Neutron-scattering study of short-range order in a model two-dimensional ferroelectric

Copper formate tetrahydrate is a layered, hydrogen-bonded substance which undergoes a phase transition from a state in which hydrogen atoms are positionally disordered into an ordered state in which two-dimensional ferroelectric planes are stacked so that the polarization alternates in sign from layer to layer. We report here the results of a neutron-scattering study of the positional correlations between hydrogen atoms in the disordered phase. The results show that long-wavelength intralayer polarization fluctuations are suppressed in the disordered phase, even though a long-ranged polarization develops in the ordered phase. Fluctuations at intermediate wavelengths increase as the phase-transition temperature is approached. These results are discussed in terms of the two-dimensional dimer model. A qualitative understanding of the short-range order can be achieved if one takes into account a conservation law which holds for six-vertex models: in any allowed configuration of the lattice, polarization is conserved from one row to the next