Quantum and Classical Relaxation in the Proton Glass

Abstract

The hydrogen-bond network formed from a crystalline solution of ferroelectric RbH 2 PO 4 and antiferroelectric NH 4 H 2 PO 4 demonstrates glassy behavior, with proton tunneling the dominant mechanism for relaxation at low temperature. We characterize the dielectric response over seven decades of frequency and quantitatively fit the long-time relaxation by directly measuring the local potential energy landscape via neutron Compton scattering. The collective motion of protons rearranges the hydrogen bonds in the network. By analogy with vortex tunneling in superconductors, we relate the logarithmic decay of the polarization to the quantum-mechanical action. DOI: 10.1103/PhysRevLett.97.145501 PACS numbers: 61.43.Fs, 66.35.+a, 77.22.ÿd, 77.84.Fa Glasses become trapped in a restricted set of local configurations and evolve extraordinarily slowly over time. Delineating the relationship between the structure and the dynamics is a critical element in establishing the essential nature of the glassy state, but this correspondence remains difficult to access in most systems. The proton glass [1], a structural analogue to magnetic spin glasses [2] with competing ferroelectric (FE) and antiferroelectric (AFE) order, is different. By combining dielectric spectroscopy over seven decades in frequency with a direct mapping of the real-space energy potential via neutron Compton scattering [3], we are able to describe quantitatively the highly choreographed proton dynamics within a hydrogen-bond network. Proton tunneling controls correlations between neighboring hydrogen bonds and dominates the long-time relaxation.The hydrogen bond plays an important role in physics, chemistry, and biology [4], but it is probably most familiar from ice, where the freedom of different static configurations to accommodate Pauling's rule generates a macroscopic ground state and extra entropy contributing to the latent heat [5]. The hydrogen-bond network formed by Pauling's rule exists as well in other crystalline materials, for example, the piezoelectric KH 2 PO 4 (KDP) family [1,6]. Protons in four O-H-O bonds attached to each PO 4 3ÿ group are constrained to maintain singly charged H 2 PO 4 ÿ groups. Six distinct electrical dipole moments along three orthogonal axes can be formed with different Slater configurations [6]. While pure phases of RbH 2 PO 4 (RDP) and NH 4 H 2 PO 4 (ADP) are FE and AFE, respectively, at low temperature, a solid state solution creates a dipolar glass, Rb 1ÿx NH 4 x H 2 PO 4 (RADP:100x), for concentrations 0:22 < x < 0:74 [1]. The disorder, combined with the ''frustration'' arising from the competition between FE ordering along the c axis in RDP and AFE ordering within the ab plane for ADP, leads to the characteristic broad and frequency-dependent peak in the dielectric susceptibility vs temperature T [1,2] and no more than short-range structural correlations [7]. The proton's pivotal role in relaxation is confirmed by the strong isotope effect on low T thermal properties [8].The dielectric spectroscopy is performed f...

Proton Disorder in NH···N Bonded [dabcoH]+I− Relaxor: New Insights into H-Disordering in a One-Dimensional H2O Ice Analogue

“…The linear parts of the spectra converge at f 0 ≈ 3 × 10 6 Hz. A similar logarithmic behavior of the low-temperature dielectric response has been reported recently for crystalline solutions of ferroelectric RbH 2 PO 4 and antiferroelectric NH 4 H 2 PO 4 , and was explained by proton tunneling in the OH···O − hydrogen bonds . By combining dielectric and neutron Compton-scattering data, the frequency of 10 11 Hz corresponding to the convergence point f 0 has been identified as the transition rate for the tunneling process.…”

Dynamically disordered hydrogen bonds in the hureaulite-type phosphatic oxyhydroxide Mn5[(PO4)2(PO3(OH))2](HOH)4

“…2(a)]. This local proton-hopping process obviously exhibits glassy freezing and, similar to the findings in our previous work on a rockbridgeite-type compound, 61 Mnhureaulite approaches a "proton glass" state 62,63 at low temperatures. The corresponding glass-transition temperature T g can be deduced by applying the usual criterion τ (T g ) = 100 s. 54 This leads to T g = 187 and 212 K for the H-and D-form, respectively, implying that the deuterium dynamics freezes at higher temperature.…”

Monopolar and dipolar relaxation in spin ice Ho 2 Ti 2 O 7

“…In glass-forming systems, the relaxation time distribution typically broadens upon cooling (36). A concomitant decrease in  is an alternate indicator of glassy heterogeneous relaxation as in proton glasses, which display logarithmic time dependence ( → 0) (37). In Ho 2 Ti 2 O 7 , on the other hand, the width of the peak in ″[ log (f )] actually narrows upon cooling.…”