A general formalism is developed for describing nuclear-spin-lattice relaxation for quadrupolar perturbed nuclear magnetic resonance (NMR) in structurally incommensurately (IC) modulated crystals in terms of the elementary excitations of these systems. Our discussion deviates from previous ones as regards the identification of the amplitudon and phason induced relaxation rates 1/${\mathit{T}}_{1\mathit{A}}$ and 1/${\mathit{T}}_{1\mathrm{\phi }}$ in the plane wave limit as well as the temperature dependence of ${\mathit{T}}_{1\mathrm{\phi }}$ in the soliton limit. Measurements are reported for the spin-lattice relaxation of the ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$ satellite transitions in the normal, incommensurate, and commensurate phases of the prototype incommensurate system ${\mathrm{Rb}}_2$${\mathrm{ZnCl}}_4$. At ambient temperature the variation of the nuclear magnetic relaxation rate is measured over the incommensurately broadened distribution of resonance frequencies for two crystal orientations. The ${\mathit{T}}_1$ model developed is applied to these data, making use of the Fourier series of the static electric field gradient determined from the NMR satellite spectra in the IC phase. A strict agreement is found. The temperature dependence of ${\mathit{T}}_1$ is determined in that crystal orientation where a well-defined assignment of ${\mathit{T}}_{1\mathit{A}}$ and ${\mathit{T}}_{1\mathrm{\phi }}$ can be given. In the low-temperature part of the incommensurate phase, our data reflect the local softening of phase fluctuations in the discommensurations or the flattening out of the corresponding acoustic branch what is in accordance with our theoretical prediction and in contrast to previous results. The relevance of phason gaps previously derived from NMR data is discussed.

• Received 25 July 1994

DOI:https://doi.org/10.1103/PhysRevB.50.16192