Tunneling in proton glasses: Stochastic theory of NMR line shape.

Abstract

The effects of the tunneling motion of hydrogen on the NMR line shape in randomly mixed ferroelectric crystals of the type ${\mathrm{Rb}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$(${\mathrm{NH}}_{4}$${)}_{\mathit{x}}$${\mathrm{H}}_{2}$${\mathrm{PO}}_{4}$, known as proton glasses, is studied. The line shapes are calculated for the Clauser-Blume model with use of mean-field theory applied to the infinite-range model of an Ising spin glass in a transverse field, which describes the tunneling frequency of a proton in the O-H...O bond. The interplay of tunneling and spin-glass-like ordering phenomena leads to characteristic features in the NMR, NQR, and EPR spectral line shapes. Magnetic-resonance line-shape measurements thus permit discrimination between coherent tunneling processes and classical thermally activated intrabond hopping across the potential barrier in proton glasses.