NMR in Random Fields: Glass Transition in Rb_1-x(NH₄)_xD₂PO₄

Abstract

The mixed crystal Rb1-x(NH4)xH2PO4 is a frustrated H-bonded system where the local cluster polarization (describing the ordering of the protons between the two possible sites in the H-bonds) represents a random field which modulates the electric quadrupole coupling of nuclei with non-zero quadrupole moments. In contrast to pure RbH2PO4 or NH4H2PO4 there is no sharp change of the NMR frequency or spin-lattice relaxation rate at any well defined transition temperature. Instead one finds an inhomogeneous broadening of the NMR lines which continuously increases with decreasing temperature and which can be used to determine the random field characterizing the quasi-static cluster polarization distribution. Spin-lattice relaxation measurements further allow for a determination of the random field autocorrelation function which turns out to be of the stretched exponential type. The presence of 87Rb and O–D—O deuteron T1 minima in both deuterated and undeuterated crystals demonstrates the tremendous slowing down of the notion of the hydrogens between the two equilibrium sites in the O–H—O bonds due to the hierarchical nature of the cluster dynamics in the formation of the pseudo-spin glass state.