Low temperature fluctuations of vortices in layered superconductors

Data on the ${}_{}{}^{205}{}_{}{}^{}\mathrm{Tl}$ NMR frequency shift and linewidth due to the magnetic field variation in the mixed state of ${\mathrm{Tl}}_2$ ${\mathrm{Ba}}_2$ ${\mathrm{Ca}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{10+\mathrm{\delta }}$ are presented. These data, which are commonly used to extract the London penetration depth, show a near linear temperature dependence at T≪${\mathit{T}}_{\mathit{c}}$. We offer an explanation of this effect as being caused by thermal fluctuations of vortices in weakly coupled layered systems. We argue that the fluctuations cannot be ignored in interpretation of NMR and Muon-Spin-resonance data for materials with large penetration depths even at low T.