Theory of nuclear relaxation in superconducting high-Tcoxides

In connection with the anomalous temperature dependence of the nuclear relaxation rate $\frac{1}{T_1}$ of Cu in $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-y}$, the nuclear relaxation in the system is theoretically investigated, and the anomalous temperature dependence is found to be explained on the basis of the Bardeen-Cooper-Schrieffer (BCS) pairing, if the strong correlation effect of electrons is properly taken into account. The spin fluctuations make the superconducting state gapless near $T_c$ and erase the hump of $\frac{1}{T_1}$ which is usually observed in BCS superconductors. The spin-fluctuation vertex is highly renormalized in the superconducting state and thus $\frac{1}{T_1}$, enhanced by the spin fluctuations in the normal state, is drastically suppressed in the superconducting state. The above two effects combined give a sharp decrease of $\frac{1}{T_1}$ below $T_c$, which has been observed in the superconducting state of $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-y}$.