Vortices in Layered Superconductors"In a recent Letter [ll, Song et al. presented data on the Tl NMR linewidth in partly oriented T128a2ca2-Cu30/Q powders. In the model used [2,3], the variance of the field distribution is reduced by the motion of pancake vortices around their equilibrium positions. The model seems only valid if the mean square deviation from equilibrium is small. Using the 3D Lindemann melting criterion this would imply that T/T, has to be lower than 0.4. Numerical simulation of vortex motion in a single and a multilayer system with vortices coupled only magnetically [4] showed a similar line narrowing. Because in these simulations the line profiles were directly calculated via the relevant correlation function, they do not show whether vortex I]uctuation or diffusion is responsible for the line narrowing (although vortex diffusion was suggested to dominate).Here we will calculate the diffusion constant D directly from the experimental line profile and see how it compares with the numerical simulation of D [5]. The line profile for a time dependent field is given by F(to) Jdt G(t) exp( itat) [-6]. We assume that G(t) is related to the correlation time for vortex motion r via G(t) = exp(itaot ) exp[ -ta~r '[exp(t/r ) -I +t/r ]], and that D is of the order of D = a$/2r; to~i s a measure for the linewidth in the absence of vortex motion, t00/2tr denotes the nuclear precession frequency, and an the fiux lattice constant. In Fig. 1 we show D as a function of T in a field of 4.7 T for Bllc [7]. D varies with T from 10 ' around 20 K to 10 around 80 K. Normal state linewidths (FWHH) were fitted by 103 -7.66&10 T (kHz). For the low temperature value we used 390 kHz (as measured at 0.4 K). The precise values of these parameters are important especially below 20 K or above 80 K [8]. In the same figure we show the simulated D values for Bllc without pinning for a field of I T (by extrapolation of the simulations we estimate D in 4.7 T to be a factor of 2-3 lower). If weak pinning is included the diffusion coefficient might increase by about a factor of 3 [4]. As can be seen from Fig. I, within the crude approximations made here, simulated and measured values agree rather well. Also in muon spin rotation there are indications of vortex diffusion [9].ln conclusion, numerical simulations strongly suggest that apart from vortex vibration, vortex diA'usion plays an important role in the line narrowing in highly anisotropic superconductors like the Tl-based high T
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