NMR spectra and relaxation in incommensurate systems in the presence of a devil's staircase

Abstract

2014 La possibilité de faire la différence entre des phases vraiment incommensurables et des structures à longue période est discutée. Les résultats théoriques sont comparés avec ceux d'expériences effectuées sur Rb2ZnCl4, Rb2ZnBr4, et [N(CH3)4]2ZnCl4. Dans la plupart des cas, les effets dus à la présence d'un escalier du diable sont masqués par ceux des défauts.

Statics and dynamics of the modulation in incommensurate Rb2ZnBr4 as detected by NMR

“…The behavior of the isomorphous substance Rb2ZnBr4 (RZB) as reported so far in the literature is by far less well known. Whereas first publications [9,10] seem to demonstrate the existence of floating in our previous investigation [111 no hints for a behavior of such a type could be verified. This unsatisfactory state is very likely due to the fact that highquality single crystals of RZB are much more difficult to grow than RZC single crystals.…”

“…In particular, the fact that the misfit parameter of the wavenumber in RZB is nearly temperature-independent in a broad temperature interval [24] gave rise to the suspicion that the IC phase of RZB is actually a higher-order commensurate phase. In contrast to a genuine continuous NMR frequency distribution of an IC phase, the spectrum of a higher-order commensurate phase consists in a distribution of discrete lines over the spectrum [10]. As long as the C modulation can be approximated by a plane wave, the respective frequencies can be calculated from v" = vo + v2 cos(2ncq + tp,), n = 0,..., N -1, (1) where q, = c *M/N denotes the commensurate wave vector.…”

Incommensurate Systems

“…Only when the dominant contribution to the NMR resonance frequency comes from a region whose dimensions are small compared with the wavelength of the incommensurate modulation wave can the relationship between ν i and u i be treated as local, so that equation (3) becomes strictly valid. 2 In the nonlocal case equation (10) yields the spatial dependence of the NMR frequency 2…”

Soliton density inRb2ZnBr4

“…Here A 2 is determined from the experiment by fitting the observed line shape to Eqs. (16) and (17).…”

“…Expression (17) yields up to n new "commensurate" lines for a-o in addition to the incommensurate edge singularities arising from dv/dtf!---+0. The new lines will appear for A« 1 when cos 2 [n(t/f-t/lol/2]=0, i.e., when t/1=(2m+lhrln+tf>o, m=0,1,2, ... ,n-1.…”