Progressive saturation NMR relaxation

The NMR spin-lattice relaxation rate, T₁^-1, can be measured precisely by progressive saturation. This efficient technique is useful when T₁ is long and the NMR signal is weak. We derive the quasiequilibrium spin response to excitation in the case of a Zeeman spectrum in the presence of quadrupolar interactions. Exact solutions for the recovery of magnetization under the influence of purely magnetic fluctuations for I=1/2, 3/2, and 5/2 are presented. This is the general solution to a problem that has been previously solved only for the I=1/2 case. An important example for the application of this technique is ¹⁷O NMR in cuprate superconductors (I=5/2). We show comparisons of the theory with the relaxation measured for high-temperature superconducting materials and the NMR-rates measured by this technique across the vortex-broadened spectrum at low temperature.