Unique 1-q and 3-q incommensurate phases in proustite: As-75 NQR line-shape and spin-lattice relaxation study

As-75 NQR spectra and spin-lattice relaxation time T-1 have been measured b etween room temperature and 4.2 K in a proustite (Ag3AsS3) single crystal. In agreement with x-ray scattering data we find that the phase between T-l = 60 K and T-L = 49 K is triple-q (3-q) incommensurably modulated. Our resu lts show unambiguously that we deal here with three independent noncoplanar incommensurate modulation wave vectors. Such a phase seems to be unique in a sense that other phases with three incommensurate modulation waves known so far (e.g., in charge-density-wave systems) are either a superposition o f differently oriented 1-q modulated domains, or the three modulation waves are confined to a plane and are thus not independent. In addition the 75As NQR line shape suggests that the phase just below T-l is a single-q (1-q) modulated stripe phase. This is confirmed by the variation of TI over the N QR line in the 1-q and 3-q phases. On further cooling further into the inco mmensurate phase the volume fraction of the 3-q phase gradually increases a nd the crystal becomes fully 3-q modulated about 2 K below T-1. The nonclas sical critical exponents for the amplitude of the order parameter were dete rmined to be beta(1) = 0.3 +/- 0.02 in the 1-q stripe phase and beta(3) = 0 .4 +/- 0.02 in the 3-q phase. On approaching the lock-in transition tempera ture in the low-temperature part of the 3-q incommensurate phase the phases of the modulation waves become nonlinear functions of the corresponding sp atial coordinates, resulting in sharp peaks superimposed on the broad bell- shape frequency distribution. A comparison between experimental and theoret ical line shapes allowed for a quantitative determination of the temperatur e dependence of the soliton density.