Longitudinal and transverse spin dynamics of a one-dimensionalXYsystem studied by chlorine nuclear relaxation in PrCl3

$T_1$ and $T_2$ measurements of Cl nuclear-quadrupole resonance in Pr${\mathrm{Cl}}_3$ are explained with the assumption of one-dimensional $\mathrm{XY}$ spin dynamics for the Pr spins. The Cl nuclei are relaxed both by fluctuating magnetic fields due to the longitudinal Pr moments, and also by fluctuating electric field gradients due to the transverse Pr moments. Accurate spin-echo measurements of the relative relaxation rates for the two Cl isotopes and of the echo decay functions allow identification of the two mechanisms. $T_1$ relaxation is primarily magnetic throughout the temperature range of one-dimensional ordering, while $T_2$ relaxation is quadrupolar at lower temperatures and probably magnetic at higher temperatures. As a result $T_1$ and $T_2$ have opposite temperature dependences. The data are consistent with calculations of the relaxation due to longitudinal- and transverse-moment fluctuations for $\mathrm{XY}$ chains.