Local structure and its implications for the relaxor ferroelectric Cd_{2}Nb_{2}O_{7}

Abstract

The relaxor ferroelectric transition in Cd_{2}Nb_{2}O_{7} is thought to be described by the unusual condensation of two Γ-centered phonon modes, Γ_{4}^{−} and Γ_{5}^{−}. However, their respective roles have proven to be ambiguous, with disagreement between ab initio studies, which favor Γ_{4}^{−} as the primary mode, and global crystal refinements, which point to Γ_{5}^{−} instead. Here, we resolve this issue by demonstrating from x-ray pair distribution function measurements that locally, Γ_{4}^{−} dominates, but globally, Γ_{5}^{−} dominates. This behavior is consistent with the near degeneracy of the energy surfaces associated with these two distortion modes found in our own ab initio simulations. Our first-principles calculations also show that these energy surfaces are almost isotropic, providing an explanation for the numerous structural transitions found in Cd_{2}Nb_{2}O_{7}, as well as its relaxor behavior. Our results point to several candidate descriptions of the local structure, some of which demonstrate two-in/two-out behavior for Nb displacements within a given Nb tetrahedron. Although this suggests the possibility of a charge analog of spin ice in Cd_{2}Nb_{2}O_{7}, our results are more consistent with a Heisenberg-like description for dipolar fluctuations rather than an Ising one. We hope this encourages future experimental investigations of the Nb and Cd dipolar fluctuations, along with their associated mode dynamics.