Abstract
${}^{75}\mathrm{As}$ NQR spectra and spin-lattice relaxation time ${T}_{1}$ have been measured between room temperature and 4.2 K in a proustite $({\mathrm{Ag}}_{3}{\mathrm{AsS}}_{3})$ single crystal. In agreement with x-ray scattering data we find that the phase between ${T}_{I}=60\mathrm{K}$ and ${T}_{L}=49\mathrm{K}$ is triple-q $(3\ensuremath{-}q)$ incommensurably modulated. Our results 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 of differently oriented $1\ensuremath{-}q$ modulated domains, or the three modulation waves are confined to a plane and are thus not independent. In addition the ${}^{75}\mathrm{As}$ NQR line shape suggests that the phase just below ${T}_{I}$ is a single-q $(1\ensuremath{-}q)$ modulated stripe phase. This is confirmed by the variation of ${T}_{1}$ over the NQR line in the $1\ensuremath{-}q$ and $3\ensuremath{-}q$ phases. On further cooling further into the incommensurate phase the volume fraction of the $3\ensuremath{-}q$ phase gradually increases and the crystal becomes fully $3\ensuremath{-}q$ modulated about 2 K below ${T}_{I}.$ The nonclassical critical exponents for the amplitude of the order parameter were determined to be ${\ensuremath{\beta}}_{1}=0.3\ifmmode\pm\else\textpm\fi{}0.02$ in the $1\ensuremath{-}q$ stripe phase and ${\ensuremath{\beta}}_{3}=0.4\ifmmode\pm\else\textpm\fi{}0.02$ in the $3\ensuremath{-}q$ phase. On approaching the lock-in transition temperature in the low-temperature part of the $3\ensuremath{-}q$ incommensurate phase the phases of the modulation waves become nonlinear functions of the corresponding spatial coordinates, resulting in sharp peaks superimposed on the broad bell-shape frequency distribution. A comparison between experimental and theoretical line shapes allowed for a quantitative determination of the temperature dependence of the soliton density.
Published Version
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