Thallium magnetic resonance in superconducting ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{Ca}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{10+\mathrm{\delta }}$

Significant frequency shifts of the thallium nuclear-magnetic-resonance (NMR) spectrum have been observed in the super- conducting state of the high-temperature superconductor ${\mathrm{Tl}}_2$ ${\mathrm{Ba}}_2$ ${\mathrm{Ca}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{10+\mathrm{\delta }}$. Measurements at two different magnetic fields indicate that the origin of these shifts is mainly due to the field distribution associated with vortices in the mixed state. The spin-lattice relaxation measurements are consistent with an anisotropic energy gap. The NMR linewidth varies significantly with temperature and magnetic field, apparently inconsistent with the BCS theory.