Al NMR Probe of Local Moments Induced by an Al Impurity in High- $T_c$ Cuprate ${\mathrm{La}}_{1.85}{\mathrm{Sr}}_{0.15}{\mathrm{CuO}}_4$

${}^{27}\mathrm{Al}$ and ${}^{63}\mathrm{Cu}$ NMR measurements in 3% Al-doped ${\mathrm{La}}_{1.85}{\mathrm{Sr}}_{0.15}{\mathrm{CuO}}_4$ (LSCO) have revealed that the $T$ dependences of the Knight shift, ${}^{27}K\left(T\right)$, and the nuclear-spin-lattice relaxation rate, ${}^{27}\left(1/T_1\right)$, are dominated by local moments induced at neighboring Cu sites by the Al impurity. These experiments prove that spin fluctuation of induced moments is mainly due to the local spin-exchange coupling, $J_{\mathrm{sd}}$, with conducting holes. This novel $T$ dependence of ${}^{27}\left(1/T_1\right)$ has led to a reliable estimation of $J_{\mathrm{sd}}=0.055\mathrm{eV}$, and the extraction of the $T_c$ reduction rate, $\Delta T_c=0.62\mathrm{}\mathrm{K}/\mathrm{Al}\%$ based on the magnetic pair-breaking scheme, which is by more than 1 order of magnitude smaller than the experimental value of $\Delta T_c=23\mathrm{}\mathrm{K}/\mathrm{Al}\%$.