Finite block pseudo-spin approach of proton glass
Introduction
None of the early known pyroelectric materials were ferroelectric in the sense of long-range ordering for reorientational electric dipole moments until 1920 when Valasek [1] discovered the spontaneous polarization in the crystal of sodium potassium tartrate tetrahydrate (NaKC4H4O6·4H2O) better known as Rochelle salt. Since the discovery of KH2PO4 (KDP) with a ferroelectric transition at 122 K and NH4H2PO4 (ADP) with an antiferroelectric transition at 148 K [2], [3], the XH2YO4 (X=K, Rb, Cs, NH4, Tl; Y=P, As) family has been one of the most extensively studied hydrogen-bonded ferroelectric crystals [4], [5], [6], [7], [8], [9], [10]. The Ising-type pseudo-spin formalism of the proton configurations in double potential wells for the XH2YO4 family crystals was well developed [4], [5]. The proton tunneling model [4], [11], [12] was also suggested with a focus on quantum tunneling of protons between two potential wells. Phenomenological analysis based on the Landau–Ginzburg theory of structural phase transitions [4], where gradient and surface terms are taken into account, was successfully applied for various multiferroic and nanoferroic phenomena irrespective of the different microscopic theories [13], [14]. The renormalization group theoretical treatment [15] of critical fluctuations in the ferroelectric materials was also developed. Even though electron–phonon interaction (EPI) effects are considered as a driving mechanism of ferroelectricity from the strong support from the isotope shift of [16], a systematic and microscopic approach on EPI is still necessary.
Ever since the 1970s, spin glass has been the focus of considerable attention as a research topic in the physics of condensed matter [17], [18], [19] . An early approach by Edwards and Anderson [20] made use of a theory that focused on short-range interactions, in which a proper order parameter was defined as being the mean of the squares of the averages of the local spin operators that have nonzero values below a finite temperature. This work was later extended by using the Sherrington-Kirkpatrick (SK) model [21], which yielded the corresponding long-range interactions by using a mean field approximation.
The first types of spin glass systems consisted of dilute solutions of magnetic transition metal impurities within the noble metal hosts. The atomic moments of the impurities induce a magnetic polarization of the conduction electrons in the surrounding host metal. The polarization is positive in some locations and negative in others. The impurity moments are then susceptible to the local magnetic field produced by the polarized conduction electrons, which tend to align themselves along the randomly distributed local fields. Other systems of spin glasses have also been found in magnetic insulators and amorphous alloys, in which dependence on the distance of the interaction between the local moments is in random competition, and is entirely different in nature from that found in the crystalline metallic systems [17], [18], [19]. For specific dielectrics and alloys, a glassy state as a spin glass analog is driven by frustration and competing interaction, now called polar (dipolar and quadrupolar) and strain glasses [19], [22], [23], [24], [25].
The proton glass, classified as a subclass of dipole glass, is attained in the mixed crystals of Rb1−x(NH4)xH2PO4 and Rb1−x(NH4)xH2AsO4 due to the competing interaction between the ferroelectric ordering of RbH2PO4 (RbH2AsO4) and the antiferroelectric ordering of NH4H2PO4 (NH4H2AsO4) [19], [23], [24], [26], [27], [28]. The disappearance of long-range order and the existence of short-range order within clusters are evidences of frozen-in state of protons. This proton glass transition shows frequency dispersion in its temperature-dependent dielectric constant and follow Vogel–Fulcher law. In this paper, we propose an alternative finite block pseudo-spin phenomenology of proton glass.
Section snippets
The finite block pseudo-spin theory
The nucleus of hydrogen(H)-bond nomenclature is the distinction between donor and acceptor. In any D−H···:A bond, D−H is the H-bond donor (and also a Brønsted acid, a Lewis acid, and an electron acceptor) and :A the H-bond acceptor (and also a Brønsted base, a Lewis base, and an electron donor) [29]. Hydrogen bonding occurs between a proton-donor group D−H and a proton-acceptor group A, where D is an electronegative atom, O, N, S, X (F, Cl, Br, I) or C, and the acceptor group is a lone pair of
Experimental data fitting
The resulting real part of the dielectric constant, (in SI units), is fitted to the experimental data for Rb1−x(NH4)xH2P1−yAsyO4 freezing to the proton glass phase [28], as shown in Fig. 2, Fig. 3. One of the main peculiarities of the spin and polar glass transitions is strong frequency dispersion of the real and imaginary parts of their linear dynamic magnetic and dielectric susceptibilities: the cusp or the rounded maximum defining a freezing temperature is sensitive to the
Conclusion
To conclude, renormalization group theory [15], [17] has been extended to the finite block pseudo-spin systems in order to explain the phenomenology of the proton glass. The occurrence of quenched states in proton glasses increases the degree of randomness in the spin directions of electrons and yields larger block spins. The normal phase of proton glass can be explained in terms of the short-range ferroelectric arrangements between block spins made up of many random spins with resulting
Acknowledgments
This work was supported by the National Research Foundation of Korea (Project no. 2013057555, Proton Users Program 2015M2B2A4029012, and NRF-2010-0027963).
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