Equilibrium properties of a quadrupolar glass.

Abstract

We introduce a semimicroscopic discrete-state model appropriate to the orientational glass phase in mixed alkali halide cyanides with 〈111〉 equilibrium orientations of the ${\mathrm{CN}}^{\mathrm{\ensuremath{-}}}$ ions, such as K(CN${)}_{\mathit{x}}$${\mathrm{Br}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$. The order-parameter fields are defined as symmetry adapted combinations of the occupation number operators along the cubic body diagonals, which transform according to the ${\mathit{T}}_{2\mathit{g}}$ representation of the cubic group. These interact via an infinite-range random interaction in the presence of quenched local random strains. We then use the replica formalism to derive a replica-symmetric solution for the components of the orientational-glass order parameter, the linear susceptibilities, and the elastic compliances. The high-temperature orientational-glass phase is characterized by an isotropic order-parameter matrix with only the diagonal elements ${\mathit{q}}_{\mathrm{\ensuremath{\mu}}}$ being nonzero. At high temperatures, the behavior of the order parameter q=${\mathrm{\ensuremath{\Sigma}}}_{\mathrm{\ensuremath{\mu}}}$${\mathit{q}}_{\mathrm{\ensuremath{\mu}}}$/3 is similar to that of an Ising spin glass, however, at intermediate and low temperatures the two models differ significantly. We also derive the instability line ${\mathit{T}}_{\mathit{f}}$(\ensuremath{\Delta}) separating the replica-symmetric isotropic phase from the low-temperature anisotropic orientational glass phase, which is characterized by broken replica symmetry. In contrast to the random-bond--random-field model of an Ising spin glass, the instability temperature increases with random-field variance, implying that in quadrupolar glasses replica-symmetry breaking may be relevant already at relatively high temperatures. Finally, an expression for the distribution of local strains related to the NMR line shape is derived. It is also shown that the quadrupolar glass order parameter can be determined by NMR.