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

Abstract

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${\mathrm{Br}}_{6}^{2\ensuremath{-}}$ 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 ${\overline{\ensuremath{\omega}}}_{\ensuremath{\nu}}$ 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 ${\overline{\ensuremath{\omega}}}_{{T}_{1}}$ 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 ${\overline{\ensuremath{\omega}}}_{\ensuremath{\nu}}$ and ${\overline{\ensuremath{\omega}}}_{{T}_{1}}$ is due to a difference in weighting of the rotary-mode frequency near the Brillouin-zone center. In particular, the dramatic temperature dependence of ${\overline{\ensuremath{\omega}}}_{{T}_{1}}$ 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.