Effects of Electron-Electron Interactions on the Nuclear Spin-Lattice Relaxation Times in Aluminum

The "dipolar" spin-lattice relaxation time in aluminum has been measured for temperatures between $1.3°\mathrm{K}<T<\mathrm{}295\mathrm{}°\mathrm{K}$. In contrast to the Zeeman spin-lattice relaxation time $T_{1z}$, the dipolar time does not vary linearly with $\frac{1}{T}$. This is interpreted in terms of cross relaxation between different groups of nuclear spins, some of which experience quadrupole interactions as a result of defects in the lattice, and others which are well removed from such defects. Both cross-relaxation and spin-lattice effects have been measured by our technique; a three-bath model of the nuclear-spin system permits a separation of these effects, with a true dipolar relaxation time $T_{1dd}$ related to $T_{1z}$ by $\delta =\frac{T_{1z}}{T_{1dd}}=2.15\mathrm{}\pm 0.07$, $\delta$ being independent of temperature. This enhancement of $\delta$ over the value 2.00 and the enhancement of the Korringa relation between $T_{1z}$ and $K$, the Knight shift, are discussed and compared with the predictions of the theory of Wolff in which the effects of electron-electron interactions are considered. A similar analysis in sodium is included for comparison, sodium being the metal to which the theory is best applicable.