Magnetically "tagged" nuclear relaxation in superionic conductors

Introducing paramagnetic atoms into a superionic conductor may produce large, temperature-dependent effects on the transverse T₂^-1 and longitudinal T₁^-1 relaxation rates of the NMR of the nuclei of the diffusing ions. Such effects have been observed for the first time in a study of the ¹⁹F NMR in PbF₂, substitutionally doped with Mn²⁺ ions at concentrations c ranging from 0.01 to 1 mole%. The relaxation induced by the ¹⁹F-Mn²⁺ near-neighbor-transferred hyperfine interaction, ${{→}}{I}·{}{ ̃ \~{}{}}{A}·{}{{→}}{S}$, results in a single peak in ${T}₂^{{-}1}$ vs $T$ and two peaks in ${T}₁^{{-}1}$ vs $T$, with the rates proportional to $c$. A unified treatment of both the statistical aspects of the ${F}^{{-}}$ ion motion and the dynamical evolution of the $¹⁹F$ magnetization during the encounters with the ${Mn}²⁺$ spins is given within the framework of an "impact" model theory. This approach is contrasted with an earlier perturbative treatment by Richards and is shown to differ from it in several important respects. With the help of recently measured values of ̃ \~A for Mn²⁺ in PbF₂ and estimates of the Mn²⁺ electronic spin-lattice relaxation obtained from EPR studies, a comparison between theory and experiment is made. Agreement is found at all but the highest temperatures for T₂^-1, indicating a larger spectral density of low-frequency fluctuations than is expected.