Dynamic approach to local-polarization distribution and NMR line shape in deuteron glasses

The path-integral formulation of Glauber dynamics by Sommers is applied to calculate the deuteron NMR line shape in structural glasses such as ${\mathrm{Rb}}_{1\mathrm{-}\mathit{x}}$(${\mathrm{ND}}_4$ ${)}_{\mathit{x}}$ ${\mathrm{D}}_2$ ${\mathrm{PO}}_4$. The system is described by a classical pseudospin Ising model with infinite-range exchange interactions and quenched random electric fields. It is shown that in the fast-motion limit the NMR line shape is directly related to the average probability distribution of local deuteron polarization and that the observable truncated second moment of the NMR line ${\mathit{M}}_2^{\mathrm{tr}}$ is proportional to the Edwards-Anderson order parameter ${\mathit{q}}_{\mathrm{EA}}$. Leading dynamic corrections due to the slowing down of deuteron jumps in the ergodic phase are evaluated, and the behavior of ${\mathit{M}}_2^{\mathrm{tr}}$ at the crossover between the fast- and the slow-motion regimes is discussed.