Softening of the Rotary Lattice Mode inK2PtBr6as Detected by Nuclear Quadrupole Resonance

Measurements of the ${}_{}{}^{79}{}_{}{}^{}\mathrm{Br}$ nuclear-quadrupole-resonance frequency and spin-lattice relaxation time in a polycrystalline sample of ${\mathrm{K}}_2$Pt${\mathrm{Br}}_6$ from 4 to 450 K are reported. The frequency data indicate that structural phase transitions occur at 78, 105, 137, 143, and 169 K. The relaxation-time data are extemely sensitive to the phase transition at 169 K. At the high-temperature phase transition the structure of the substance changes from cubic to tetragonal. On the basis of previous comprehensive studies in ${\mathrm{K}}_2$Re${\mathrm{Cl}}_6$ it is likely that the phase transition is second order and is driven by the rotary lattice mode. As a model for this transition it is assumed that the Pt${\mathrm{Br}}_6^{2-}$ octahedra remain undistorted but that they rotate within the cages defined by neighboring ${\mathrm{K}}^{+}$ ions and that the cages elongate in the directions of the axes of rotation of the octahedra. The frequency data in the high-temperature phase are analyzed to yield the temperature dependence of a certain average ${\overline{\omega }}_{\nu }$ of the rotary-lattice-mode frequency over the Brillouin zone; a 12% softening is deduced. The relaxation data in the high-temperature phase are analyzed to yield the temperature dependence of a second average ${\overline{\omega }}_{T_1}$ of the rotary-mode frequency over the Brillouin zone; a 40% softening is deduced. It is shown that the difference between the temperature dependence of ${\overline{\omega }}_{\nu }$ and ${\overline{\omega }}_{T_1}$ is due to a difference in weighting of the rotary-mode frequency near the Brillouin-zone center. In particular, the dramatic temperature dependence of ${\overline{\omega }}_{T_1}$ can only be accounted for through the anharmonic Raman process and not the ordinary Raman process for quadrupolar-dominated spin-lattice relaxation. Below 169 K, two $T_1$ values, one approximately twice the other, are observed at each temperature. It is shown that this observation is consistent with the model postulated for the phase transition. The average rotary-mode frequency is found to harden as the temperature decreases below 169 K. That $T_1$ is insensitive to the phase transitions at lower temperatures is thought to imply that these transitions are not driven by the rotary-lattice mode.