Antiferrodistortive soft mode in PbZr$_{0.024}$Ti$_{0.976}$O$_{3}$ crystal

Antiferrodistortive (AFD) soft mode at the M point of the Brillouin zone in the PbZr$_{0.024}$Ti$_{0.976}$O$_{3}$ crystal is detected using inelastic scattering of synchrotron radiation. Group-theoretical analysis and calculations of inelastic structural factors made it possible to unambiguously correlate the critical excitation with rotations of oxygen octahedra. The temperature evolution of the soft mode frequency is revealed and it is shown that it obeys the Curie–Weiss law with the Curie temperature of $T_{\mathrm{AFD}}$ = 438 $\pm$ 5 K, which is close to the ferroelectric Curie temperature of $T_{\mathrm{FE}}$ = 438 $\pm$ 5 K. The frequency of the antiferrodistortive soft mode is less than the frequency of the doubly degenerate acoustic vibration at the M point. Consequently, intermode interaction and anticrossing when deviating from the Brillouin zone boundary are inevitable.