${\mathrm{Tl}}^{2+}$ EPR study of the dynamics of the proton-glass transition in ${\mathrm{Rb}}_{1\mathrm{-}\mathit{x}}$(${\mathrm{NH}}_4$${)}_{\mathit{x}}$${\mathrm{H}}_2$${\mathrm{PO}}_4$

The temperature dependence of the ${\mathrm{Tl}}^{2+}$ EPR line shapes and second moments in Tl-doped ${\mathrm{Rb}}_{1\mathrm{-}\mathit{x}}$(${\mathrm{NH}}_4$ ${)}_{\mathit{x}}$ ${\mathrm{H}}_2$ ${\mathrm{PO}}_4$ between 160 and 10 K allows for a direct determination of the static and dynamic features of the glass transition in this system. The static features can be described by a random-field smearing of a random-bond Ising pseudo-spin-glass transition with a nominal glass temperature of ${\mathit{T}}_{\mathit{G}}$=30 K and a random-field contribution of ${\mathit{T}}_{\mathit{f}}$=60 K, whereas the dynamic features show up on a slowing down of the proton intra O-H...O bond motion. The comparison of the theoretical and experimental line shapes provides a check of the validity of a recently developed dynamic approach to the local-polarization distribution and magnetic-resonance line shape in proton and deuteron glasses.