A pure nuclear-quadrupole-resonance study of the temperature dependence of the chlorine nuclear relaxation times in the concentrated paramagnet ${\mathrm{K}}_{2}$Ir${\mathrm{Cl}}_{6}$ is reported. It is shown that three different relaxation mechanisms contribute to the observed spin-lattice relaxation times. For temperatures less than 40\ifmmode^\circ\else\textdegree\fi{}K, ${T}_{1}$ is dominated by the hyperfine interaction between the chlorine nuclear spins and the electron spins of the ${\mathrm{Ir}}^{4+}$ ions. At 4.2\ifmmode^\circ\else\textdegree\fi{}K, the isotopic ratio of ${T}_{1}$ values is measured to be 1.47\ifmmode\pm\else\textpm\fi{}0.03, in good agreement with the theoretical ratio 1.442 for a magnetic relaxation mechanism. For temperatures greater than 40\ifmmode^\circ\else\textdegree\fi{}K, two quadrupole relaxation mechanisms which result from torsional oscillation and hindered rotational motions of the ${[\mathrm{I}\mathrm{r}{\mathrm{Cl}}_{6}]}^{2\ensuremath{-}}$ complexes about their symmetry axes become important, the hindered-rotation mechanism dominating the relaxation at the highest temperatures studied. The echo amplitudes were observed to decay exponentially with time; they provided temperature-independent and rather short spin-spin relaxation times. The explanation is that the resonance line is substantially narrowed by the presence of the strong electron-exchange interaction and has a width determined by the hyperfine interaction. It is shown that the low-temperature ${T}_{1}$ value depends only on the hyperfine parameter $B$, whereas the ${T}_{2}$ value depends only on hyperfine parameter $A$, a behavior which results from the large asymmetry of the transferred hyperfine interaction in ${[\mathrm{I}\mathrm{r}{\mathrm{Cl}}_{6}]}^{2\ensuremath{-}}$ ions. Using a value of the exchange parameter $J$ taken from EPR and magnetic-susceptibility measurements, hyperfine parameters $A=1.62\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ and $B=3.86\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ are deduced from the measured relaxation rates. These values are believed to provide better than order of magnitude estimates of the true hyperfine parameters.
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