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

Abstract

We show that the relaxation function of the dipolar order is given by exp[-(t/${\mathrm{T}}_{1\mathrm{d}}^{\mathrm{a}}$${)}^{\mathrm{\ensuremath{\alpha}}}$]exp(-t/${\mathrm{T}}_{1\mathrm{d}}^{\mathrm{b}}$) where ${\mathrm{T}}_{1\mathrm{d}}^{\mathrm{a}}$ and ${\mathrm{T}}_{1\mathrm{d}}^{\mathrm{b}}$ are spin-lattice relaxation times: ${\mathrm{T}}_{1\mathrm{d}}^{\mathrm{a}}$ due to direct interaction of a given nuclear spin with paramagnetic centers and ${\mathrm{T}}_{1\mathrm{d}}^{\mathrm{b}}$ due to indirect interaction with the paramagnetic centers through neighboring nuclear spins. For a homogeneous distribution of paramagnetic centers and nuclear spins, \ensuremath{\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 \ensuremath{\alpha}=(D+d)/6. The dipolar relaxation is measured in fluorinated graphite. Data from this experiment and from ${\mathrm{CaF}}_{2}$ doped with ${\mathrm{Mn}}^{2+}$ in the literature are consistent with this model.