Weak-coupling model of spin fluctuations in the superconducting state of the layered cuprates

Previous work on the modeling of normal-state spin fluctuations in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ is extended to the superconducting state. In this paper the effect of superconductivity on the spin fluctuations is approximately treated by using the BCS result for the irreducible susceptibility that enters the random-phase-approximation expression for the dynamic spin susceptibility. The resulting susceptibility is then used to calculate Cu(2) and O(2,3) Knight shifts and nuclear relaxation rates. Calculations are done using both s- and d-wave gap symmetries. A comparison of the results with the experimental NMR data on ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ is presented.