisotropy of the dispersion surfaces near the $R$ point.