Spin-lattice relaxation in the mixed state of the high-$T_c$ cuprates: electronic spin-flip scattering versus spin-fluctuations

Recent experimental and theoretical studies have established that the spin-lattice relaxation rate, $1\mathrm{/}{T}_1$, measured in nuclear magnetic resonance (NMR) experiments is a site-sensitive probe for the electronic spectrum in the mixed state of the high-$T_c$ cuprates. While some groups suggested that $1\mathrm{/}{T}_1$ is solely determined by spin-flip scattering of BCS-like electrons, other groups stressed the importance of antiferromagnetic spin-fluctuations. We show that these two relaxation mechanisms give rise to a {\it qualitatively} different temperature and frequency dependence of ${}^{17}$O $1\mathrm{/}{T}_1$. A comparison of our results with the experimental ${}^{17}$O $1\mathrm{/}{T}_1$ data provides support for a relaxation mechanism dominated by antiferromagnetic spin-fluctuations.