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 $\Gamma$-centered phonon modes, ${\Gamma }_4^{-}$ and ${\Gamma }_5^{-}$. However, their respective roles have proven to be ambiguous, with disagreement between $\text{ab initio}$ studies, which favor ${\Gamma }_4^{-}$ as the primary mode, and global crystal refinements, which point to ${\Gamma }_5^{-}$ instead. Here, we resolve this issue by demonstrating from x-ray pair distribution function measurements that locally, ${\Gamma }_4^{-}$ dominates, but globally, ${\Gamma }_5^{-}$ dominates. This behavior is consistent with the near degeneracy of the energy surfaces associated with these two distortion modes found in our own $\text{ab initio}$ 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.

9 pages, 6 figures, published in Physical Review Research

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