Application of the SPin Glass Formalism to the Quadrupolar Glass Na(CN)xCl1-x

Abstract

The mixed alkali halide-cyanide crystals such as Na(CN) xCl1_x , K(CN)xBr1-x etc. with x Tg(x) these systems show the cubic structure, where the sides of anions are statistically occupied by halide ions and dumbbell-shaped CNmolecular groups, which rotate nearly freely. When the temperature is lowered and crosses Tg (x), CNions freeze into random directions. To the lowest temperature no long range order is observed and the global symmetry of the system remains cubic. This can be compared with the random freeze-out of the spins in a canonical spin glass. However, the frustration which leads to the QG ordering is more subtle and more complex than in spin systems. In addition, because of the coupling between rotational and translational degrees of freedom [2] the random freezing of orientations of CNions leads to local static lattice deformations and hence QG has some properties of a structural glass. Various experiments provide an evidence for an existence of QG phase of mixed alkali halide-cyanide crystals [3]. One of basic characteristic is the temperature dependence of the central peak intensity of quasi-elastic neutron scattering [3] and of the NMR frequency distribution [4]. An important feature of QG transition is the considerable softening and successive hardening of the elastic constant C44 [3]. In view of the limited space available for the present work, we will restrict ourselves to a short presentation of the proposed model and its physical consequences. A detailed description is given elsewhere [5]. The starting point is the semi-microscopic Hamiltonian obtained in a result of a coarse-graining procedure [6]. It contains the following effective interactions: