Ferroelectric order in positionally frozen dipolar systems

Abstract

We discuss the possibility of long-range ferroelectric order in an amorphous dipolar system. Our model consists of spheres with frozen positions and freely rotating three-dimensional dipole moments. Correlation functions are calculated by means of the hypernetted-chain integral theory combined with the replica method. Our results suggest that inhomogeneities in the frozen spatial structure induce a gradual local freezing of the dipole axes upon decreasing temperature. However, at sufficiently high densities and dipole moments, the long-range interactions dominate the short-range frustration, resulting in a ferroelectric transition. The estimated transition temperatures depend strongly on the degree of spatial correlation in the underlying system of frozen spheres. For a randomly frozen system, we find that the transition temperature is considerably lower than that predicted by mean field theory, and also lower than the temperature where simulations indicate the onset of glass-like behavior. Strong positional correlations can push the transition toward temperatures higher even than those observed for dipolar fluids.