NMR Studies of Spin Excitations in Superconducting ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ Single Crystals

The oxygen NMR shift and the Cu nuclear spin-lattice relaxation rate ($\frac{1}{T_1}$) were measured in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ single crystals. While both the shift and $\frac{1}{T_{1}T}$ decrease sharply near $T_c$, $\frac{1}{T_{1}T}$ becomes nearly constant at low temperatures, indicating a gapless superconducting state with finite density of states at the Fermi level. From the oxygen shift data, the residual spin susceptibility at $T=0\mathrm{}$ is estimated to be 10% of the value at room temperature. Our results are most consistent with a $a$-wave pairing model with strong (resonant) impurity scattering.