Effects of self-consistency on spin-lattice relaxation

We propose a new quadrupolar $T_1$ spin-lattice relaxation process that is independent of both magnetic field strength and temperature, and yields exponential decay in both laboratory and rotating-frame experiments with comparable decay rates. Numerical estimates indicate that this process may be dominant at low temperatures in nuclear spin systems with $I>\mathrm{}\frac{1}{2}$ that are reasonably free from paramagnetic impurities. It may also be the dominant process in the relaxation of certain paramagnetic ions in systems with concentrations of ions that are not too small and where inhomogeneous broadening is minimal. The process depends upon the fact that the lattice vibrations which relax the spins acquire an enhanced spectral density arising from thermal spin fluctuations. It bears some resemblance to phonon-induced spin-spin coupling or virtual phonon mechanisms. It is further shown that this effect of the spins on the lattice vibrations can be expressed exactly in terms of the time-dependent correlation functions for the spins.