Nuclear spin-lattice relaxation of dipolar order caused by paramagnetic impurities

We show that the relaxation function of the dipolar order is given by exp[-(t/T-1d(aalpha))]exp(-t/T-1d(b)) where T-1d(a) and T-1d(b) are spin-lattice relaxation times: T-1d(a) due to direct interaction of a given nuclear spin with paramagnetic centers and T-1d(b) due to indirect interaction with the paramagnetic centers through neighboring nuclear spins. For a homogeneous distribution of paramagnetic centers and nuclear spins, alpha=D/6 where D is the sample dimensionality. For an inhomogeneous distribution, the sample is divided into d-dimensional subsystems, each containing one paramagnetic center, yielding alpha=(D+d)/6. The dipolar relaxation is measured in fluorinated graphite. Data from this experiment and from CaF2 doped with Mn2+ in the literature are consistent with this model.