Determination of magnetic penetration depth from saddle-point field analysis in ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{Ca}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{10+\mathrm{\delta }}$

${}_{}{}^{205}{}_{}{}^{}\mathrm{Tl}$ NMR spectra and spin-lattice relaxation in the normal and superconducting states were measured on an aligned sample of ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{Ca}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{10+\mathrm{\delta }}$. The spin-lattice relaxation time, ${\mathit{T}}_1$, was found to be isotropic and, in the normal state, 1/${\mathit{T}}_1$T to be temperature dependent, indicating the presence of spin fluctuations in the thallium-oxygen plane similar to that found in the copper-oxygen plane of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$. $ sup 205—Tl NMR spectra at 5 K were studied and the angular dependence of the field shift at the saddle points of the magnetic-field distribution was found to be consistent with the anisotropic London theory. The average penetration depth was inferred to be 7040±350 Å. Our approach to determine the penetration depth, the saddle-point field analysis, is insensitive to distortion of the flux lattice associated with pinning. This is in contrast to the more commonly used second-moment method.